Jérôme Dumortier
email: jerome.dumortier@chu-lyon.fr

Vincent Leroy

Christophe Duvoux

Victor De Ledinghen

Claire Francoz

Pauline Houssel-Debry

Sylvie Radenne

Louis D'alteroche

Claire Fougerou-Leurent

Valérie Canva

Vincent Di Martino

Filomena Conti

Nassim Kamar

Christophe Moreno

Pascal Lebray

Albert Tran

Camille Besch

Alpha Diallo

Alexandra Rohel

Emilie Rossignol

Armand Abergel

Danielle Botta- Fridlund

Audrey Coilly

Didier Samuel

Jean-Charles Duclos-Vallee

Georges- Philippe Pageaux

Jérôme Pr

Dumortier

Georges-Philippe Pageaux

Jean-Charles Duclos- Vallée

manuscript. Jérôme Vincent Dumortier

Christophe Leroy

Victor Duvoux

Claire De Ledinghen

Pauline Francoz

Sylvie Houssel-Debry

Radenne

Valérie Louis D'alteroche

Vincent Canva

Filomena Di Martino

Nassim Conti

Christophe Kamar

Pascal Moreno

Albert Lebray

Camille Tran

Armand Besch

Danielle Abergel

Audrey Botta-Fridlund

Georges-Philippe Coilly

Jean-Charles Pageaux

Duclos-Vallée

Sofosbuvir-based treatment of hepatitis C with severe fibrosis (METAVIR F3/F4) after liver transplantation: results from the CO23 ANRS CUPILT study Short Title: Treatment of post-transplant HCV recurrence with severe fibrosis

Keywords: liver transplantation, hepatitis C virus, fibrosis, cirrhosis, treatment, sofosbuvir

Recurrence of HCV after liver transplantation (LT) can rapidly lead to liver graft cirrhosis, and therefore graft failure and re-transplantation or death. The aim of the present study was to assess efficacy and tolerance of sofosbuvir (SOF)-based regimens for the treatment of HCV recurrence in patients with severe fibrosis after LT. The CUPILT study is a prospective multicenter cohort including patients with HCV-recurrence following LT treated with second generation direct antivirals. The present study focused on patients included between Oct 2013 and Nov 2014 and diagnosed with HCV recurrence and liver graft extensive fibrosis (METAVIR F3/F4). A SOF-based regimen was administered to 125 patients fulfilling inclusion criteria. The median delay from LT was 95.9 ± 69.6 months. The characteristics of patients were: mean age: 59.4 ± 9.0 years; male: 78.4%, infected by HCV G1: 78.2%, mean HCV RNA: 6.1 ± 1.0 log IU/ml. Eighty patients had failed previous post-LT antiviral therapy (64.0%) including triple therapy with first generation protease inhibitors in 19 (15.2%) cases. The main combination regimen was SOF/daclatasvir (73.6%). Ribavirin was used in 60 patients. Sustained virological response 12 weeks after treatment was 92.8% (on an intent-to-treat basis); seven cases of virological failure were observed.

Serious adverse-events occurred in 25.6% of the patients during antiviral treatment. During antiviral treatment and follow-up, 3 patients were re-transplanted and 4 patients died. In conclusion, SOF-based antiviral treatment shows very promising results in patients with HCV recurrence and severe fibrosis after LT.

Introduction

Liver disease related to hepatitis C virus (HCV), including cirrhosis and hepatocellular carcinoma (HCC), is the main indication for liver transplantation (LT) [START_REF] Adam | Evolution of liver transplantation in Europe: report of the European Liver Transplant Registry[END_REF][START_REF] Merion | Current status and future of liver transplantation[END_REF]. In patients transplanted with detectable HCV RNA, HCV infection of the graft is an almost universal phenomenon responsible for an increased risk of mortality and graft loss [START_REF] Forman | The association between hepatitis C infection and survival after orthotopic liver transplantation[END_REF]. Chronic liver disease caused by HCV infection progresses more rapidly in immunosuppressed individuals than in immunocompetent individuals, leading to cirrhosis in up to 20-30% of patients, five years after LT [START_REF] Feray | European collaborative study on factors influencing outcome after liver transplantation for hepatitis C. European Concerted Action on Viral Hepatitis (EUROHEP) Group[END_REF][START_REF] Gane | The natural history of recurrent hepatitis C and what influences this[END_REF]. The use of second-generation direct acting antivirals (DAAs) could be a major advance in these difficult-to-treat patients because of their antiviral potency and their usual good tolerance, especially when used as interferon-free combinations. Sofosbuvir (SOF) is a potent inhibitor of the HCV NS5b polymerase that has a pangenotypic activity and a high genetic barrier to resistance, and has been available in France since October 2013, initially in the frame of the French early access program. The ANRS C023 "Compassionate use of Protease Inhibitors in viral C Liver Transplantation" (CUPILT) study is a prospective multicenter cohort study sponsored and funded by ANRS (France REcherche Nord&Sud Sida-hiv Hépatites) that has enrolled liver transplant recipients with HCV-recurrence treated with second generation DAAs. The aim of the present study was to describe the virological, biochemical and clinical outcome of patients included in the CUPILT cohort, presenting with severe recurrence of hepatitis C according to METAVIR fibrosis stage (F3 or F4) and treated with SOF-based therapy.

Patients and methods

Patients

The ANRS CO23-CUPILT study is conducted in 25 French and Belgium LT centers (ClinicalTrials.gov number NCT01944527). To be included in the cohort, patients had to be transplanted for HCV-related liver complication, presented with allograft HCV recurrence, and treated with second generation DAA.

The main criteria for exclusion were age less than 18 years and pregnancy. From October 2013 to December 2015, 699 patients with HCV recurrence have been included in the cohort.

Study design

The present study focuses on patients included in the CUPILT study presenting hepatitis C recurrence with severe fibrosis, who were followed at least 12 weeks after the end of their antiviral treatment. The assessment of severe fibrosis (METAVIR F3/F4) was established according to histological analysis of a liver biopsy and/or the result of transient elastography (Fibroscan © ). For the latter, patients who had liver stiffness ranging from 9.6 kPa to 14.4 kPa were considered to have F3 METAVIR stage and patients who had values equal or above 14.5 kPa were considered F4 [START_REF] Ziol | Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with chronic hepatitis C[END_REF]. SOF, daclatasvir (DCV), simeprevir (SMV) and ledipasvir (LDV) (in fixed combination with SOF for the last three) have been successively available throughout the inclusion period. Treatment regimens were at the discretion of investigators. RBV use and dosing were at investigator's discretion according to weight and renal function. Planned duration of treatment was 12 or 24 weeks. However, investigators were allowed to extend treatment duration according to their clinical judgment in case of sub-optimal response. Modifications in the dose of calcineurin and mTOR inhibitors were performed at investigator's discretion on the basis of trough levels of tacrolimus, cyclosporine, sirolimus and everolimus.

The patients were not randomized, thus the study did not allow comparisons between the treatment regimens.

The protocol was conducted in accordance with the Declaration of Helsinki and French law for biomedical research and was approved by the "Sud Méditerranée I" Ethics Committee (France).Written informed consent was obtained from each patient before enrolment.

