We propose a qualitatively new mechanism for generating cosmological fluctuations from inflation. The non-equilibrium excitation of interacting scalar fields often evolves into infra-red (IR) and ultra-violet (UV) cascading, resulting in an intermediate scaling regime. We observe elements of this phenomenon in a simple model with inflaton ϕand iso-inflaton χfields interacting during inflation via the coupling g^2 (ϕ-ϕ_0)^2 χ^2. Iso-inflaton particles are created during inflation when they become instantaneously massless at ϕ=ϕ_0, with occupation numbers not exceeding unity. We point out that very quickly the produced χparticles become heavy and their multiple re-scatterings off the homogeneous condensate ϕ(t) generates bremschtrahlung radiation of light inflaton IR fluctuations with high occupation numbers. The subsequent evolution of these IR fluctuations is qualitatively similar to that of the usual inflationary fluctuations, but their initial amplitude is different. The IR cascading generates a bump-shaped contribution to the cosmological curvature fluctuations, which can even dominate over the usual fluctuations for g^2>0.06. The IR cascading curvature fluctuations are significantly non-gaussian and the strength and location of the bump are model-dependent, through g^2 and ϕ_0. The effect from IR cascading fluctuations is significantly larger than that from the momentary slowing-down of ϕ(t). With a sequence of such bursts of particle production, the superposition of the bumps can lead to a new broad band non-gaussian component of cosmological fluctuations added to the usual fluctuations. Such a sequence of particle creation events can, but need not, lead to trapped inflation.
Interactions between the inflaton and any additional fields can lead to isolated bursts of particle production during inflation (for example from parametric resonance or a phase transition). Inflationary particle production leaves localized features in the spectrum and bispectrum of the observable cosmological fluctuations, via the Infra-Red (IR) cascading mechanism. We focus on a simple prototype interaction g^2 (ϕ-ϕ_0)^2χ^2 between the inflaton, ϕ, and iso-inflaton, χ; extending previous work on this model in two directions. First, we quantify the magnitude of the produced nongaussianity by …
We propose a model for early universe cosmology without the need for fundamental scalar fields. Cosmic acceleration and phenomenologically viable reheating of the universe results from a series of energy transitions, where during each transition vacuum energy is converted to thermal radiation. We show that this `cascading universe' can lead to successful generation of adiabatic density fluctuations and an observable gravity wave spectrum in some cases, where in the simplest case it reproduces a spectrum similar to slow-roll models of inflation. We also find the model provides a reasonable rehe…
Inflationary observables, like the power spectrum, computed at one- and higher-order loop level seem to be plagued by large infra-red corrections. In this short note, we point out that these large infra-red corrections appear only in quantities which are not directly observable. This is in agreement with general expectations concerning infra-red effects.
Self-energies of a minimally coupled scalar field with quartic and trilinear interactions are calculated in a de Sitter background, using a position space propagator. For quartic interactions, we recover earlier results for the seagull diagram, namely that it contributes an effective mass for the scalar field at leading order in the infrared enhancement in a steady-state de Sitter background. We further show that the sunset diagram also contributes to this effective mass and argue that these two contributions are sufficient in order to determine a self-consistent dynamical mass. In addition, t…
We examine the emergence of the infrared logarithms in the cosmological perturbation theory applied to the minisuperspace scalar slow-roll inflation. Not surprisingly, in the single scalar field model the curvature perturbation $ζ$ is conserved and no $\ln a_B$ behavior appears, where $a_B(t)$ is the background scale factor of the universe. On the other hand, in the presence of a spectator scalar the $n$'th order perturbation theory gives an $(\ln a_B)^n$ correction to $ζ$. However, a nonperturbative estimate shows that $ζ$ actually becomes the sum of a constant and a mildly evolving $\ln a_B$…
It has been an issue of debate whether the inflationary infrared(IR) divergences are physical or not. Our claim is that, at least, in single-field models, the answer is "No," and that the spurious IR divergence is originating from the careless treatment of the gauge modes. In our previous work we have explicitly shown that the IR divergence is absent in the genuine gauge-invariant quantity at the leading order in the slow-roll approximation. We extend our argument to include higher-order slow-roll corrections and the contributions from the gravitational waves. The key issue is to assure the ga…
