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We revisit one-loop corrections to the power spectrum of curvature perturbations $\zeta$ in an inflationary scenario containing a transient ultra-slow-roll (USR) period. In Ref.[1], it was argued that one-loop corrections to the power spectrum of $\zeta$ can be larger than the tree-level one within the parameter region generating the seeds of primordial black holes during the USR epoch, which implies the breakdown of perturbation theory. We prove that this is not the case by using a master formula for one-loop corrections to the power spectrum obtained in Ref.[2]. We derive the same formula within the path-integral formalism, which is simpler than the original derivation in [2]. To show the smallness of one-loop corrections, the consistency relations and the effective constancy of tree-level mode functions of $\zeta$ for super-Hubble modes play essential roles, with which the master formula gives a simple expression for one-loop corrections. For concreteness, we provide a reduced set of interactions including the leading-order one, while establishing the consistency relations in a self-consistent manner. We also show how the consistency relations of various operators hold explicitly, which plays a key role in proving the absence of large one-loop corrections., Comment: 46 pages, 11 figures

We revisit the properties of total time-derivative terms as well as terms proportional to the free equation of motion (EOM) in a Schwinger-Keldysh formalism. They are relevant to the correct calculation of correlation functions of curvature perturbations in the context of inflationary Universe. We show that these two contributions to the action play different roles in the operator or the path-integral formalism, but they give the same correlation functions as each other. As a concrete example, we confirm that the Maldacena's consistency relations for the three-point correlation function in the slow-roll inflationary scenario driven by a minimally coupled canonical scalar field hold in both the operator and path-integral formalisms. We also give some comments on loop calculations., Comment: 15 pages

We provide a quantum-field theoretic formulation of dressed particle dynamics that systematically include particle production and scattering/decay processes in the preheating era. Our approach is based on the so-called perturbation theory in the Furry picture, in which coherent background fields (i.e., inflaton and the expanding Universe) are treated non-perturbatively whereas interactions between dressed particles are taken into account perturbatively. As application, we consider the instant preheating mechanism and compute the number of produced particles explicitly, assuming that the coherent fields are adiabatic. We find a novel non-perturbative particle-production mechanism, which is kinematically forbidden within the conventional perturbative calculation and produces particles exponentially efficiently than the perturbative one does., Comment: 30 pages, 5 figures, v2:comments added, typos fixed, v3: comments added

We develop sequestered inflation models, where inflation occurs along flat directions in supergravity models derived from type IIB string theory. It is compactified on a ${\mathbb{T}^6 \over \mathbb{Z}_2 \times \mathbb{Z}_2}$ orientifold with generalized fluxes and O3/O7-planes. At Step I, we use flux potentials which 1) satisfy tadpole cancellation conditions and 2) have supersymmetric Minkowski vacua with flat direction(s). The 7 moduli are split into heavy and massless Goldstone multiplets. At Step II we add a nilpotent multiplet and uplift the flat direction(s) of the type IIB string theory to phenomenological inflationary plateau potentials: $\alpha$-attractors with 7 discrete values $3\alpha = 1, 2, 3, ..., 7$. Their cosmological predictions are determined by the hyperbolic geometry inherited from string theory. The masses of the heavy fields and the volume of the extra dimensions change during inflation, but this does not affect the inflationary dynamics., Comment: 24pages, 7 figures, v2: reference added, accepted for publication in Fortschritte der Physik, v3: addendum after BICEP/Keck18 release added in Sec. 7

We construct supergravity models allowing to sequester the phenomenology of inflation from the Planckian energy scale physics. The procedure consists of two steps: At Step I we study supergravity models, which might be associated with string theory or M-theory, and have supersymmetric Minkowski vacua with flat directions. At Step II we uplift these flat directions to inflationary plateau potentials. We find certain conditions which ensure that the superheavy fields involved in the stabilization of the Minkowski vacua at Step I are completely decoupled from the inflationary phenomenology., Comment: 15 pages, 4 figures, v2: refs added, accepted for publication in Fortschritte der Physik