Study assessments

Clinical evaluation including clinical signs of decompensated liver disease (ascites, hepatic encephalopathy) and laboratory tests were performed at baseline and at scheduled visits throughout treatment and follow-up periods (weeks [START_REF] Merion | Current status and future of liver transplantation[END_REF][START_REF] Feray | European collaborative study on factors influencing outcome after liver transplantation for hepatitis C. European Concerted Action on Viral Hepatitis (EUROHEP) Group[END_REF][START_REF] Coilly | Safety and efficacy of protease inhibitors to treat hepatitis C after liver transplantation: a multicenter experience[END_REF][START_REF] Leroy | Efficacy of Sofosbuvir and Daclatasvir in Patients with Fibrosing Cholestatic Hepatitis C After Liver Transplantation[END_REF][START_REF] Berenguer | HCV-related fibrosis progression following liver transplantation: increase in recent years[END_REF][START_REF] Brown | Interferon-free therapy for genotype 1 hepatitis C in liver transplant recipients: Real-world experience from the hepatitis C therapeutic registry and research network[END_REF][START_REF] Charlton | Ledipasvir and Sofosbuvir Plus Ribavirin for Treatment of HCV Infection in Patients with Advanced Liver Disease[END_REF]36). HCV RNA level was measured with a real-time PCR-based assay, either COBAS AmpliPrep ® or COBAS TaqMan ® (Roche Molecular Systems, Pleasanton, California) with a lower limit of quantification of 15 IU/mL or m2000 SP /m2000 RT (Abbott Molecular, Des Plaines, Illinois), with a lower limit of quantification of 12 IU/mL.

End-points

Study primary end point was the sustained virological response (SVR) defined as undetectable HCV RNA during and 12 weeks after treatment discontinuation (SVR12). Secondary end points included laboratory liver tests, evaluation of drug-drug interactions with immunosuppressive drugs and evaluation of safety over the full duration of treatment.

Safety

The following adverse events were collected if they occurred after initiation of therapy and up to 48 weeks after the end of treatment (follow-up): serious adverse event (SAE), defined in the Table 6, clinical and laboratory grade 3 or 4 adverse events (assessed with the Inserm-ANRS scale for grading of adverse events seriousness v6 of September 9th 2003 given in Appendix Y) and any grade of adverse events related to neutrophils, platelets, prothrombin, bilirubin, creatinin, haemoglobin or infections. The management of anemia (RBV dose reductions and/or erythropoietin administration, authorized in France when the hemoglobin level is below 10 g/dL, and/or blood transfusion) was at the investigator's discretion.

Statistical analyses were performed with an intent-to-treat basis using SAS statistical software (SAS Institute, Cary, NC, USA). Continuous variables were expressed by mean and standard deviation and categorical variables were expressed by the number of patients and percentages. Differences in baseline characteristics between groups were evaluated using one-way analysis of variance for continuous data and the chi-square test or Fisher's exact test for categorical data. A paired t-test was used to test for change over time in continuous variable.

Results

Study population

The study population consisted in 125 patients included between Oct 2013 and Nov 2014: 75 patients with METAVIR F4 HCV recurrence and 50 patients with METAVIR F3 HCV recurrence. The main characteristics of patients are presented in Table 1. The majority of patients was male (78.4%), infected by HCV genotype 1 (78.2%), had failed previous post-LT antiviral therapy (63.7%) including triple therapy with first generation protease inhibitors in 19 (15.2%) patients and SOF/RBV combination in 2 patients. Resistance testing before starting antiviral treatment was not systematically performed. This has been added. Four patients (3.2%) were co-infected with HIV. Immunosuppression was based on cyclosporine (30.4%) or tacrolimus (56.0%), and mycophenolate mofetil in 56.8% of cases. The mean time between LT and treatment initiation was 95.9 ± 69.6 months. Among the 73 cirrhotic patients with available data, 14 (19.2%) had ascites.

The following antiviral regimens were used (Table 2): SOF/RBV, SOF/PEG/RBV, SOF/DCV±RBV, SOF/LDV/RBV, SOF/SMV. RBV was used in 60 patients (48.0%). Daily dosages were as follows: 200 mg (n=2 (3.4%)), 400 mg (n=10 (16.9%)), 600 mg (n=18 (30.5%)), 800 mg (n=13 (22.0%)), 1000 mg (n=10 (16.9%)), 1200 mg (n=6 (10.2%)). Planned duration of treatment was 12 (14.4%) or 24 weeks (85.6%). Eventually, 2 patients received 28 weeks of treatment, 4 patients received 32 weeks, 3 patients received 36 weeks and 1 patient received 48 weeks of treatment. This was done because of slow virological response. Treatment regimens were SOF+DCV (n=7), SOF+DCV+RBV (n=1), SOF+RBV (n=1) and SOF+SMV/SOF+DCV (n=1).

Virological response

Table 3 summaries the rates of virological response. A rapid HCV RNA decline was observed in all patients after initiation of treatment. As shown in Figure 1, viral kinetics were similar between F3 and F4 groups. All but one patient had undetectable HCV RNA at end of treatment (EOT). In addition, 6 patients experienced relapse: at follow-up week 4 in 5 patients and at follow-up week 12 in one patient in whom follow-up week 4 time point was missing. Characteristics of the 7 patients who presented virological failure are summarized in Table 4. On an intention-to-treat basis analysis, global SVR12 rate was 92.8%.

It was 68.4% in patients who received a SOF/RBV combination (n=19), 100.0% in patients who received the SOF/PEG/RBV (n=5) and 97.0% in patients who received a combination of 2 DAA (n=101). Figure 2 describes the SVR12 rates according to treatment regimen, genotype, duration of treatment and previous HCV therapy post-LT.

Evolution of liver function tests

A rapid decrease of ALT, AST, and γGT serum levels was observed after treatment initiation (Table 5). At the end of antiviral treatment and according to the stage of fibrosis, the rate of patients with normal values was 91.8% and 84.1% for ALT, 89.8% and 73.9% for AST, and 63.3% and 41.8% for γGT, for F3 or F4 groups, respectively.

Clinical and liver function outcome

Evolution of biological liver function parameters is described in Table 5. BMI, albumin level and platelet count significantly improved, INR and bilirubin level did not change and creatinine and GFR significantly worsened. In summary, between D0 and EOT, in the group of 75 cirrhotic patients, Child score (when available, n=47) improved in 21 cases (44.7%) and worsened in 5 cases (10.6%) and MELD score (when available, n=64) improved in 25 cases (39.1%) and worsened in 26 cases (40.6%). In addition, between D0 and follow-up week 12, in the group of 75 cirrhotic patients, Child score (when available, n=45) improved in 20 cases (44.4%) and worsened in 5 cases (11.1%) (Figure 3A) and MELD score (when available, n=54) improved in 22 cases (40.7%) and worsened in 19 cases (35.2%) (Figure 3B). Based on Child score, liver disease progression (between D0 and end of treatment) was observed in 5 patients. One patient presented virological relapse. One patient was treated with PEG.

In parallel, mild ascites reversal was observed in 6/7 patients and refractory ascites reversal was observed in 5/7 patients. Two patients developed refractory ascites during treatment and 2 patients developed mild ascites. From the 14 patients with ascites at initiation of antiviral treatment, one had virological failure.