We have previously derived the effect of soft graviton modes on the quantum state of de Sitter using spontaneously broken asymptotic symmetries. In the present paper we reinterpret this effect in terms of particle production and relate the quantum states with and without soft modes by means of Bogoliubov transformations. This also enables us to address the much discussed issues regarding the observability of infrared effects in de Sitter from a new perspective. While it is commonly agreed that infrared effects are not visible to a single sub-horizon observer at late times, we argue that the qu…
If the large scale anomalies in the temperature power spectrum of the cosmic microwave background are of primordial origin, they may herald modifications to the slow roll inflationary paradigm on the largest scales. We study the possibility that the origin of the large scale power suppression is a modification of initial conditions during slow roll as a result of a pre-slow roll phase during which the inflaton evolves rapidly. This stage is manifest in a potential in the equations for the Gaussian fluctuations during slow roll and modify the power spectra of scalar perturbations via an initial…
During de Sitter inflation massless particles of minimally coupled scalar fields acquire a mass and a decay width thereby becoming \emph{quasiparticles}. For bare massless particles non-perturbative infrared radiative corrections lead to a self-consistent generation of mass, for a quartic self interaction $M \propto λ^{1/4} H$, and for a cubic self-interaction the mass is induced by the formation of a non-perturbative \emph{condensate} leading to $M \propto λ^{1/3} H^{2/3}$. These radiatively generated masses restore de Sitter invariance and result in anomalous scaling dimensions of superhoriz…
We show non-perturbatively that the power spectrum of a self-interacting scalar field in de Sitter space-time is strongly suppressed on large scales. The cut-off scale depends on the strength of the self-coupling, the number of e-folds of quasi-de Sitter evolution, and its expansion rate. As a consequence, the two-point correlation function of field fluctuations is free from infra-red divergencies.
We study reheating in some one and two field realizations of {\it Fibre Inflation}. We find that reheating begins with a phase of preheating in which long wavelength fluctuation modes are excited. In two field models there is a danger that the parametric amplification of infrared fluctuations in the second scalar field - associated with an entropy mode - might induce an instability of the curvature fluctuations. We show that, at least in the models we consider, the entropy mode has a sufficiently large mass to prevent this instability. Hence, from the point of view of reheating the models we c…
Based on the stochastic gravity, we study the loop corrections to the scalar and tensor perturbations during inflation. Since the loop corrections to scalar perturbations suffer infrared (IR) divergence, we consider the IR regularization to obtain the finite value. We find that the loop corrections to the scalar perturbations are amplified by the e-folding; in other words there appear the logarithmic correction, just as discussed by M.Sloth et al. On the other hand, we find that the tensor perturbations do not suffer from infrared divergence.
We place observational likelihood constraints on braneworld and non-commutative inflation for a number of inflaton potentials, using Planck, WMAP polarization and BAO data. Both braneworld and non-commutative scenarios of the kind considered here are limited by the most recent data even more severely than standard general-relativity models. At more than 95 % confidence level, the monomial potential $V(ϕ) \propto ϕ^p$ is ruled out for $p \geq 2$ in the Randall--Sundrum (RS) braneworld cosmology and, for $p>0$, also in the high-curvature limit of the Gauss--Bonnet (GB) braneworld and in the infr…
We consider k-inflation models where the action is a non-linear function of both the inflaton and the inflaton kinetic term. We focus on a scalar-tensor extension of k-inflation coupled to matter for which we derive a modified Mukhanov-Sasaki equation for the curvature perturbation. Significant corrections to the power spectrum appear when the coupling function changes abruptly along the inflationary trajectory. This gives rise to a modification of Starobinsky's model of perturbation features. We analyse the way the power spectrum is altered in the infrared when such features are present.