We investigate supersymmetry (SUSY) breaking scenarios where both SUSY and Lorentz symmetry are broken spontaneously. For concreteness, we propose models in which scalar fluid or vector condensation breaks Lorentz symmetry and accordingly SUSY. Then, we examine whether such scenarios are viable for realistic model buildings. We find, however, that the scalar fluid model suffers from several issues. Then, we extend it to a vector condensation model, which avoids the issues in the scalar fluid case. We show that accelerated expansion and soft SUSY breaking in matter sector can be achieved. In our simple setup, the soft SUSY breaking is constrained to be less than $\mathcal{O}(100)$TeV from the constraints on modification of gravity., Comment: 19 pages, v2: references added, v3: typo fixed, published version

We discuss the adiabatic basis dependence of particle number in time-dependent backgrounds. In particular, we focus on preheating after inflation, and show that, for the optimal basis, the time dependence of the produced particle number can be well approximated by a simple connection formula, which can be obtained by analysing Stokes phenomenon in given backgrounds. As we show explicitly, the simple connection formula can describe various parameter regions such as narrow and broad resonance regime in a unified manner., Comment: 37 pages, 15 figures, v2: references added, v3:comments added, accepted for publication in JCAP

Gravitational counterpart of the chiral magnetic effect, which is referred as the chiral gravitational effect, can also be of interest in a cosmological setup. In this study, we investigate this effect in the time-dependent chiral asymmetric fermion background and in the expanding spacetime by formulating the effective action of gravitational waves. We also analyze the anomaly equation to see how the backreaction from gravitational waves to thermal chiral plasma occurs. We find that the non-trivial time dependence of chiral chemical potential, which can be induced in some scenarios of baryogenesis, is the key ingredient of the chiral gravitational effect. It turns out that the "memory" of the effect is imprinted on the high frequency gravitational waves propagating in the plasma. Cosmological implications and potential effects on the gravitational wave observation are briefly discussed., Comment: 25 pages, 2 figures; v3: references are added

We revisit gravitational particle production from the Stokes phenomenon viewpoint, which helps us make a systematic way to understand asymptotic behavior of mode functions in time-dependent background. One of our purposes of this work is to make the method more practical for evaluation of non-perturbative particle production rate. In particular, with several examples of time-dependent backgrounds, we introduce some approximation methods that make the analysis more practical. Specifically, we consider particle production in simple expanding backgrounds, preheating after $R^2$ inflation, and a transition model with smoothly changing mass. As we find several technical issues in analyzing the Stokes phenomenon of each example, we discuss how to simplify the problems while showing the accuracy of analytic estimation under the approximations we make., Comment: 23 + 18 pages, 13 + 7 figures, [v2] Minor revision

We study M-theory compactified on twisted 7-tori with $G_2$-holonomy. The effective 4d supergravity has 7 chiral multiplets, each with a unit logarithmic K\"ahler potential. We propose octonion, Fano plane based superpotentials, codifying the error correcting Hamming (7,4) code. The corresponding 7-moduli models have Minkowski vacua with one flat direction. We also propose superpotentials based on octonions/error correcting codes for Minkowski vacua models with two flat directions. We update phenomenological $\alpha$-attractor models of inflation with $3\alpha=7,6,5,4,3,1$, based on inflation along these flat directions. These inflationary models reproduce the benchmark targets for detecting B-modes, predicting 7 different values of $r = 12\alpha/N_{e}^{2}$ in the range $10^{-2}\gtrsim r \gtrsim 10^{-3}$, to be explored by future cosmological observations., Comment: 63 pages, 25 figures, v2: comments added, typos fixed, v3: improved formulation presented in Sec.7 and refs added. The new formulation does not change inflationary predictions, but the potentials for decoupled heavy modes are simplified compared with the ones in the previous versions

We consider the renormalization in the pseudo-scalar inflation models with the gravitational Chern-Simons term. In this model, lepton asymmetry is generated from the chiral gravitational waves produced due to the Chern-Simons term through the gravitational chiral anomaly. However, it is known that the naive estimate of the expectation value of the gravitational Chern-Pontryagin density as well as the resultant lepton number density depend on the UV-cutoff scale, which raises a question on their validity. In this paper, we propose a way to renormalize the expectation value of the Chern-Pontryagin density to remove the UV-cutoff dependence. We also discuss the renormalized lepton number density when we adopt the minimal subtraction scheme and the viability of the gravitational leptogenesis scenario., Comment: 22 pages, 3 figures; v3: published version