During antiviral treatment and follow-up, 3 patients were re-transplanted (at week 16 (n=1), between week 4 and week 24 post-treatment (n=2)) and 4 patients died (at week 1 (n=1), between week 4 and week 12 post-treatment (n=2), after week 24 post-treatment (n=1)). Causes of death were sepsis (n=2) or liver failure (n=2). All the 4 patients who died were cirrhotic; the 3 patients who died after treatment had virological failure; treatment regimens were SOF+RBV (n=3) or SOF+DCV+RBV (n=1). Deaths were considered unrelated to antiviral treatment in all cases; 3/4 occurred after end of treatment (5, 12 and 25 weeks). Re-transplantation was performed because of liver failure (week 16, n=1), chronic rejection (FU week 16, n=1), or de novo HCC (FU week 7, n=1). One patient presented virological relapse.

Safety

Thirty-two patients (25.6%) experienced at least one serious adverse event (Table 6). Infection was the most common serious adverse event (8.0%). Anemia was more frequent and more severe in patients who received RBV but was not related to fibrosis stage (Table 7).

Dosing of immunosuppressive drugs

Modifications in the dose of calcineurin and mTOR inhibitors, or MMF during antiviral treatment were performed at investigator's discretion. Dose changes during antiviral treatment were required in 25 patients (34.7%) on tacrolimus, 14 (36.8%) patients on cyclosporine, 6 (50.0%) patients on everolimus, and 7 (9.7%) patients on MMF. Only minimal dose modifications were required, on average of +10.7% for tacrolimus, -3.7% for cyclosporine, -1.7% for everolimus and +0.1% for MMF between baseline and end of treatment. Regarding the main antiviral treatment regimens used, dose changes of tacrolimus or cyclosporine were more frequent in patients treated with SOF+DCV+RBV (51.7%) when compared to patients treated with SOF+DCV (34.0%) or SOF+RBV (18.8%).

No significant over or under-dosage was observed, and one patient had graft rejection during antiviral therapy.

Discussion

Treatment of HCV recurrence after LT is a major goal and results have been impaired for a long time because of poor efficacy and high toxicity of PEG/RBV, even in combination with first generation protease inhibitors [START_REF] Antonini | Therapy with boceprevir or telaprevir in HIV/hepatitis C virus co-infected patients to treat recurrence of hepatitis C virus infection after liver transplantation[END_REF][START_REF] Coilly | Safety and efficacy of protease inhibitors to treat hepatitis C after liver transplantation: a multicenter experience[END_REF]. To our knowledge, the present study is one of the largest series of patients with recurrent hepatitis C and severe fibrosis (n=125), treated with SOF-based antiviral therapy.

After LT, recurrent hepatitis C begins with a first phase of acute hepatitis and can have thereafter two distinct clinical and histological patterns. The first one is the most frequent and the same than described in non-transplanted patients, characterized by a progression from chronic hepatitis to cirrhosis. The second type of recurrent hepatitis C after LT is specific for immunosuppressed patients and has been described as fibrosing cholestatic hepatitis (FCH). FCH leads to an inexorable deterioration of liver function [START_REF] Davies | Hepatic histological findings after transplantation for chronic hepatitis B virus infection, including a unique pattern of fibrosing cholestatic hepatitis[END_REF][START_REF] Zylberberg | Hepatitis C virus-related fibrosing cholestatic hepatitis after renal transplantation[END_REF], and is associated with a high probability of death (> 50%) [START_REF] Narang | Post-liver transplant cholestatic hepatitis C: a systematic review of clinical and pathological findings and application of consensus criteria[END_REF]. We recently reported, from 23 patients included in the CUPILT cohort and presenting FCH, that SOF-based antiviral therapy could be highly effective, since all patients survived, without retransplantation, and 22 patients (96%) achieved a SVR12 [START_REF] Leroy | Efficacy of Sofosbuvir and Daclatasvir in Patients with Fibrosing Cholestatic Hepatitis C After Liver Transplantation[END_REF]. The present study focused on patients with severe fibrosis (METAVIR F3 and F4), outside the field of FCH, and confirms these promising results in a different population with severe hepatitis C recurrence.

Indeed, in addition to fibrosis progression, natural history of recurrent HCV cirrhosis is also accelerated after LT. The probability of liver decompensation is > 40% at 1 year and >70% at 3 years in LT recipients vs. <5% and <10%, respectively, in immuno-competent patients (13, Berenguer, 2000(13, Berenguer, #1195, 14-16), 14-16). The rate of progression from liver decompensation to death is also accelerated, with a 3-year survival of <10% following the first decompensation vs. >60% in immuno-competent patients (13, Berenguer, 2000(13, Berenguer, #1195, 15, 16), 15, 16). This explains that long-term graft and patient survival is significantly reduced in patients undergoing LT for HCV-related liver disease as compared to other indications (3). Therefore, viral eradication in patients with severe fibrosis is a major goal, in order to avoid death, or re-transplantation.

The main result of our study is the high rate of SVR12, observed in a difficult-to-treat population (92.8%). These results look better than that initially reported by Charlton et al. [START_REF] Charlton | Sofosbuvir and ribavirin for treatment of compensated recurrent hepatitis C virus infection after liver transplantation[END_REF] and Forns et al. [START_REF] Forns | Sofosbuvir compassionate use program for patients with severe recurrent hepatitis C following liver transplantation[END_REF], from the first series using SOF after LT, in which only 70% and 59% of SVR12 were achieved, respectively. This was probably due to a non-optimal antiviral regimen used (SOF/RBV in all patients), as confirmed in our cohort in the subgroup of patients who received the SOF/RBV combination (68.4% of SVR rate). More recently, Pungpapong et al. reported the results from a multicenter study including 123 patients (all genotype 1, 30% METAVIR F3-F4) treated with a combination of SOF and SMV with or without RBV for 12 weeks ; a SVR12 was achieved in 90% of patients (19). These results were confirmed in the TARGET cohort, from 151 patients (all genotype 1) treated with SOF/SMV ± RBV, for 12 weeks for most patients; a SVR12 was achieved in 88% of patients [START_REF] Brown | Interferon-free therapy for genotype 1 hepatitis C in liver transplant recipients: Real-world experience from the hepatitis C therapeutic registry and research network[END_REF]. Similarly, Gutierrez et al.

reported a 93.4% rate of SVR12 in a cohort of 61 genotype 1 HCV patients (37.7% METAVIR F3-F4), treated with a combination of SOF and SMV for 12 weeks; interestingly, in METAVIR F3 and F4 patients infected with HCV genotype 1a, SVR12 was only 67% [START_REF] Gutierrez | Sofosbuvir and simeprevir for treatment of hepatitis C virus infection in liver transplant recipients[END_REF]. Kwo et al. reported a 97% SVR12 rate in a small cohort of 34 LT recipients treated with the combination of ombitasvir/paritaprevir/dasabuvir ± RBV, but only patients with no fibrosis or mild fibrosis were included [START_REF] Kwo | An interferon-free antiviral regimen for HCV after liver transplantation[END_REF]. Finally, our good virological results are probably related to the frequent use in our series of a combination of SOF and DCV (73.6% of the patients); this is probably due to the pangenotypic effect of this combination and is in accordance with the excellent results of the phase 2 study evaluating this combination in non-transplanted patients [START_REF] Sulkowski | Daclatasvir plus sofosbuvir for previously treated or untreated chronic HCV infection[END_REF].

