We examine the spectrum of inflaton fluctuations resulting from any given long period of exponential inflation. Infrared and ultraviolet divergences in the inflaton dispersion summed over all modes do not appear in our approach. We show how the scale-invariance of the perturbation spectrum arises. We also examine the spectrum of scalar perturbations of the metric that are created by the inflaton fluctuations that have left the Hubble sphere during inflation and the spectrum of density perturbations that they produce at reentry after inflation has ended. When the inflaton dispersion spectrum is renormalized during the expansion, we show (for the case of the quadratic inflaton potential) that the density perturbation spectrum approaches a mass-independent limit as the inflaton mass approaches zero, and remains near that limiting value for masses less than about 1/4 of the inflationary Hubble constant. We show that this limiting behavior does not occur if one only makes the Minkowski space subtraction, without the further adiabatic subtractions that involve time derivatives of the expansion scale factor $a(t)$. We also find a parametrized expression for the energy density produced by the change in $a(t)$ as inflation ends. If the end of inflation were sufficiently abrupt, then the temperature corresponding to this energy density could be very significant. We also show that fluctuations of the inflaton field that are present before inflation starts are not dissipated during inflation, and could have a significant observational effect today. The mechanism for this is caused by the initial fluctuations through stimulated emission from the vacuum.
We characterise the primordial perturbations produced due to both inflaton and curvaton fluctuations in models where the curvaton has a quadratic, cosine or hyperbolic potential, and the inflaton potential is characterised by the usual slow-roll parameters. Isocurvature curvaton field perturbations can produce significant non-Gaussianity in the primordial density field, in contrast with adiabatic inflaton field perturbations which produce negligible non-Gaussianity for canonical scalar fields. A non-self-interacting curvaton with quadratic potential produces a local-type non-Gaussianity that i…
We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing…
Radiative Corrections to the Inflaton Potential as an Explanation of Suppressed Large Scale Power in Density Perturbations and the Cosmic Microwave Background
We investigate the inflaton decay and reheating period after the end of inflation in the non-minimal derivative coupling (NDC) model with chaotic potential. In general, this model is known to provide an enhanced slow-roll inflation caused by gravitationally enhanced friction. We find violent oscillations of Hubble parameter which induces oscillations of the sound speed squared, implying the Lagrangian instability of curvature perturbation $ζ$ under the comoving gauge $φ=0$. Also, it is shown that the curvature perturbation blows up at $\dotϕ=0$, leading to the breakdown of the comoving gauge a…
We have carried out detailed $k$-mode analysis of single-inflaton slow-roll inflationary perturbations including quantum fluctuations by setting up non-linear coupled differential equations of inflaton field ($ϕ$), its perturbation ($δϕ$) and the metric perturbation (the Bardeen potential, $Φ_B$), and calculated the number of e-folds ($N$), scalar spectral index ($n_s$), tensor spectral index ($n_h$), scalar power spectrum ($Δ_s$), tensor power spectrum ($Δ_h$), tensor-to-scalar ratio ($r$) and the Hubble parameter ($H$) for different $k$ values at the horizon crossing. In these calculations w…
We show that density perturbations seeded by the inflaton can be suppressed when having additional light degrees of freedom contributing to the production of perturbations. The inflaton fluctuations affect the light field dynamics by modulating the length of the inflationary period, hence produce additional density perturbations in the post-inflationary era. Such perturbations can cancel those generated during inflation as both originate from the same inflaton fluctuations. This allows production of large gravitational waves from small-field inflation, which is normally forbidden by the Lyth b…
We study sound speed resonance (SSR) mechanism for primordial black hole (PBH) formation in an early universe scenario with inflaton and curvaton being mixed. In this scenario, the total primordial density perturbations can be contributed by the fluctuations from both the inflaton and curvaton fields, in which the inflaton fluctuations lead to the standard adiabatic perturbations, while the sound speed of the curvaton fluctuations are assumed to be oscillating during inflation. Due to the narrow resonance effect of SSR mechanism, we acquire the enhanced primordial density perturbations on smal…