We study the constraints imposed by the requirement of Asymptotic Safety on a class of inflationary models with an inflaton field non-minimally coupled to the Ricci scalar. The critical surface in the space of theories is determined by the improved renormalization group flow which takes into account quantum corrections beyond the one loop approximation. The combination of constraints deriving from Planck observations and those from theory puts severe bounds on the values of the parameters of the model and predicts a quite large tensor to scalar ratio. We finally comment on the dependence of th…
We study a class of non-local, purely gravitational models which have the correct structure to reproduce the leading infrared logarithms of quantum gravitational back-reaction during the inflationary regime. These models end inflation in a distinctive phase of oscillations with slight and short violations of the weak energy condition and should, when coupled to matter, lead to rapid reheating. By elaborating this class of models we exhibit one that has the same behaviour during inflation, goes quiescent until the onset of matter domination, and induces a small, positive cosmological constant o…
It is well known that the correlation functions of a scalar field in a quasi-de Sitter space exhibit at the loop level cumulative infra-red effects proportional to the total number of e-foldings of inflation. Using the in-in formalism, we explore the behavior of these infra-red effects in the large N limit of an O(N) invariant scalar field theory with quartic self-interactions. By resumming all higher-order loop diagrams non-perturbatively, we show that the connected four-point correlation function, which is a signal of non-Gaussianity, is non-perturbatively enhanced with respect to its tree-l…
Ward Identity Constraints on Loop Corrections in Non-Attractor Inflation
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 Science, Jiangsu University of Science and Technology（江苏科技大学理学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学学院）
We investigate particle production near extra species loci (ESL) in a higher dimensional field space and derive a speed limit in moduli space at weak coupling. This terminal velocity is set by the characteristic ESL-separation and the coupling of the extra degrees of freedom to the moduli, but it is independent of the moduli's potential if the dimensionality of the field space is considerably larger than the dimensionality of the loci, D >> d. Once the terminal velocity is approached, particles are produced at a plethora of nearby ESLs, preventing a further increase in speed via their backreac…
We consider a set of scalar fields, consisting of a single flat direction and one or several non-flat directions. We take our cue from the MSSM, considering separately D-flat and F-flat directions, but our results apply to any supersymmetric scenario containing flat directions. We study the field fluctuations during pure de Sitter Inflation, following the evolution of the infrared modes by numerically solving the appropriate Langevin equations. We demonstrate that for the Standard Model U(1), SU(2) or SU(3) gauge couplings, as well as for large enough Yukawa couplings, the fluctuations along t…
We propose one way to regularize the fluctuations generated during inflation, whose infrared (IR) corrections diverge logarithmically. In the case of a single field inflation model, recently, we proposed one solution to the IR divergence problem. There, we introduced new perturbative variables which better mimic actual observable fluctuations, and proved the regularity of correlation functions with respect to these variables. In this paper, we extend our previous discussions to a multi field inflation model. We show that, as long as we consider the case that the non-linear interaction acts for…
During inflationary preheating, the energy stored in the inflaton field is rapidly converted into excitations of other entropy fields. This stage is characterized by exponential particle production due to parametric resonance and is notoriously difficult to analyze using analytic methods. We develop a detailed numerical simulation to investigate inflationary preheating when the potential of the inflaton is a power-law function with arbitrary power index. To achieve a successful graceful exit from a primordial inflationary phase to a smooth, oscillatory phase during preheating, we assume the in…
Fixing the Renormalization of Inflationary Loops via Ward Identities
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 Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础科学与数学学院）
We review some perturbative results obtained in quantum gravity in an accelerating cosmological background. We then describe a class of non-local, purely gravitational models which have the correct structure to reproduce the leading infrared logarithms of quantum gravitational back-reaction during the inflationary regime. These models end inflation in a distinctive phase of oscillations with slight and short violations of the weak energy condition and should, when coupled to matter, lead to rapid reheating. By elaborating this class of models we exhibit one that has the same behaviour during i…
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $ε$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $ξ$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $…
We revisit the scenario where inflation is preceded by a radiation era by considering that the inflaton too could have been in thermal equilibrium early in the radiation era. Hence we take into account not only the effect of a pre-inflationary era on the inflaton mode functions but also that of a frozen thermal distribution of inflaton quanta. We initially discuss in detail the issues relevant to our scenario of a pre-inflationary radiation dominated era and then obtain the scalar power spectrum for this scenario. We find that the power spectrum is free from infrared divergences. We then use t…
We study the non-Gaussianity in the simplest infrared (IR) model of the DBI inflation. We show that the non-Gaussianity in such a model is compatible with the current observational bound, and is within the sensitivity of future experiments. We also discuss the scale dependence of the non-Gaussianity. In the DBI inflation, such a feature can be used as a probe to the properties of the background geometry of the extra dimensions or internal space.