An open and extremely relevant question is that of the potential clinical improvement after HCV eradication. We reported a dramatic improvement of liver function in our previous series of LT patients presenting FCH [START_REF] Leroy | Efficacy of Sofosbuvir and Daclatasvir in Patients with Fibrosing Cholestatic Hepatitis C After Liver Transplantation[END_REF]. In the present cohort, we observed in a majority of our cirrhotic patients, an improvement of liver function, based on Child score, during antiviral therapy. This was not the same when regarding MELD score but this was due to the worsening of renal function (and not liver function), in a cohort of "old" LT patients (8 years) with previous renal impairment. This observation is consistent with the results from Charlton et al. [START_REF] Charlton | Ledipasvir and Sofosbuvir Plus Ribavirin for Treatment of HCV Infection in Patients with Advanced Liver Disease[END_REF]. In a phase 2 study, the efficacy of a combination SOF/LDV/RBV was evaluated from 337 patients infected with HCV genotypes 1 or 4, including a majority of cirrhotic patients, with mild, moderate, or severe hepatic impairment (including LT patients).

The vast majority of patients with Child-Pugh class B and C disease who had or not undergone LT, had improved MELD and Child scores at post-treatment week4 compared with baseline. Similarly, on the cohort of Forns et al., clinical status of compensated and decompensated LT cirrhotic patients receiving SOF/RBV improved in 45% of the cases [START_REF] Forns | Sofosbuvir compassionate use program for patients with severe recurrent hepatitis C following liver transplantation[END_REF]. Nevertheless, evolution of renal function during and after antiviral therapy is of great concern. We observed that worsening of MELD score was less frequent when evaluated at follow-up week 12 (vs. EOT), strongly suggesting that impaired renal function observed during antiviral treatment, partially resolved after the end of treatment. This needs to be more extensively evaluated from larger cohort.

Safety was carefully investigated in our study population with severe fibrosis and multiple comedications. In our cohort, SAE were not very frequent (25.6% of the patients). The most frequent SAE was bacterial infection, with favorable outcome (no patient's death during antiviral treatment). Anemia was a frequent adverse event, observed in both patients with or without RBV, leading to RBV dose reduction or early interruption, EPO administration and even blood transfusions. As expected, anemia was more frequent and severe in patients treated with RBV, and this arises with the major issue of the optimal use of RBV (and dosage) in order to provide a significant benefit regarding antiviral efficacy. In the study by Charlton et al. [START_REF] Charlton | Sofosbuvir and ribavirin for treatment of compensated recurrent hepatitis C virus infection after liver transplantation[END_REF] evaluating the SOF/RBV combination the initial dose of ribavirin was 400 mg followed by an escalation dose protocol based on hemoglobin levels. Despite this protocol, still one quarter of patient required RBV dose reduction and 33% had severe anemia. Thus, avoiding RBV from antiviral therapy would undoubtedly increase safety. Interestingly, it has been suggested that RBV could not add any benefit in non-cirrhotic patients treated by SOF/DCV irrespective to genotype and prior treatment exposition [START_REF] Sulkowski | Daclatasvir plus sofosbuvir for previously treated or untreated chronic HCV infection[END_REF]. Nevertheless, extrapolation of these results to LT patients, especially with severe fibrosis, needs further evaluation. Last but not least, SOF, DCV, SMV and LDV are not supposed to have significant drug-drug interactions with calcineurin inhibitors and mTOR inhibitors [START_REF] Soriano | Drug interactions with new hepatitis C oral drugs[END_REF]. Close monitoring of calcineurin inhibitors and mTOR inhibitors concentrations performed in our study confirmed that only mild changes of dosages were required during the antiviral treatment period.

Our study had several limitations. The first one is sample size that was not sufficient to allow precise evaluation of sub-groups according to fibrosis stage, HCV genotype or antiviral treatment regimen. Nevertheless, our results do not support a strong impact of fibrosis stage (F3 vs. F4). We acknowledge that the liver stiffness cut-offs chosen for the diagnosis of F3 and F4 fibrosis stages have been validated in HCV-infection outside the LT setting [START_REF] Ziol | Noninvasive assessment of liver fibrosis by measurement of stiffness in patients with chronic hepatitis C[END_REF]. In their systematic review on the diagnostic performance of transient elastography in HCV-recurrence after LT, Cholangitas et al. found variable cut-offs, ranging from 7.9 to 10.1 kPa and from 10.5 to 26.5 kPa for the diagnosis of F3 and F4, respectively [START_REF] Cholongitas | Noninvasive tests for evaluation of fibrosis in HCV recurrence after liver transplantation: a systematic review[END_REF]. Given these data, we assumed that the use of the well validated cut-offs, falling in the same range than that described in LT, were the most appropriate as a non-invasive estimate of fibrosis in our study population.

The second limitation is that it is a cohort study with heterogeneous treatment regimens, which was not designed to determine the optimal antiviral regimen (drugs and duration). Nevertheless, combination of SOF and DCV, with or without RBV, for 24 weeks was the main regimen used in our population and could therefore be considered as the standard option, regarding its pangenotypic activity, when available.

In addition, since 6 out of our 7 patients who experienced virological failure were treated with SOF/RBV, this regimen should be used strictly for genotype 2 HCV only. Finally, due to relatively short follow-up we have been unable to provide clinical and histological outcome after HCV eradication; long-term data on survival (graft and patient) and reversion of fibrosis will be of great interest.

In conclusion, our study shows that SOF-based regimens allow achievement of SVR in the vast majority of patients presenting HCV recurrence with severe fibrosis following LT. These promising results are likely to dramatically change the prognosis in this difficult-to-treat population, with expected guarded long-term prognosis. Quantitative results are expressed as mean ± SD.

n number of missing data Quantitative results are expressed as mean ± SD (range;IQR;median) n : number of missing data. a A serious adverse event refers to any untoward medical occurrence or effect that at any dose:

• results in death,

• is life-threatening,

• results in persistent or significant disability or incapacity,

• requires hospitalization or prolongation of existing hospitalization,

• is a congenital anomaly or birth defect,

• is a grade 4 clinical adverse event,

• is a grade 4 biological adverse event,

• is an "important medical event" (medical events, based upon appropriate medical judgment, which may jeopardize the subject or may require medical or surgical intervention to prevent one of the above characteristics/consequences).

