We study initial conditions for inflation in scenarios where the inflaton potential has a plateau shape. Such models are those most favored by Planck data and can be obtained in a large number of model classes. As a representative example, we consider Higgs inflation with and without an $R^2$ term in the context of Palatini gravity. We show that inflation with a large number of e-folds generically occurs in a large part of the parameter space without any fine-tuning of parameters even when the scale of inflation and the inflaton field value during inflation are much smaller than the Planck scale. We discuss consequences for detection of primordial gravitational waves and spectral tilt of curvature perturbations, as well as the recently proposed "Trans-Planckian Censorship" conjecture.
We explored a Higgs inflationary scenario in the SUGRA embedding of the MSSM in Einstein frame where the inflaton is contained in the $SU(2)$ Higgs doublet. We include all higher order non-renormalizable terms to the MSSM superpotential and an appropriate Kähler potential which can provide slow-roll inflaton potential in the $D-$flat direction. In this model, a plateau-like inflation potential can be obtained if the imaginary part of the neutral Higgs acts as the inflaton. The inflationary predictions of this model are consistent with the latest CMB observations. The model represents a success…
We describe how monomial chaotic inflation becomes compatible with the latest CMB data thanks to radiative corrections producing a plateau. The interactions of the inflation with other fields, required for reheating, can flatten the potential and moderate the production of primordial gravitational waves, keeping these below the current upper bound. We show that the appearance of a plateau requires that the inflaton couples to fermions and to another scalar or a gauge group. We give concrete examples of minimal particle physics models leading to plateaus for quadratic and quartic chaotic inflat…
Inflation with plateau potentials give the best fit to the CMB observables as they predict tensor to scalar ratio stringently bounded by the observations from Planck and BICEP2/Keck. In supergravity models it is possible to obtain plateau potentials for scalar fields in the Einstein frame which can serve as the inflation potential by considering higher dimensional Planck suppressed operators and by the choice of non-canonical Kähler potentials. We construct a plateau inflation model in MSSM where the inflation occurs along a sneutrino-Higgs flat direction. A hidden sector Polonyi field is used…
Plateau inflation is an experimentally consistent framework in which the scale of inflation can be kept relatively low. Close to the edge of the plateau, scalar perturbations are subject to a strong tachyonic instability. Tachyonic preheating is realized when, after inflation, the oscillating inflaton repeatedly re-enters the plateau. We develop the analytic theory of this process and expand the linear approach by including backreaction between the coherent background and growing perturbations. For a family of plateau models, the analytic predictions are confronted with numerical estimates. Ou…
In the absence of CMB precision measurements, a Taylor expansion has often been invoked to parametrize the Hubble flow function during inflation. The standard "horizon flow" procedure implicitly relies on this assumption. However, the recent Planck results indicate a strong preference for plateau inflation, which suggests the use of Padé approximants instead. We propose a novel method that provides analytic solutions of the flow equations for a given parametrization of the Hubble function. This method is illustrated in the Taylor and Padé cases, for low order expansions. We then present the re…
Within the $α$-attractors framework we investigate scalar potentials with the same pole as the one featured in the kinetic term. We show that, in field space, this leads to directions without a plateau. Using this, we present a proposal, which manages to overcome the initial conditions problem of inflation with a plateau. An earlier period of proto-inflation, beginning at Planck scale, accounts for the Universe expansion and arranges the required initial conditions for inflation on the plateau to commence. We show that, if proto-inflation is power-law, it does not suffer from a sub-Planckian e…
We investigate a scale-invariant $B-L$ scenario where the Standard Model (SM) is supplemented with a dark scalar $ϕ$ which has gauge \& Yukawa interactions, with the couplings $g_{BL}$ and $y$, respectively, leading to radiative plateau inflation at scale $ϕ=M$ in the ultraviolet (UV), while dynamically generating the Electroweak and Seesaw scales \textit{á lá} Coleman-Weinberg in the infrared (IR). This is particularly achieved by implementing threshold corrections at an energy scale $μ_T$ arising due to the presence of vector-like fermions. We show that implementing the inflationary observab…