It is known that in single scalar field inflationary models the standard curvature perturbation ζ, which is supposedly conserved at superhorizon scales, diverges during reheating at times dΦ/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge ϕ=0, where ϕ denotes the inflaton perturbation, breaks down when dΦ/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of ζ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smoot…
The effect of string and quantum gravity inspired minimum-length deformed quantization on a free, massless scalar field is studied on de Sitter background at the level of second quantization. Analytic solution of a field operator is obtained to the first order in deformation parameter. Using this solution we then estimate the two point and four point correlation functions (with respect to the Bunch-Davies vacuum). The field operator shows up a non-linear dependence on creation and annihilation operators, therefore the perturbation spectrum proves to be non-Gaussian. The correction to the power…
We construct a model of cosmological inflation and perturbation based on the higher-dimensional gauge theory. The inflaton and curvaton are the scalar fields arising from the extra space components of the gauge field living in more than four dimensions. We take the six-dimensional (6D) Yang-Mills theory compactified on $T^2$ as a toy model, and apply the one-loop effective potential of the inflaton and the curvaton to the curvaton scenario. We have found that the curvaton is subdominant for the linear curvature perturbation, but that a significant non-Gaussianity and a sizable tensor to scalar…
In a broad class of scenarios, inflation is followed by an extended era of matter-dominated expansion during which the inflaton condensate is nonrelativistic on subhorizon scales. During this phase density perturbations grow to the point of nonlinearity and collapse into bound structures. This epoch strongly resembles structure formation with ultra-light axion-like particles. This parallel permits us to adapt results from studies of cosmological structure formation to describe the nonlinear dynamics of this post-inflationary epoch. We show that the inflaton condensate fragments into "inflaton …
The next generation of cosmic microwave background, gravitational wave, and large scale structure, experiments will provide an unprecedented opportunity to probe the primordial power spectrum on small scales. An exciting possibility for what lurks on small scales is a sharp rise in the primordial power spectrum: This can lead to the formation of primordial black holes, providing a dark matter candidate or the black holes observed by the LIGO-Virgo collaboration. In this work we develop a mechanism for the amplification of the small-scale primordial power spectrum, in the context of single-fiel…
Many controlled realizations of chaotic inflation employ pseudo-scalar axions. Pseudo-scalars ϕare naturally coupled to gauge fields through c ϕF \tilde{F}. In the presence of this coupling, gauge field quanta are copiously produced by the rolling inflaton. The produced gauge quanta, in turn, source inflaton fluctuations via inverse decay. These new cosmological perturbations add incoherently with the "vacuum" perturbations, and are highly nongaussian. This provides a natural mechanism to generate large nongaussianity in single or multi field slow-roll inflation. The resulting phenomenological…
We study the inflation scenario with the non-minimally derivative coupling $XR^{(3)}$, where $X=\nabla_μϕ\nabla^μϕ$, $ϕ$ is the inflaton and $R^{(3)}$ is the 3-dimensional intrinsic Ricci scalar on the spacelike hypersurface, and analytically calculate the corrections of $XR^{(3)}$ on the power spectra of primordial perturbations. It is found that for the $ϕ^2$ inflation model, the corresponding predictions can be driven to the best-fit region of the $n_s$-$r$ diagram.
We study a variant of the Chromo-Natural Inflation (CNI) mechanism in which the inflaton interacts only gravitationally with the CNI fields. Integrating out all the non-dynamical scalar fields of the model results in a coupling between the perturbations of the inflaton and of the CNI pseudo-scalar which is significantly greater than the one obtained in the absence of the gauge CNI dynamics. We compute how this greater coupling impacts the power spectrum of the inflaton perturbations that are sourced nonlinearly by the unstable (tensor) gauge CNI modes, and we require that the amplitude of thes…
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 consider power-law inflation with a Gauss-Bonnet correction inspired by string theory. We analyze the stability of cosmological perturbations and obtain the allowed parameter space. We find that for GB-dominated inflation ultra-violet instabilities of either scalar or tensor perturbations show up on small scales. The Gauss-Bonnet correction with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio in the potential-dominated case. We place tight constraints on the model parameters by making use of the WMAP 5-year data.
