In this paper, we would like to figure out whether a k-inflation model admits the Bianchi type I metric as its inflationary solution under a constant-roll condition in the presence of the supergravity motivated coupling between scalar and vector fields, $f^2(ϕ)F_{μν}F^{μν}$. As a result, some novel anisotropic inflationary solutions are shown to appear along with a power-law one in this scenario. Furthermore, these solutions are numerically confirmed to be attractive, in contrast to the prediction of the Hawking's cosmic no-hair conjecture.
For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio up to the first order by using the method of Bessel function approximation. The derived $n_s-r$ results for the constant-roll inflation are also compared with the observations, we find that only one constant-roll inflation is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflat…
The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid. We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter $η_H$ is not small. More accurate method is needed for calculating the primordial power spectrum for constant-roll i…
We consider an inflationary scenario where the rate of inflaton roll defined by $\ddotϕ/H\dot ϕ$ remains constant. The rate of roll is small for slow-roll inflation, while a generic rate of roll leads to the interesting case of `constant-roll' inflation. We find a general exact solution for the inflaton potential required for such inflaton behaviour. In this model, due to non-slow evolution of background, the would-be decaying mode of linear scalar (curvature) perturbations may not be neglected. It can even grow for some values of the model parameter, while the other mode always remains consta…
In this work we generalize the constant-roll condition for minimally coupled canonical scalar field inflation. Particularly, we shall assume that the scalar field satisfies the condition $\ddotϕ=α(ϕ) V'(ϕ)$, and we derive the field equations under this assumption. We call the framework extended constant-roll framework. Accordingly we calculate the inflationary indices and the corresponding observational indices of inflation. In order to demonstrate the inflationary viability, we choose three potentials that are problematic in the context of slow-roll dynamics, namely chaotic, linear power-law …
We generalize the notion of constant-roll inflation earlier introduced in General Relativity (GR) and $f(R)$ gravity to inflationary models in more general scalar-tensor gravity. A number of novel exact analytic solutions for a FLRW spatially flat cosmological background is found for this case. All forms of the scalar field potential and its coupling to gravity producing the exact de Sitter solution, while the scalar field is varying, are presented. In the particular cases of induced gravity and GR with a non-minimally coupled scalar field, all constant-roll inflationary solutions are found. I…
We discuss the constant-roll inflation with constant $ε_2$ and constant $\barη$. By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of $ε_1$. The model with constant $ε_2$ is ruled out by the observations at the $3σ$ confidence level, and the model with constant $\barη$ is consistent with the observations at the $1σ$ confidence level. The potential for the model with constant $\barη$ is also obtained from the Hamilton-Jaco…
We present a complete formulation of the scalar bispectrum in the unified effective field theory (EFT) of inflation, which includes the Horndeski and beyond-Horndeski Gleyzes-Langlois-Piazza-Vernizzi classes, in terms of a set of simple one-dimensional integrals. These generalized slow-roll expressions remain valid even when slow-roll is transiently violated and encompass all configurations of the bispectrum. We show analytically that our expressions explicitly preserve the squeezed-limit consistency relation beyond slow-roll. As an example application of our results, we compute the scalar bis…
In this paper we investigate the inflationary phenomenology of an Einstein-Gauss-Bonnet theory compatible with the GW170817 event, by imposing the constant-roll evolution on the scalar field. We develop the constant-roll GW170817-compatible Einstein-Gauss-Bonnet formalism, and we calculate the slow-roll indices and the observational indices of inflation, for several models of interest. As we demonstrate, the phenomenological viability of the models we study is achieved for a wide range of the free parameters. In addition, for the same values of the free parameters that guarantee the inflationa…
We discuss the cosmological inflation in the context of $f(Q)$ non-metric gravity, where $Q$ is the non-metric scalar. After introducing conformal transformations for $f(Q)$ gravity, we first focus on the potential-slow-roll inflation by studying the corresponding potentials for different forms of the function $f(Q)$ in the Einstein frame. Secondly, we investigate the Hubble-slow-roll inflation for three classes of inflationary potentials considered for the specific form $f(Q)\propto Q^{2}$, in the Jordan frame. We compare results in both approaches with observations coming from Planck and BIC…
We explore the possibility of a blue-tilted gravitational wave spectrum from potential-driven slow-roll inflation in the Horndeski theory. In Kamada et al. (2012), it was claimed that a blue gravitational wave spectrum cannot be obtained from stable potential-driven slow-roll inflation within the Horndeski framework. However, it has been demonstrated that the spectrum of primordial gravitational waves can be blue in inflation with the Gauss-Bonnet term, where the potential term is dominant and slow-roll conditions as well as the stability conditions are satisfied. To fill in this gap, we clari…
We study constant-roll inflation in the presence of a gauge field coupled to an inflaton. By imposing the constant anisotropy condition, we find new exact anisotropic constant-roll inflationary solutions which include anisotropic power-law inflation as a special case. We also numerically show that the new anisotropic solutions are attractors in the phase space.