Figure 1 :

 1 Figure 1:

Figure 2 :

 2 Figure 2:

Figure 3 :

 3 Figure 3:

Table 1 : Baseline demographics and disease characteristics

 1

		Global (n=125)	F3 (n=50)	F4 (n=75)
	Gender (male)	98 (78.4%)	39 (78.0%)	59 (78.7%)
	Age (years)	59.4 ± 9.0	59.5 ± 8.5	59.3 ± 9.4
	Body mass index (kg/m²)	24.4 ± 4.0 19	24.2 ± 4.0 9	24.6 ± 4.1 10
	HIV co-infection	4 (3.2%)	3 (6.0%)	1 (1.3%)
	Indication for LT
	Cirrhosis	52 (41.6%)	16 (32.0%)	36 (48.0%)
	HCC	65 (52.0%)	29 (58.0%)	36 (48.0%)
	HCV ReLT	7 (5.6%)	5 (10.0%)	2 (2.7%)
	Other	1 (0.8%)	0 (0.0%)	1 (1.3%)
	Delay after LT (months)	95.9 ± 69.6	82.4 ± 71.4	104.9 ± 67.3
	Immunosuppressive drugs
	Cyclosporine	38 (30.4%)	20 (40.0%)	18 (24.0%)
	Tacrolimus	70 (56.0%)	22 (44.0%)	48 (64.0%)
	Sirolimus	1 (0.8%)	1 (2.0%)	0 (0.0%)
	Everolimus	11 (8.8%)	7 (14.0%)	4 (5.3%)
	MMF	71 (56.8%)	30 (60.0%)	41 (54.7%)
	Previous therapy post-LT
	Treatment-naive	45 (36.0%)	23 (46.0%)	22 (29.3%)
	RBV	2 (1.6%)	0 (0.0%)	2 (2.7%)
	PEG+RBV	57 (45.6%)	19 (38.0%)	38 (50.7%)
	PEG+RBV+BOC	5 (4.0%)	2 (4.0%)	3 (4.0%)
	PEG+RBV+TLV	14 (11.2%)	5 (10.0%)	9 (12.0%)
	RBV+SOF	2 (1.6%)	1 (2.0%)	1 (1.3%)
	Previous course of HCV Therapy	1		1
	post-LT
	Treatment-naive	45 (36.3%)	23 (46.0%)	22 (29.7%)
	Breakthrough	9 (7.3%)	5 (10.0%)	4 (5.4%)
	Relapse	14 (11.3%)	7 (14.0%)	7 (9.5%)
	Non-responders	30 (24.2%)	9 (18.0%)	21 (28.4%)
	Intolerance	26 (21.0%)	6 (12.0%)	20 (27.0%)
	HCV Genotype	1	1
	1	97 (78.2%)	36 (73.5%)	61 (81.3%)
	2	1 (0.8%)	0 (0%)	1 (1.3%)
	3	14 (11.3%)	7 (14.3%)	7 (9.3%)
	4	11 (8.9%)	5 (10.2%)	6 (8.0%)
	5	1 (0.8%)	1 (2.0%)	0 (0%)

HCV Viral load (log10 IU/mL) 6.1 ± 1.0 6.3 ± 0.6 6.0 ± 1.2

Baseline CHILD score 6.4 ± 1.3 12 -6.4 ± 1.3

12

Baseline CHILD class

12 12

Class A (5-6 points) 39 (61.9%) -39 (61.9%)

Table 2 : Antiviral therapy regimens

 2

	Expected duration

Table 3 : Virological response during and after treatment (intent-to-treat analysis)

 3

	Variable(s)	Global (n=125)	Stage F3 (n=50)	Stage F4 (n=75)
	W0*
	HCV RNA < LLOQ	2 (1.6%)	0 (0.0%)	2 (2.7%)
	W4
	HCV RNA < LLOQ	58 (46.4%)	26 (52.0%)	32 (42.7%)
	Causes of treatment failure	death (n=1),	non response (n=23),	death (n=1),
		non response (n=64),	missing data (n=1)	non response (n=41),
		missing data (n=2)		missing data (n=1)
	W8
	HCV RNA < LLOQ	106 (84.8%)	45 (90.0%)	61 (81.3%)
	Causes of treatment failure	death (n=1),	non response (n=5)	death (n=1),
		non response (n=16),		non response (n=11),
		missing data (n=2)		missing data (n=2)
	W12
	HCV RNA < LLOQ	119 (95.2%)	48 (96.0%)	71 (94.7%)
	Causes of treatment failure	death (n=1),	non response (n=2)	death (n=1),
		non response (n=5)		non response (n=3)
	EOT
	HCV RNA < LLOQ	121 (96.8%)	49 (98.0%)	72 (96.0%)
	Causes of treatment failure	death (n=1),	virological breakthrough (n=1)	death (n=1),
		virological breakthrough (n=1),		missing data (n=2)
		missing data (n=2)
	FUW4
	HCV RNA < LLOQ	115 (92.0%)	47 (94.0%)	68 (90.7%)
	Causes of treatment failure	death (n=1),	virological breakthrough (n=1),	death (n=1),
		virological breakthrough (n=1),	virological relapse (n=1),	virological relapse (n=5),
		virological relapse (n=6),	lost to follow-up (n=1)	missing data (n=1)
		lost to follow-up (n=1),
		missing data (n=1)
	FUW12
	HCV RNA < LLOQ	116 (92.8%)	47 (94.0%)	69 (92.0%)
	Causes of treatment failure	death (n=1),	virological breakthrough (n=1),	death (n=1),
		virological breakthrough (n=1),	virological relapse (n=1),	virological relapse (n=5)
		virological relapse (n=6),	lost to follow-up (n=1)
		lost to follow-up (n=1)

* 2 patients had undetectable HCV RNA at initiation of SOF (lead-in phase with PEG/RBV)

Table 4 : Characteristics of patients with treatment failure Patient Antiviral treatment failure Antiviral treatment regimen

 4

	Antiviral treatment duration	Outcome	Genotype	Fibrosis stage

Table 5 : Outcome of clinical features and laboratory tests during antiviral treatment

 5

	Variable(s)*	J0 (n=125)	EOT (n=124)	p J0 vs EOT
	BMI	106	89	p = .04
		24.4 ± 4.0	25.1 ± 4.6
		(16.3 ; 21.6 ; 24.2 ; 27.2 ; 35.9)	(15 ; 22 ; 24.2 ; 28.2 ; 40.1)
	AST (IU/L)	124	118	p < .001
		91.6 ± 70.9	31.1 ± 14.4
		(21.0 ; 45.5 ; 74.0 ; 109.5 ; 548.0) (0.7 ; 22.0 ; 28.0 ; 38.0 ; 111.0)
	ALT (IU/L)	124	118	p < .001
		81.2 ± 53.4	26.0 ± 13.3
		(12.0 ; 36.0 ; 72.0 ; 111.5 ; 279.0)	(0.5 ; 16.0 ; 23.0 ; 33.0 ; 67.0)
	GGT (IU/L)	124	116	p < .001
		278.3 ± 295.1	99.9 ± 122.8
		(16.0 ; 66.5 ; 153.5 ; 342.5 ; 1537.0) (14.0 ; 34.0 ; 53.5 ; 105.0 ; 727.0)
	AP (IU/L)	113	109	p < .001
		153.0 ± 103.3	114.9 ± 72.4
		(52.0 ; 99.0 ; 128.0 ; 171.0 ; 847.0) (47.0 ; 79.0 ; 96.0 ; 134.0 ; 665.0)
	Bilirubin (total) (µmol/L)	121	117	p = .80
		20.9 ± 16.9	22.7 ± 74.2
		(5.0 ; 10.0 ; 16.0 ; 24.0 ; 116.3)	(3.0 ; 8.4 ; 13.0 ; 19.0 ; 809.0)
	Creatinine (µmol/L)	125	121	p = .002
		116.5 ± 62.8	128.3 ± 90.4
		(48.0 ; 81.0 ; 102.0 ; 128.0 ; 486.0) (52.0 ; 88.0 ; 106.0; 142.0 ; 849.0)
	eGFR MDRD (mL/min)	125	121	p < .001
		67.5 ± 26.6	62.9 ± 24.3
		(8.8 ; 48.2 ; 64.7 ; 86.3 ; 170.3)	(6.0 ; 45.5 ; 63.3 ; 76.2 ; 124.4)
	Albumin (g/L)	111	108	p < .001
		36.3 ± 6	38.4 ± 5.4
		(21.0 ; 32.0 ; 36.4 ; 40.5 ; 56.0)	(21.6 ; 35.3 ; 39.0 ; 42.1 ; 48.0)
	Platelets (G/L)	125	120	p < .001
		119.5 ± 67.4	133.8 ± 66.6
		(19.0 ; 69.0 ; 111.0 ; 163.0 ; 389.0) (27.0 ; 81.0 ; 128.0 ; 170.5 ; 343.0)
	INR	118	113	p = .96
		1.2 ± 0.3	1.2 ± 0.3
		(0.9 ; 1.0 ; 1.1 ; 1.2 ; 2.4)	(0.9 ; 1.0 ; 1.1 ; 1.3 ; 2.7)