We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) local gauge-invariant observables such as the linearised Weyl tensor, which have better infrared properties than the graviton and inflaton fields. Special cases include the equivalence between the compactly supported gauge-invariant graviton observabl…
It is known that infrared (IR) quantum fluctuations in de Sitter space could break the de Sitter symmetry and generate time dependent observable effects. In this paper, we consider a dilaton-gravity theory. We find that gravitational IR effects lead to a time dependent shift on the vev of the dilaton and results in a screening (temporal) of the cosmological constant/Hubble parameter. In the Einstein frame, the effect is exponentiated and can give rises to a much more notable amount of screening. Taking the dilaton as inflaton, we obtain an inflationary expansion of the slow roll kind. This inf…
The wave function for the matter field fluctuations in the infrared sector is studied within the framework of inflationary cosmology. These fluctuations are described by a coarse-grained field which takes into account only the modes with wavelength much bigger than the size of the Hubble horizon. The case of a power-law expanding universe is considered and it is found that the relevant phase-space remains coherent under certain circumstances. In this case the classical stochastic treatment for matter field fluctuations is not valid, however, for $p > 4.6$, the system loses its coherence and a …
Due to the tremendous red-shift that occurs during the inflationary epoch in the early universe, it has been realized that trans-Planckian physics may manifest itself at energies much lower than the Planck energy. The presence of a fundamental scale suggests that local Lorentz invariance may be violated at sufficiently high energies. Motivated by this possibility, recently, different models that violate Lorentz invariance locally have been used to evaluate the trans-Planckian corrections to the inflationary density perturbation spectrum. However, certain astrophysical observations seem to indi…
A naive computation of the correlation functions of fluctuations generated during inflation suffers from logarithmic divergences in the infrared (IR) limit. In this paper, we propose one way to solve this IR divergence problem in the single-field inflation model. The key observation is that the variables that are commonly used in describing fluctuations are influenced by what we cannot observe. Introducing a new perturbation variable which mimics what we actually observe, we propose a new prescription to solve the time evolution of perturbation in which this leakage of information from the uno…
We present a relatively simple operator formalism which reproduces the leading infrared logarithm of the one loop quantum gravitational correction to the fermion mode function on a locally de Sitter background. This rule may serve as the basis for an eventual stochastic formulation of quantum gravity during inflation. Such a formalism would not only effect a vast simplification in obtaining the leading powers of $\ln(a)$ at fixed loop orders, it would also permit us to sum the series of leading logarithms. A potentially important point is that our rule does not seem to be consistent with any s…
We study the preheating process in a model of DBI inflation with a DBI-type inflaton coupling to a canonical entropy field. At the end of inflation, the inflaton field oscillates around its vacuum which can arise from an infrared cutoff parameter on the warp factor and correspondingly the evolution of its fluctuations can be approximately described by a generalized Hill's equation in third order. We study the field fluctuations numerically and show that they could grow exponentially since the instability bands commonly exist in the DBI models if the amplitudes of background oscillations are of…
Recent models of axion monodromy inflation in string theory link the inflationary potential and the moduli stabilization potential. Realistic inflationary models require mechanisms to moderately suppress the inflaton mass with respect to the moduli stabilization scale. In this paper we explore the realization of this idea using warped throats, whose redshifted infrared region supports the inflaton mode. The inflaton potential and its monodromy arise from couplings to the fluxes supporting the throat. We provide explicit realizations of such throats in type IIB with NSNS and RR 3-form field str…
We consider cosmological inflation generated by a scalar field slowly rolling off from a de Sitter maximum of its potential. The models belong to the class of hilltop models and represent the most general model of this kind in which the scalar potential can be written as the sum of two exponentials. The minimally coupled Einstein-scalar gravity theory obtained in this way is the cosmological version of a two-scale generalization of known holographic models, allowing for solitonic solutions interpolating between an AdS spacetime in the infrared and scaling solutions in the ultraviolet. We then …
We use dimensional regularization to evaluate the one loop contribution to the graviton self-energy from a massless, minimally coupled scalar on a locally de Sitter background. For noncoincident points our result agrees with the stress tensor correlators obtained recently by Perez-Nadal, Roura and Verdaguer. We absorb the ultraviolet divergences using the $R^2$ and $C^2$ counterterms first derived by 't Hooft and Veltman, and we take the $D=4$ limit of the finite remainder. The renormalized result is expressed as the sum of two transverse, 4th order differential operators acting on nonlocal, d…