A Remedy of the Trans-Planckian Censorship Problem with Smooth Slow-roll to Power-law Inflation Transitions in Scalar Field Theory
Institute of Space Sciences (ICE, CSIC)（空间科学研究所）；ICREA（加泰罗尼亚高级研究学院）；L.N. Gumilyov Eurasian National University - Astana（欧亚国立大学）；Department of Physics, Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学物理系）
We show that a corpuscular description of gravity can lead to an inflationary scenario similar to Starobinsky's model without requiring the introduction of the inflaton field. All relevant properties are determined by the number of gravitons in the cosmological condensate or, equivalently, by their Compton length. In particular, the relation between the Hubble parameter $H$ and its time derivative $\dot H$ required by CMB observations at the end of inflation, as well as the (minimum) initial value of the slow-roll parameter, are naturally obtained from the Compton size of the condensate.
We propose a new approach to constant-roll warm inflation as a generalization of constant-roll inflation. Based on the $β$-function formalism, it is shown that constant-roll warm inflation models with a natural end fall into universality classes defined by three different types of $β$-functions, under the assumption that radiation energy density is quasi-stable. Given that warm inflation is completely specified by the $β$-function and dissipation coefficient ratio, we investigate whether or not the inflation can physically be realized for enough number of e-foldings at the background level for…
Slow roll solutions to inflationary potentials have been widely believed to be the only universal attractor. Over the last few years there has been growing interest in a new class of inflationary models known as Constant-Roll Inflation. Constant roll solutions are a generalization of "ultra-slow roll" dynamics, where the first slow roll parameter is small, but the second slow roll parameter $η$ is larger than unity. In Ultra-slow Roll Inflation, the large-$η$ solution is a dynamical transient, relaxing exponentially to the attractor de Sitter solution. In the constant roll generalization, rece…
From the assumption that the slow roll parameter $ε$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained, as succinctly studied in \cite{Benisty:2020xqm}. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs and satisfies the condition to climb from small values of $ε$ to $1$ at the end of the inflationary epoch. We find the corresponding scalar Quintessential Inflationary potential with two flat regions. Moreover, a reheating mechanism is suggested with numerical estimation for …
We develop a nonperturbative method through the Hartree factorization to examine the quantum fluctuation effects on the single-field inflationary models in a spatially flat FRW cosmological space-time. Apart from the background field equation as well as the Friedmann equation with the corrections of quantum field fluctuations, the modified Mukhanov-Sasaki equations for the mode functions of the quantum scalar field are also derived by introducing the nonzero $Δ_B$ term. We consider the Universe undergoing the slow roll (SR)-ultra slow roll (USR) -slow roll (SR) inflation where in particular th…
It is often claimed that the ultra-slow-roll regime of inflation, where the dynamics of the inflaton field are friction dominated, is a non-attractor and/or transient. In this work we carry out a phase-space analysis of ultra-slow roll in an arbitrary potential, $V(ϕ)$. We show that while standard slow roll is always a dynamical attractor whenever it is a self-consistent approximation, ultra-slow roll is stable for an inflaton field rolling down a convex potential with $M_{\scriptscriptstyle{\mathrm{Pl}}} V''>|V'|$ (or for a field rolling up a concave potential with $M_{\scriptscriptstyle{\mat…
In this work we shall investigate the phenomenological implications of the constant-roll condition on a $k$-Inflation theory of gravity. The latter theories are particularly promising, since these remained robust to the results of GW170817, since these have a gravitational wave speed $c_T=1$ in natural units. We shall mainly focus on the phenomenology of the $k$-Inflation models, with the only assumption being the slow-roll condition imposed on the first and fourth slow-roll parameters, and the constant-roll condition for the evolution of the scalar field. We present in detail the final form o…