Table 6 : Safety profile of antiviral therapy regimens

 6

	Global (n=125)	F3 (n=50)	F4 (n=75)

Table 7 : Anemia during antiviral therapy (according to RBV use and fibrosis stage)

 7

	Anemia

Liver Transplantation

NCT01944527

Grant support: The study was sponsored and funded by The National Agency for Research on AIDS and Viral Hepatitis (ANRS).


Joseph M Carrasco

Renata Kallosh

Andrei Linde

Inflatino-less Cosmology

. When local supersymmetry is gauge-fixed in the unitary gauge, these models describe theories with only a single real scalar (the inflaton), a graviton and a gravitino. Critically, there is no inflatino, no sgoldstino, and no sinflaton in these models. This dramatically simplifies cosmological models which can simultaneously describe inflation, dark energy and SUSY breaking.

Introduction. In this letter we show that the recently constructed models of supergravity with orthogonal nilpotent superfields [START_REF] Ferrara | Cosmology with orthogonal nilpotent superfields[END_REF] significantly simplify construction of cosmological models which simultaneously describe inflation, dark energy and SUSY breaking. Now one can achieve this goal using the absolutely minimal number of ingredients: graviton, gravitino, and a single real scalar, the inflaton. Our methods apply to a broad class of inflationary theories, but they are especially suitable for describing α-attractors [START_REF] Kallosh | Universality Class in Conformal Inflation[END_REF], which provide a very good fit to the latest cosmological data [START_REF] Ade | Planck 2015 results. XX. Constraints on inflation[END_REF].

Orthogonal nilpotent superfields. Global supersymmetry models with orthogonal nilpotent superfields were studied in [START_REF] Komargodski | From linear SUSY to constrained superfields[END_REF][START_REF] Kahn | The goldstone and goldstino of supersymmetric inflation[END_REF]. Their generalization to local supergravity interacting with orthogonal nilpotent multiplets was presented in [START_REF] Ferrara | Cosmology with orthogonal nilpotent superfields[END_REF]. The models depend on two constrained chiral superfields 1 , S and Φ. A stabilizer S has a nilpotency of degree two, S n = 0 for n ≥ 2. This constraint removes the complex scalar S(x), sgoldstino, from the bosonic spectrum. The chiral inflaton multiplet Φ has as a first component a complex scalar Φ(x) = φ(x) + ib(x).

One can form a real superfield B ≡ 1 2i Φ -Φ with the first component b(x), the sinflaton, and impose the orthogonality constraint SB = 0. As a result, fields in the inflaton multiplet are no longer independent: the sinflaton b(x), inflatino χ φ and the auxiliary F φ become functions of the spin 1/2 field χ s in the S-multiplet. All of these fields vanish in the unitary gauge χ s = 0, which fixes the local supersymmetry of the action.

It follows from S 2 = 0 and SB = 0 that B is nilpotent of degree 3, B m = 0 for m ≥ 3. The second real superfield which can be formed from the chiral inflaton superfield is A = 1 2 Φ + Φ . It starts with one real inflaton scalar field, φ(x).

The unusual property of these models is that in the 1 We use bold face letters for superfields which in global case are functions of (x, θ, θ). For example, the chiral superfield S means that S = S(x) + √ 2θχ s + θ 2 F s , and

Φ = Φ(x) + √ 2θχ φ + θ 2 F φ .
unitary gauge, fixing local supersymmetry, there is only one real scalar φ(x), a massless graviton and a massive gravitino. There is no sgoldstino, no sinflaton and no inflatino. An essential property of these models is that the form of the potential is different from the standard supergravity potentials, as shown in [START_REF] Ferrara | Cosmology with orthogonal nilpotent superfields[END_REF]:

V = e K (|D S W | 2 -3W 2 ) S= S=Φ-Φ=0 . (1)
First, the 3 scalars S, S and Φ -Φ vanish, there is no need to stabilize them. Secondly, the terms which would normally be present in the potential, quadratic and linear in D Φ W , are absent, despite the fact that D Φ W can be arbitrary. This is because the auxiliary field F φ from the inflaton multiplet is fermionic as a consequence of the orthogonality constraint SB = 0.

Here we will study supergravity models with constrained superfields

K(S , S; Φ, Φ), W = f (Φ)S+g(Φ), S 2 = SB = 0. (2)
The consistency of these models with the constraints was studied in [START_REF] Ferrara | Cosmology with orthogonal nilpotent superfields[END_REF] where it was shown that the superfield Kähler potential can be also brought to the form K(S , S; Φ, Φ) = S S + h(A)B 2 .

(

This means, in particular that the Kähler potential in supergravity vanishes when the bosonic constraints are imposed:

K(S S; Φ, Φ) S= S=Φ-Φ=0 = 0 . (4)
Note, however, that the bosonic constraints S = S = Φ -Φ = 0, when deriving the supergravity action, have to be applied only after the relevant derivatives over S and S and Φ and Φ are taken.

For models with orthogonal nilpotent superfields, the inflaton action is very simple. Taking into account [START_REF] Komargodski | From linear SUSY to constrained superfields[END_REF] and with a proper normalization of S, we find

e -1 L infl = -K Φ, Φ∂Φ∂ Φ + [3g 2 (Φ) -f 2 (Φ)] Φ= Φ . (5) arXiv:1512.00546v1 [hep-th] 2 Dec 2015
Kähler potentials in models with S2 = SB = 0. Many successful inflationary models in supergravity are based on theories where the Kähler potential either vanishes along the inflaton direction, or can be represented in such form after some Kähler transformations, see for example [START_REF] Goncharov | Chaotic Inflation Of The Universe In Supergravity[END_REF][START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF][START_REF] Kallosh | New models of chaotic inflation in supergravity[END_REF][START_REF] Kallosh | Escher in the Sky[END_REF][START_REF] Carrasco | The Hyperbolic Geometry of Cosmological Attractors[END_REF][START_REF] Carrasco | Cosmological Attractors and Initial Conditions for Inflation[END_REF][START_REF] Carrasco | α-Attractors: Planck, LHC and Dark Energy[END_REF][START_REF] Kallosh | Chaotic Inflation in Supergravity after Planck and BICEP2[END_REF]. In models with S 2 = SB = 0, where B = (Φ -Φ)/(2i), this requirement is naturally satisfied (3), ( 4).