In the recent time, inflationary cosmology is facing an existential crisis due to the proposed Swampland criterion which aims to evade any (meta-)stable de Sitter construction within the String landscape. It is been realised that a single field slow roll inflation is inconsistent with the Swampland criterion unless the inflationary model in realised in some non standard scenario such as Warm inflation or the Braneworld scenario. In \cite{Dimopoulos}, Dimopoulos and Owen introduced a new class of model of inflation dubbed as the power law plateau inflation in the standard cold inflationary scen…
We study radiative plateau-like inflation \& Z$_{BL}$-portal freeze-in fermionic dark matter (DM) in a minimal B-L extended model. The U(1)$_{B-L}$ Higgs, responsible for heavy neutrino masses, also drives inflation in the early universe, thanks to radiative corrections from the heavy neutrinos \& the Z$_{BL}$ gauge boson. In our benchmark choice for the U(1)$_{B-L}$ gauge coupling $g_{B-L}\sim10^{-4}$, a light Z$_{BL}$ boson can be explored by current and future lifetime frontier experiments, such as FASER and FASER 2 at the LHC, SHiP, Belle II and LHCb. For the benchmark, the Hubble scale of…
Isocurvature-Free QCD Axion Dark Matter from Inflaton-Driven Early QCD: the Necessity of Inflationary Plateaus
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Stockholm University（斯德哥尔摩大学）；Nordic Institute for Theoretical Physics (NORDITA)（北欧理论物理研究所）；Harvard University（哈佛大学）；University of Utah（犹他大学）
Controlled Penumbral Inflation from Monodromic Valleys
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Physics, Henan Normal University（河南师范大学物理学院）
With the growing consensus on simple power law inflation models not being favored by the PLANCK observations, dynamics for the non-standard inflation gain significant interest in the recent past. In this paper, we analyze in detail a class of supergravity inspired phenomenological inflationary models with non-polynomial potential based on Maity (Nucl.Phys. B919 (2017) 560), and compare the model predictions with the currently most favored Starobinsky and its generalized $α$-attractor models in the ($n_s$ , $r$) plane constrained by PLANCK. Importantly for a wide range of parameter space, our m…
In this paper we investigate the induced inflation with two flat regions: one Starobinsky-like plateau in big field regime and one shorter plateau around the saddle point of the Einstein frame potential. This multi-phase inflationary scenario can be used to solve the problem of classical cosmology. The inflation at the saddle-point plateau is consistent with the data and can have arbitrarily low scale. The results can be useful in the context of the Higgs-Axion relaxation and in a certain limit they are equivalent to the $α$-attractors.
We study a new class of inflation model parametrized by the Hubble radius, such that $aH\propto \exp(-kϕ^n)$. These potentials are plateau-like, and reduce to the power-law potentials in the simplest case $n=2$. We investigate the range of model parameters that is consistent with current observational constraints on the scalar spectral index and the tensor-to-scalar ratio. The amplitude of primordial gravitational waves in these models is shown to be accessible by future laser interferometers such as DECIGO. We also demonstrate how these observables are affected by the temperature and equation…
We study preheating in the Palatini formalism with a quadratic inflaton potential and an added $αR^2$ term. In such models, the oscillating inflaton field repeatedly returns to the plateau of the Einstein frame potential, on which the tachyonic instability fragments the inflaton condensate within less than an e-fold. We find that tachyonic preheating takes place when $α\gtrsim 10^{13}$ and that the energy density of the fragmented field grows with the rate $Γ/H \approx 0.011 \times α^{0.31}$. The model extends the family of plateau models with similar preheating behaviour. Although it contains…
We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation…
We discuss two-stage dilaton-axion inflation models [1] and describe $α$-attractor models with either exponential or polynomial approach to the plateau. We implement one of the models of primordial black hole production proposed in [2] in the $α$-attractor context, and develop its supergravity version. The predictions of this model following from its polynomial attractor properties are: $n_s$ and $r$ are $α$-independent, $r$ depends on the mass parameter $μ$ defining the approach to the plateau. The tachyonic instability at the transition point between the two stages of inflation is proportion…
We have studied the preheating phase for a class of plateau inflationary model considering the four-legs interaction term $(1/2)g^2ϕ^2χ^2$ between the inflaton $(ϕ)$ and reheating field $(χ)$. We specifically focus on the effects of a parameter $ϕ_*$ that controls inflationary dynamics and the shape of the inflaton potential. For $ϕ_* < M_p$, the departure of the inflaton potential from the usual power-law behavior $ϕ^n$ significantly modifies the microscopic behavior of the preheating dynamics. We analyze and compare the efficiency of production, thermalization and the final equation of state…