In inflationary models where the source of scalar perturbations is not the inflaton, but one or more scalars with negligible coupling with the inflaton, the resulting perturbations are not only scale invariant, but fully conformally invariant with conformal dimension close to zero. This is closely related to the fact that correlation functions can only depend on the de Sitter invariant distances. These properties follow from the isometries of the inflationary de Sitter space and are thus completely independent of the dynamics. The 3-point function is fixed in terms of two constants, while the …
We propose a new mechanism to generate primordial curvature perturbations, based on the resonant production of particles during inflation. It is known that this phenomenon can trap the inflaton for a fraction of e-fold. This effect is governed by the mass of the produced particles and by their coupling to the inflaton, parameters which can depend on the expectation value of other fields. If one of such additional fields - a 'modulaton' - is light, then its fluctuations, acquired during the earlier stages of inflation, will induce a spatial modulation of the trapping, and thus of the end of inf…
We investigate the possibility that the primordial perturbation has two sources: the inflaton and a spectator field, which is not dynamically important during inflation but which after inflation can contribute to the curvature perturbation. The recent Planck results on the power spectrum and non-Gaussianity allow us to put constraints on such mixed models. In the generic case, where no specific model for the inflaton or the spectator is assumed, one finds that in the mixed scenario it is possible to have a large trispectrum with tau_NL >> (f_NL)^2. The constraints on inflation models in the pl…
We analyze the class of models where a suitable coupling between the inflaton field and the vector field gives rise to scale-invariant vector perturbations. We exploit the fact that the de Sitter isometry group acts as conformal group on the three-dimensional Euclidean space for the super-Hubble fluctuations in order to characterize the correlators involving the inflaton and the vector fields.
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.
Recently, an interesting inflationary scenario, named Gauss-Bonnet inflation, is proposed by Kanti et al.~\cite{Kanti:2015pda,Kanti:2015dra}. In the model, there is no inflaton potential but the inflaton couples to the Guass-Bonnet term. In the case of quadratic coupling, they find inflation occurs with graceful exit. The scenario is attractive because of the natural set-up. However, we show there exists the gradient instability in the tensor perturbations in this inflationary model. We further prove the no-go theorem for the Gauss-Bonnet inflation without an inflaton potential.
We present a method to analytically compute the quantum corrected two-point correlation function of a scalar field in leading order at each loop in a homogeneous, isotropic and spatially flat spacetime where the expansion rate is time dependent and express the quantum corrected power spectrum $Δ^2(k)$ as a time derivative of the coincident correlation function evaluated at time $t_k$ of the first horizon crossing of a mode with comoving wave number $k$. To facilitate the method, we consider the simplest version of inflation driven by a massive, minimally coupled inflaton endowing a quartic sel…
Trapped inflation is a mechanism in which particle production from the moving inflaton is the main source of friction in the inflaton equation of motion. The produced fields source inflaton perturbations, which dominate over the vacuum ones. We employ the set of equations for the inflaton zero mode and its perturbations which was developed in the original work on trapped inflation, and which we extend to second order in the perturbations. We build on this study by updating the experimental constraints, and by replacing the existing approximate solutions with more accurate ones. We obtain a dif…
Sharp shapes in the inflaton potentials often lead to short departures from slow roll which, in turn, result in deviations from scale invariance in the scalar power spectrum. Typically, in such situations, the scalar power spectrum exhibits a burst of features associated with modes that leave the Hubble radius either immediately before or during the epoch of fast roll. Moreover, one also finds that the power spectrum turns scale invariant at smaller scales corresponding to modes that leave the Hubble radius at later stages, when slow roll has been restored. In other words, the imprints of brie…
Several models of inflation employing a triplet of SU(2) vectors with spatially orthogonal vacuum expectation values (VEVs) have been recently proposed. One (tensor) combination $t$ of the vector modes is amplified in some momentum range during inflation. Due to the vector VEVs, this combination mixes with gravitational waves (GW) at the linear level, resulting in a GW amplification that has been well studied in the literature. Scalar perturbations in this class of models have been so far studied only at the linear level. We perform a first step toward the nonlinear computation using as an exa…