Here we study the cosmological models with orthogonal nilpotent superfields (2) over several different Kähler potentials. The simplest Kähler potential with a flat direction describing a canonically normalized inflaton field φ = Re Φ is given by [START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF][START_REF] Kallosh | New models of chaotic inflation in supergravity[END_REF]

K = 1 4 (Φ -Φ) 2 + S S . (6)
Here the geometry of the moduli space is flat.

We will be especially interested in the Kähler potentials for a broad class of cosmological attractors describing Escher-type hyperbolic geometry [START_REF] Kallosh | Escher in the Sky[END_REF][START_REF] Carrasco | The Hyperbolic Geometry of Cosmological Attractors[END_REF] of the inflaton moduli space. Compatibility of the constraints S 2 = SB = 0 with the hyperbolic geometry is demonstrated in the Appendix. Examples of such Kähler potentials include

K = - 3 2 α log (1 -Φ Φ) 2 (1 -Φ 2 )(1 -Φ 2 ) + S S . (7)
It describes hyperbolic geometry in disk variables. The same geometry can be described in half-plane variables by the Kähler potential

K = - 3 2 α log (Φ + Φ) 2 4Φ Φ + S S . (8)
These two versions correspond to equivalent ways of describing the Kähler geometry of α-attractors. See refs. [START_REF] Carrasco | The Hyperbolic Geometry of Cosmological Attractors[END_REF][START_REF] Carrasco | Cosmological Attractors and Initial Conditions for Inflation[END_REF][START_REF] Carrasco | α-Attractors: Planck, LHC and Dark Energy[END_REF] for a detailed discussion of this issue. 2 One may also consider these Kähler potentials with the term S S under the logarithm. In all of these cases, the Kähler potential vanishes for Φ = Φ, and K S, S = 1 or can be brought to K S, S = 1 by a holomorphic transformation defined in [START_REF] Ferrara | Cosmology with orthogonal nilpotent superfields[END_REF]. The inflaton action is given by ( 5), and the inflaton potential is given by a simple expression

V = f 2 (φ) -3g 2 (φ) . ( 9
)
This result is similar to the expression V = f 2 (φ) for the family of models with W = Sf (Φ) developed in [START_REF] Kallosh | New models of chaotic inflation in supergravity[END_REF].

The new generation of models is different in two respects. First of all, it describes a non-vanishing gravitino mass

m 3/2 (φ) = g(φ) . (10)
Additionally, it may also describe non-vanishing vacuum energy (cosmological constant) at the minimum of the potential. Without any loss of generality one may assume that the minimum of the potential corresponding to our vacuum state is at φ = 0. The cosmological constant is equal to

Λ = f 2 (0) -3g 2 (0) . (11)
The condition that φ = 0 is a minimum implies that f (0) = √ 3g (0), up to small corrections vanishing in the limit Λ → 0. These conditions, plus the requirement that the functions f (φ) and g(φ) are holomorphic, leave lots of freedom to describe observational data. Indeed there are many ways to do so, depending on the choice of the Kähler potential.

Even though the expression of the potential V = f 2 (φ) -3g 2 (φ) is valid for all choices of the Kähler potentials described above, the field φ in the theories with the Kähler potentials ( 7) and ( 8) is not canonically normalized. In the theory [START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF] the field φ is related to the canonically normalized inflaton field ϕ as follows:

φ = tanh ϕ √ 6α . ( 12
)
Meanwhile for the theory (8) one has

φ = e - √ 2 3α ϕ . (13)
Thus, the potential V = f 2 (φ) -3g 2 (φ), expressed in terms of a canonically normalized field ϕ, depends on the choice of the Kähler potential. In the next section we will describe several realistic inflationary models in this context.

Inflationary models.

Model 1:

f (φ) = M φ 2 + a, g(φ) = b.
The potential in this model is

V = M 2 φ 4 + 2aM φ 2 + a 2 -3b 2 . ( 14
)
The cosmological constant in this model, and all other models we present here, is equal to

Λ = a 2 -3b 2 . ( 15
)
In realistic models we should have Λ ∼ 10 -120 due to an almost precise cancellation between a 2 and 3b 2 in accordance with a string landscape scenario. The gravitino mass is m If we consider a model with the simplest canonical Kähler potential (6), the potential ( 14) is quartic with respect to the canonically normalized inflaton field, which rules out this simple model.

The situation instantly improves in the theory with the logarithmic Kähler potential [START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF], which yields the following potential in terms of the canonically normalized field ϕ:

V = M 2 tanh 4 ϕ √ 6α + 2aM tanh 2 ϕ √ 6α + a 2 -3b 2 . ( 16
)
This is the typical T-model α attractor potential [START_REF] Kallosh | Universality Class in Conformal Inflation[END_REF]. Inflation occurs at the plateau where tanh ϕ √ 6α ≈ 1. In this regime the second term in ( 16) is much smaller than the first term, and both terms are much greater than Λ, so inflation is described by the quartic T-model potential

V = M 2 tanh 4 ϕ √ 6α . ( 17
)
The observational predictions of this model for α 10 practically coincide with the predictions of the simpler model V = M 2 tanh 2 ϕ √ 6α , for the same number of efoldings N [START_REF] Kallosh | Universality Class in Conformal Inflation[END_REF]. However, at the end of inflation in the model [START_REF] Kallosh | Inflation, de Sitter Landscape and Super-Higgs effect[END_REF] the inflaton field begins to oscillate in the approximately quartic potential ∼ ϕ 4 . The average equation of state during this stage is the same as of the hot plasma, p = ρ/3, as if reheating finishes immediately after inflation. This increases the required number of efoldings by ∆N ∼ 3 [START_REF] Bezrukov | Distinguishing between R 2 -inflation and Higgs-inflation[END_REF]. In its turn, this leads to a slight increase of the spectral index n s , which may provide even better fit to the recent Planck data.

Model 2: f (φ) = M φ 2 + a, g(φ) = mφ 2 + b
The potential is

V = (M 2 -3m 2 )φ 4 + 2(M a -3m b)φ 2 + a 2 -3b 2 . ( 18
)
This model is very similar to the previous one, but there is one potentially interesting difference: The gravitino mass depends on the inflaton, m 3/2 = mφ 2 + b.

Model 3: f (φ) = M 2 2 φ 2 + a 2 , g(φ) = b
The potential is

V = M 2 2 φ 2 + a 2 -3b 2 . ( 19
)
The potential for φ is exactly quadratic, plus a cosmological constant.

In the theory with the logarithmic Kähler potential [START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF] this potential becomes a potential for the simplest α-attractor model of the canonically normalized field ϕ:

V = M 2 2 tanh 2 ϕ √ 6α + a 2 -3b 2 . ( 20
)
The gravitino mass is m 3/2 = b.