Recent results from the Planck satellite combined with earlier observations from WMAP, ACT, SPT and other experiments eliminate a wide spectrum of more complex inflationary models and favor models with a single scalar field, as reported by the Planck Collaboration. More important, though, is that all the simplest inflaton models are disfavored statistically relative to those with plateau-like potentials. We discuss how a restriction to plateau-like models has three independent serious drawbacks: it exacerbates both the initial conditions problem and the multiverse-unpredictability problem and …
An appealing explanation for the Planck data is provided by inflationary models with a singular non-canonical kinetic term: a Laurent expansion of the kinetic function translates into a potential with a nearly shift-symmetric plateau in canonical fields. The shift symmetry can be broken at large field values by including higher-order poles, which need to be hierarchically suppressed in order not to spoil the inflationary plateau. The herefrom resulting corrections to the inflationary dynamics and predictions are shown to be universal at lowest order and possibly to induce power loss at large a…
We consider hybrid inflation for small couplings of the inflaton to matter such that the critical value of the inflaton field exceeds the Planck mass. It has recently been shown that inflation then continues at subcritical inflaton field values where quantum fluctuations generate an effective inflaton mass. The effective inflaton potential interpolates between a quadratic potential at small field values and a plateau at large field values. An analysis of the allowed parameter space leads to predictions for the scalar spectral index n_s and the tensor-to-scalar ratio r similar to those of natur…
We study the problem of initial conditions for slow-roll inflation along a plateau-like scalar potential within the framework of fluctuation-dissipation dynamics. We consider, in particular, that inflation was preceded by a radiation-dominated epoch where the inflaton is coupled to light degrees of freedom and may reach a near-equilibrium state. We show that the homogeneous field component can be sufficiently localized at the origin to trigger a period of slow-roll if the interactions between the inflaton and the thermal degrees of freedom are sufficiently strong and argue that this does not n…
A reformulation of inflationary model analyses appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, power-law inflation, or monomial/polynomial chaotic inflation. We demonstrate attractor beh…
We propose a novel scenario of inflation, in which the inflaton is identified as the lightest mode of an angular field in a compactified fifth dimension. The periodic effective potential exhibits exponentially flat plateaus, so that a sub-Planckian field excursion without hilltop initial conditions is naturally realized. We can obtain consistent predictions with observations on the spectral index and the tensor-to-scalar ratio.
We study preheating in plateau inflation in the Palatini formulation of general relativity, in a special case that resembles Higgs inflation. It was previously shown that the oscillating inflaton field returns to the plateau repeatedly in this model, and this leads to tachyonic production of inflaton particles. We show that a minimally coupled spectator scalar field can be produced even more efficiently by a similar mechanism. The mechanism is purely gravitational, and the scalar field mass can be of order $10^{13}$ GeV, larger than the Hubble scale by many orders of magnitude, making this a c…
We discuss the impact of the preheating stage in radiative corrections due to interaction of the inflaton to fermions to $ϕ^4$ inflation with non-minimal coupling in Palatini formulation. In Palatini inflation with large non-minimal coupling the field is allow to return to the plateau region during the reheating stage, so the average equation of state per oscillations is closer to $-1$ than to $1/3$. The incursion in the plateau leads, however, to a highly efficient tachyonic instability able to reheat the Universe in less than one e-fold. By taking into account prescription II discussed in th…
I describe the first model of chaotic inflation in supergravity, which was proposed by Goncharov and the present author in 1983. The inflaton potential of this model has a plateau-type behavior $V_{0} (1- {8\over 3}\, e^{-\sqrt 6 |ϕ|})$ at large values of the inflaton field. This model predicts $n_{s} = 1-{2\over N} \approx 0.967$ and $r = {4\over 3 N^{2}} \approx 4 \times 10^{-4}$, in good agreement with the Planck data. I propose a slight generalization of this model, which allows to describe not only inflation but also dark energy and supersymmetry breaking.