We discuss particle production associated with vacuum decay, which changes the mass of a scalar field coupled to a background field which induces the decay. By utilizing the Stokes phenomenon, we can optimally track the time-evolution of mode function and hence calculate particle production properly. In particular, we use real time formalisms for vacuum decay in Minkowski and de Sitter spacetime together with the Stokes phenomenon method. For each case, we consider the flyover vacuum decay model and stochastic inflation, respectively. Within the real time formalism, the particle production can be viewed as that caused by nontrivial external fields. This gives us a novel perspective of the real time formalism of vacuum decay., Comment: 24 pages, 4 figures, [v2] Major revision, [v3] Published in PRD

We revisit the gravitational leptogenesis scenario in which the inflaton is coupled to gravity by the Chern-Simons term and the lepton asymmetry is generated through the gravitational anomaly in the lepton number current during inflation. We constrain the possible model parameter space by requiring the absence of ghost modes below the Planck scale, which would suggest the breakdown of the effective theory, and evaluate the net baryon asymmetry for various reheating processes. We find that the mechanism with these requirements is insufficient to explain the observed baryon asymmetry of the Universe for standard reheating scenarios. We show that, however, with the kination scenario realized in e.g. the k- and G-inflation models, a sufficient baryon asymmetry can be generated within a feasible range of the model parameters., Comment: 15 pages; v3: published version with minor revisions and references added

We construct the Horndeski Lagrangian within non-linearly realized supergravity. We will show that the bosonic part of the Horndeski Lagrangian can be realized. Gravitino naturally couples to Horndeski sector in a super-covariant way. Such gravitino couplings are also free from ghosts., Comment: 5 pages

We construct the simplest inflationary $\alpha$-attractor models in supergravity: it has only one scalar, the inflaton. There is no sinflaton since the inflaton belongs to an orthogonal nilpotent superfield where the sinflaton depends on fermion bilinears. When the local supersymmetry is gauge-fixed, these models have only one single real scalar (the inflaton), a graviton and a massive gravitino. The sinflaton, sgoldstino and inflatino are all absent from the physical spectrum in the unitary gauge. The orthogonality condition leads to the simplest K\"ahler potential for the inflaton, while preserving the Poincar\'e disk geometry of $\alpha$-attractors. The models are particularly simple in the framework of the $\overline {D3}$ induced geometric inflation., Comment: 12 pages

We revisit phenomenological as well as string-theoretical aspects of D-brane inflation cosmological models. Phenomenologically these models stand out on par with $\alpha$-attractors, as models with Planck-compatible values of $n_s$, moving down to the sweet spot in the data with decreasing value of $r$. On the formal side we present a new supersymmetric version of these models in the context of de Sitter supergravity with a nilpotent multiplet and volume modulus stabilization. The geometry of the nilpotent multiplet is evaluated in the framework of string theory., Comment: 29 pages, 8 figures

We constructed a model of natural inflation in the context of $\alpha$-attractor supergravity, in which both the dilaton field and the axion field are light during inflation, and the inflaton may be a combination of the two. The T-model version of this theory is defined on the Poincare disk with radius |Z| = 1. It describes a Mexican hat potential with the flat axion direction corresponding to a circle of radius |Z| < 1. The axion decay constant $f_{a}$ in this theory can be exponentially large because of the hyperbolic geometry of the Poincare disk. Depending on initial conditions, this model may describe $\alpha$-attractor inflation driven by the radial component of the inflaton field, natural inflation driven by the axion field, or a sequence of these two regimes. We also construct the E-model version of this theory, which has similar properties. In addition, we describe generalized $\alpha$-attractor models where the potential can be singular at the boundary of the moduli space, and show that they can provide a simple solution for the problem of initial conditions for the models with plateau potentials., Comment: 25 pages, 8 figures; v2: published version with references added and discussion extended

We present a class of supergravity $\alpha$-attractors with an approximate global U(1) symmetry corresponding to the axion direction. We also develop a multi-field generalization of these models and show that the $\alpha$-attractor models with U(1) symmetries have a dual description in terms of a two-form superfield coupled to a three-form superfield., Comment: 15pages, 3 figures, v2:comments, reference, and appendix added, v3:reference added, version published in JHEP

$f(R)$ supergravity is known to contain a ghost mode associated with higher-derivative terms if it contains $R^n$ with $n$ greater than two.We remove the ghost in $f(R)$ supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism~\cite{Fujimori:2016udq}. We show that the mechanism removes the ghost supermultiplet but also terms including $R^n$ with $n\geq3$, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential., Comment: 24 pages, v2: comments, references, new section added, version published in JHEP