Model 4: f (φ) = M 2 2 φ 2 + a 2 , g(φ) = m 2 2 φ 2 + b 2 In this model one has V = M 2 -3m 2 2 φ 2 + a 2 -3b 2 . ( 21
)
In the theory with the logarithmic Kähler potential [START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF] the potential of a canonically normalized inflaton field becomes

V = M 2 -3m 2 2 tanh 2 ϕ √ 6α + a 2 -3b 2 . ( 22
)
This model is very similar to Model 3, but the gravitino

mass is φ-dependent, m 3/2 = m 2 2 φ 2 + b 2 . Model 5: f (φ) = F 2 (φ) + a 2 , g(φ) = G 2 (φ) + b 2
In this model

V = F 2 (φ) -3G 2 (φ) + a 2 -3b 2 , m 3/2 = G 2 (φ) + b 2 .
(23) Because of the freedom of choice of the holomorphic functions F and G, one can have a wide variety of potentials fitting all observational data even if the fields φ is canonically normalized, with the Kähler potential [START_REF] Goncharov | Chaotic Inflation Of The Universe In Supergravity[END_REF], see e.g. [START_REF] Kallosh | Chaotic Inflation in Supergravity after Planck and BICEP2[END_REF]. Meanwhile in the theories with the Kähler potential [START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF] one finds a family of T-model α-attractors with

V = F 2 (tanh ϕ √ 6α ) -3G 2 (tanh ϕ √ 6α ) + a 2 -3b 2 . ( 24
)
For a wide range of functions F and G, these theories have universal cosmological predictions for α 10 and any given number of e-foldings: n s = 1 -2/N , r = 12α/N 2 [START_REF] Kallosh | Universality Class in Conformal Inflation[END_REF]. However, by a proper choice of the function F one can modify the required number of e-foldings N , which can be useful for tuning the predictions for n s .

Model 6: f (φ) = (1 -φ) 2 + a 2 , g(φ) = b
It is a particular version of Model 5 for

F (φ) = M (1 -φ)
and G(φ) = 0. This yields

V = M 2 (1 -φ) 2 + Λ, Λ = a 2 -3b 2 , m 3/2 = b. ( 25
)
Using the half-plane Kähler potential (8) and the relation φ = e - √ 2 3α ϕ (13) one finds

V = M 2 1 -e - √ 2 3α ϕ 2 + Λ . (26)
This represents the family of E-model α-attractors [START_REF] Kallosh | Universality Class in Conformal Inflation[END_REF][START_REF] Kallosh | Escher in the Sky[END_REF], which reduces to the Starobinsky model for α = 1, Λ = 0 and m 3/2 = 0. Meanwhile our class of theories describes E-models with arbitrary α, Λ and m 3/2 . Conclusions. As one could see from the previous section, it is very easy to formulate and analyze models with orthogonal nilpotent fields. Previously, it was a much more complicated task because of certain constraints imposed on inflationary models with nilpotent fields, see e.g. [START_REF] Kallosh | Inflation and Uplifting with Nilpotent Superfields[END_REF][START_REF] Dall'agata | On sgoldstino-less supergravity models of inflation[END_REF][START_REF] Kallosh | Inflation, de Sitter Landscape and Super-Higgs effect[END_REF] and the more advanced models presented in [START_REF] Carrasco | α-Attractors: Planck, LHC and Dark Energy[END_REF]. These constraints where required for simplification of the fermionic sector, but they are no longer required in the new class of models where the fermionic sector is trivial because the inflatino disappears in the unitary gauge. As a result, we have lots of flexibility in finding economical models containing only inflaton, graviton and gravitino, and yet capable of simultaneously describing inflation, dark energy and SUSY breaking.

The absence of the inflatino also helps us argue that there there is no problem with the unitarity bound during inflation in this class of models. The effective cutoff in supergravity is the scale at which scattering amplitudes violate unitarity bound. In the theories with nilpotent fields, this cutoff is expected at Λ (H 2 + m 2 3/2 ) 1/4 > √ H, in units M p = 1 [START_REF] Ferrara | Cosmology with orthogonal nilpotent superfields[END_REF][START_REF] Kahn | The goldstone and goldstino of supersymmetric inflation[END_REF][START_REF] Dall'agata | On sgoldstino-less supergravity models of inflation[END_REF][START_REF] Kallosh | Superconformal symmetry, supergravity and cosmology[END_REF]. During inflation with H 1, the UV cut-off Λ > √ H is much higher than the typical energy of inflationary quantum fluctuations ∼ H. In general, there could be some additional contributions to scattering due to gravitino-inflatino mixing, but in the theory that we consider there is no inflatino, and therefore no violation of the unitarity bound is expected during inflation at sub-Planckian energy density.

We hope to return to this issue in the future, simultaneously with investigation of reheating in the new class of models. In particular, we expect that the absence of the inflatino should significantly simplify the theory of nonthermal gravitino production by an oscillating inflaton field [START_REF] Kallosh | Superconformal symmetry, supergravity and cosmology[END_REF][START_REF] Kallosh | Gravitino production after inflation[END_REF][START_REF] Giudice | Nonthermal production of dangerous relics in the early universe[END_REF][START_REF] Nilles | Nonthermal production of gravitinos and inflatinos[END_REF].

We are grateful to S. Ferrara and J. Thaler for many enlightening discussions and collaboration. JJMC is supported by the European Research Council under ERC-STG-639729, 'Strategic Predictions for Quantum Field Theories'. The work of RK and AL is supported by the SITP, and by the NSF Grant PHY-1316699. The work of AL is also supported by the Templeton foundation grant 'Inflation, the Multiverse, and Holography.' Appendix A. Hyperbolic geometry models with orthogonal nilpotent superfields Three equivalent versions of α-attractor models with S 2 (x, θ) = 0 and hyperbolic geometry of the inflaton moduli space [START_REF] Kallosh | Escher in the Sky[END_REF][START_REF] Carrasco | The Hyperbolic Geometry of Cosmological Attractors[END_REF] are given either by a disk geome-try Z Z < 1,

K = - 3 2 α log (1 -Z Z) 2 (1 -Z 2 )(1 -Z 2 ) + S S , W = A(Z) + SB(Z) , (27)
or a half-plane geometry, T + T > 0,

K = -
In all of these models the Kähler potential and the superpotential, separately, are related by a change of variables

T = 1 + Z 1 -Z , Z = tanh Φ √ 6α , T = e √ 2 3α Φ . (30)
Now we would like to impose the orthogonality constraint on our superfields. The Killing-adapted variable Φ in ( 29) is an unconstrained superfield whose scalar part is not restricted by the boundaries. Therefore we may start by imposing the orthogonality and the nilpotency constraint in the form S 2 = 0, S(Φ -Φ) = 0, (Φ -Φ) n = 0, n ≥ 3 , (31)

Using the relation between these variables, one can derive the related constraints for the disk and half-plane variables Z, and T , respectively.

S(Φ-Φ) = 0 ⇒ S(Z-Z) = 0 ⇒ S(T-T) = 0.

It can be shown also that the Kähler potentials in ( 27), (28), (29), take the form of eq. ( 3) due to orthogonality constraint.

  /2 = b, which nearly coincides with a/ √ 3. For b ∼ 10 -15 one can have the gravitino mass in the often discussed TeV range. To have a proper amplitude of scalar perturbations one should have M ∼ 10 -5 a, b.

The third equivalent choice corresponds to the choice of Kähler potential made in[START_REF] Goncharov | Chaotic Inflation Of The Universe In Supergravity[END_REF] when the nilpotency constraint B

= 0 is taken into account. It is related to[START_REF] Kawasaki | Natural chaotic inflation in supergravity[END_REF] and (8) by a change of variables[START_REF] Carrasco | The Hyperbolic Geometry of Cosmological Attractors[END_REF][START_REF] Carrasco | Cosmological Attractors and Initial Conditions for Inflation[END_REF][START_REF] Carrasco | α-Attractors: Planck, LHC and Dark Energy[END_REF], see also Appendix.