We propose yet another solution to the initial condition problem of inflation associated with homogeneity beyond the horizon at the onset of inflation, in cases where inflation is preceded by a radiation era. One may argue that causality will allow for smoothness over the causal horizon scale $H^{-1}$, but for thermal inflationary scenarios, the background inflaton field will only be correlated over the thermal correlation length $ζ\sim T^{-1}$ which is much smaller than $H^{-1}$. We argue, with examples, that if the number of relativistic degrees of freedom in the pre-inflationary era is very…
We investigate the possibility of using the only known fundamental scalar, the Higgs, as an inflaton with minimal coupling to gravity. The peculiar appearance of a plateau or a false vacuum in the renormalised effective scalar potential suggests that the Higgs might drive inflation. For the case of a false vacuum we use an additional singlet scalar field, motivated by the strong CP problem, and its coupling to the Higgs to lift the barrier allowing for a graceful exit from inflation by mimicking hybrid inflation. We find that this scenario is incompatible with current measurements of the Higgs…
We study the effects of the non-attractor initial conditions for the canonical single-field inflation. The non-attractor stage can last only several $e$-folding numbers, and should be followed by hilltop inflation. This two-stage evolution leads to large scale suppression in the primordial power spectrum, which is favored by recent observations. Moreover we give a detailed calculation of primordial non-Guassianity due to the "from non-attractor to slow-roll" transition, and find step features in the local and equilateral shapes. We conclude that a plateau-like inflaton potential with an initia…
The observational status of inflation after the Planck 2013 and 2015 results and the BICEP2/Keck Array and Planck joint analysis is discussed. These pedagogical lecture notes are intended to serve as a technical guide filling the gap between the theoretical articles on inflation and the experimental works on astrophysical and cosmological data. After a short discussion of the central tenets at the basis of inflation (negative self-gravitating pressure) and its experimental verifications, it reviews how the most recent Cosmic Microwave Background (CMB) anisotropy measurements constrain cosmic i…
We consider a broad class of inflationary models that arise naturally in supergravity. They are defined in terms of a parameter $α$ that determines the curvature and cutoff of these models. As a function of this parameter, we exhibit that the inflationary predictions generically interpolate between two attractor points. At small cutoff $α$, the resulting inflationary model is of plateau-type with $n_s = 1 - 2 / N$ and $r = 12 α/ N^2$. For $α= 1$, these predictions coincide with predictions of the Starobinsky model and Higgs inflation. In contrast, for large cutoff $α$, the theory asymptotes to…
We examine the oscillon formation in a recently proposed inflation model of the pure natural inflation, where the inflaton is an axion that couples to a strongly-coupled pure Yang-Mills theory. The plateau of the inflaton potential, which is favored by recent observations, drives the fragmentation of the inflaton and can produce spatially localized oscillons. We find that the oscillons are formed for F<~ O(0.1) M_{Pl}, with F the effective decay constant of the model. We also comment on observational implications of the oscillons.
There is a wide consensus on the correct dynamics of the background in loop quantum cosmology. In this article we make a systematic investigation of the duration of inflation by varying what we think to be the most important "unknowns" of the model: the way to set initial conditions, the amount of shear at the bounce and the shape of the inflaton potential.
We use the 3+1 formalism of numerical relativity to investigate the robustness of Starobinsky and Higgs inflation to inhomogeneous initial conditions, in the form of either field gradient or kinetic energy density. Sub-Hubble and Hubble-sized fluctuations generically lead to inflation after an oscillatory phase between gradient and kinetic energies. Hubble-sized inhomogeneities also produce contracting regions that may end up forming primordial black holes, subsequently diluted by inflation. We analyse the dynamics of the preinflation era and the generation of vector and tensor fluctuations. O…
In the no-scale supergravity with Type-I Seesaw model of Non-minimal supersymmetric standard model (NMSSM), we have analysed inflation, reheating and leptogenesis. A no-scale supergravity realization of Starobinsky model of inflation in simple Wess-Zumino model have been shown earlier by Ellis et al. Here we show a no-scale supergravity realization of Starobinsky model of inflation in Type-I Seesaw framework of NMSSM. In this framework an appropriate choice of no-scale Kähler potential results in Starobinsky like plateau inflation along a Higgs-sneutrino $D$-flat direction consistent with the …
A classical evolution in chaotic inflationary models starts at high energy densities with semi-classical initial conditions presumably consistent with universal quantum nature of all the fundamental forces. That is each quantum contributes the same amount to the energy density. We point out the upper limit on this amount inherent in this approach, so that all the quanta are inside the weak-coupling domain. We discuss this issue in realistic models with modified gravity, $R^2$- and Higgs-inflations, emphasizing the specific change of the initial conditions with metric frame, while all the quant…
I give a brief review of the status of research on the nature of initial conditions required to obtain a period of cosmological inflation. It is shown that there is good evidence that in the case of large field models, the inflationary slow-roll trajectory is a local attractor in initial condition space, whereas it is not in the case of small field models.
Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the i…
We make a case for setting initial conditions for inflation at the Planck epoch in the kinetically dominated regime. For inflationary potentials with a plateau or a hill, i.e. potentials that are bounded from above within a certain region of interest, we cannot claim complete ignorance of the energy distribution between kinetic and potential energy, and equipartition of energy at the Planck epoch becomes questionable. We analyse different classes of potentials in phase-space and quantify the fraction of the Planck surface that is kinetically dominated. For the small amplitudes of the potential…
We study a new model of quintessential inflation which is inspired by supergravity and string theory. The model features a kinetic pole, which gives rise to the inflationary plateau, and a runaway quintessential tail. We envisage a coupling between the inflaton and the Peccei-Quinn (PQ) field which terminates the roll of the runaway inflaton and traps the latter at an enhanced symmetry point (ESP), thereby breaking the PQ symmetry. The kinetic density of the inflaton is transferred to the newly created thermal bath of the hot big bang due to the decay of PQ particles. The model successfully ac…
We investigate whether Higgs inflation can occur in the Standard Model starting from natural initial conditions or not. The Higgs has a non-minimal coupling to the Ricci scalar. We confine our attention to the regime where quantum Einstein gravity effects are small in order to have results that are independent of the ultraviolet completion of gravity. At the classical level we find no tuning is required to have a successful Higgs inflation, provided the initial homogeneity condition is satisfied. On the other hand, at the quantum level we obtain that the renormalization for large non-minimal c…
A new family of inflation models is introduced and studied. The models are characterised by a scalar potential which, far from the origin, approaches an inflationary plateau in a power-law manner, while near the origin becomes monomial, as in chaotic inflation. The models are obtained in the context of global supersymmetry starting with a superpotential, which interpolates from a generalised monomial to an O'Raifearteagh form for small to large values of the inflaton field respectively. It is demonstrated that the observables obtained, such as the scalar spectral index, its running and the ten…
Inflation due to a non-minimally coupled scalar field with a large non-minimal coupling, as first proposed by Salopek, Bardeen and Bond (SBB), is in good agreement with the observed value of the spectral index and constraints on the tensor-to-scalar ratio. Here we explore the possibility that SBB inflation represents the late stage of a Universe which emerges from an early contracting era. We present a model in which the Universe smoothly transitions from an anamorphic contracting era to late-time SBB inflation without encountering a singular bounce. This corresponds to a continuous expansion …
We explore the possibility of a single field quasi-de Sitter inflationary model with general initial state for primordial fluctuations. In this paper, first we compute the power spectrum and the bispectrum of scalar perturbations with coherent state as the initial state. We find that a large class of coherent states are indistinguishable from the Bunch-Davies vacuum state and hence consistent with the current observations. In case of a more general initial state built over Bunch-Davies vacuum state, we show that the constraints on the initial state from observed power spectrum and local bispec…
Minimal chaotic models of D-term inflation predicts too large primordial tensor perturbations. Although it can be made consistent with observations utilizing higher order terms in the Kähler potential, expansion is not controlled in the absence of symmetries. We comprehensively study the conditions of Kähler potential for D-term plateau-type potentials and discuss its symmetry. They include the alpha-attractor model with a massive vector supermultiplet and its generalization leading to pole inflation of arbitrary order. We extend the models so that it can describe Coulomb phase, gauge anomaly …
The temperature and polarization anisotropies of the Cosmic Microwave Background are analyzed under the hypothesis that the same inflationary seed accounting for protogalactic magnetism also affects the Einstein-Boltzmann hierarchy whose initial conditions are assigned for typical correlation scales larger than the Hubble radius after matter-radiation equality but before decoupling. Since the primordial gauge spectrum depends on a combination of pivotal parameters of the concordance model, the angular power spectra of the temperature and of the polarization are computed, for the first time, in…