Fibre inflation is a specific string theory construction based on the Large Volume Scenario that produces an inflationary plateau. We outline its relation to $\alpha$-attractor models for inflation, with the cosmological sector originating from certain string theory corrections leading to $\alpha=2$ and $\alpha=1/2$. Above a certain field range, the steepening effect of higher-order corrections leads first to the breakdown of single-field slow-roll and after that to the onset of 2-field dynamics: the overall volume of the extra dimensions starts to participate in the effective dynamics. Finally, we propose effective supergravity models of fibre inflation based on an ${\overline {D3}}$ uplift term with a nilpotent superfield. Specific moduli dependent $\overline {D3}$ induced geometries lead to cosmological fibre models but have in addition a de Sitter minimum exit. These supergravity models motivated by fibre inflation are relatively simple, stabilize the axions and disentangle the Hubble parameter from supersymmetry breaking., Comment: 24pages, 5 figures, v2: discussion on stringy corrections re-ordered and corrected

Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The K\"ahler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and gravitino mass. We illustrate it by providing generalized versions of polynomial chaotic inflation, T- and E-models of $\alpha$-attractor type, disk merger. We also describe a multi-stage cosmological attractor regime, which we call cascade inflation., Comment: 22 pages, 7 figures, v2: typos corrected, v3: references added

Extending the work of Ferrara and one of the authors, we present dynamical cosmological models of $\alpha$-attractors with plateau potentials for $3\alpha=1,2,3,4,5,6,7$. These models are motivated by geometric properties of maximally supersymmetric theories: M-theory, superstring theory, and maximal $N = 8$ supergravity. After a consistent truncation of maximal to minimal supersymmetry in a seven-disk geometry, we perform a two-step procedure: 1) we introduce a superpotential, which stabilizes the moduli of the seven-disk geometry in a supersymmetric minimum, 2) we add a cosmological sector with a nilpotent stabilizer, which breaks supersymmetry spontaneously and leads to a desirable class of cosmological attractor models. These models with $n_s$ consistent with observational data, and with tensor-to-scalar ratio $r \approx 10^{-2}- 10^{-3}$, provide natural targets for future B-mode searches. We relate the issue of stability of inflationary trajectories in these models to tessellations of a hyperbolic geometry., Comment: 33 pages, 12 figures

We investigate the inflation model with a massive vector multiplet in a case that the action of the vector multiplet is extended to the Dirac-Born-Infeld (DBI) type one. We show the massive DBI action in 4 dimensional ${\cal N}=1$ supergravity, and find that the higher order corrections associated with the DBI-extension make the scalar potential flat with a simple choice of the matter couplings. We also discuss the DBI-extension of the new minimal Starobinsky model, and find that it is dual to a special class of the massive DBI action., Comment: 10 pages, 3 figures, v2: a reference added, v3: references and comments added

We show the effects of supersymmetric higher derivative terms on inflation models in supergravity. The results show that such terms generically modify the effective kinetic coefficient of the inflaton during inflation if the cut off scale of the higher derivative operators is sufficiently small. In such a case, the $\eta$-problem in supergravity does not occur, and we find that the effective potential of the inflaton generically becomes a power type potential with a power smaller than two., Comment: 16 pages, v2: references and comments added, some typos corrected

We study reheating processes and its cosmological consequences in the Starobinsky model embedded in the old-minimal supergravity. First, we consider minimal coupling between the gravity and matter sectors in the higher curvature theory, and transform it to the equivalent standard supergravity coupled to additional matter superfields. We then discuss characteristic decay modes of the inflaton and the reheating temperature $T_{\rm R}$. Considering a simple model of supersymmetry breaking sector, we estimate gravitino abundance from inflaton decay, and obtain limits on the masses of gravitino and supersymmetry breaking field. We find $T_{\rm R}\simeq 1.0\times10^9$ GeV and the allowed range of gravitino mass as $10^4$ GeV $\lesssim m_{3/2} \lesssim 10^5$ GeV, assuming anomaly-induced decay into the gauge sector as the dominant decay channel., Comment: 24 pages, 1 figure, appendix added for clarification, typos fixed, results unchanged, version accepted in JHEP