The effective field theory (EFT) of inflation provides an essential picture to explore the effects of the unknown high energy physics in the single scalar field inflation models. For a generic EFT of inflation, possible high energy corrections to simple slow-roll inflation can modify both the propagating speed and dispersion relations of the cosmological scalar and tensor perturbations. With the arrival of the era of precision cosmology, it is expected that these high energy corrections become more important and have to be taken into account in the analysis with future precise observational da…
In this work, we studied the slow-roll approximation of cosmic inflation within the context of $f(R,T)$ gravity, where $R$ is the scalar curvature, and $T$ is the trace of the energy-momentum tensor. By choosing a minimal coupling between matter and gravity, we obtained the modified slow-roll parameters, the scalar spectral index ($n_s$), the tensor spectral index ($n_{\textrm{T}}$), and the tensor-to-scalar ratio ($r$). We computed these quantities for a general power-law potential, Natural & Quartic Hilltop inflation, and the Starobinsky model, plotting the trajectories on the $(n_s,r)$ plan…
We consider the effect of quantum diffusion on the dynamics of the inflaton during a period of ultra-slow-roll inflation. We extend the stochastic-$δ\mathcal{N}$ formalism to the ultra-slow-roll regime and show how this system can be solved analytically in both the classical-drift and quantum-diffusion dominated limits. By deriving the characteristic function, we are able to construct the full probability distribution function for the primordial density field. In the diffusion-dominated limit, we recover an exponential tail for the probability distribution, as found previously in slow-roll inf…
Primordial perturbations from ultra-slow-roll single-field inflation with quantum loop effects
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Department of Physics, National Dong Hwa University（国立东华大学物理系）；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）
[Abridged] The primordial scalar power spectrum is well constrained on large scales, primarily by the observations of the anisotropies in the cosmic microwave background (CMB). Over the last few years, it has been recognized that a sharp rise in power on small scales will lead to enhanced formation of primordial black holes (PBHs) and also generate secondary gravitational waves (GWs) of higher and, possibly, detectable amplitudes. It is well understood that scalar power spectra with COBE normalized amplitude on the CMB scales and enhanced amplitudes on smaller scales can be generated due to de…
We study the stochastic formalism of inflation beyond the usual slow-roll approximation. We verify that the assumptions on which the stochastic formalism relies still hold even far from the slow-roll attractor. This includes demonstrating the validity of the separate universe approach to evolving long-wavelength scalar field perturbations beyond slow roll. We also explain that, in general, there is a gauge correction to the amplitude of the stochastic noise. This is because the amplitude is usually calculated in the spatially-flat gauge, while the number of e-folds is used as the time variable…
After giving a pedagogical review we clarify that the stochastic approach to inflation is generically reliable only at zeroth order in the (geometrical) slow-roll parameter $ε_1$ if and only if $ε_2^2\ll 6/ε_1$, with the notable exception of slow-roll. This is due to the failure of the stochastic $ΔN$ formalism in its standard formulation. However, by keeping the formalism in its regime of validity, we showed that, in ultra-slow-roll, the stochastic approach to inflation reproduces the power spectrum calculated from the linear theory approach.
Constant-roll inflation was recently introduced by Motohashi, Starobinsky and Yokoyama as a phenomenological way to parametrize deviations from the slow-roll scenarios. In this paper, we investigate the dynamics of both the background and the perturbations in this model, without making any slow-roll assumptions. The perturbation spectra are computed with an efficient and accurate novel method that allowed us to quickly scan the parameter space of constant-roll inflation. We derive the constraints on the model parameters from the cosmic microwave background anisotropy measurements provided by t…
By extending the potential, we propose a mechanism for the end of the constant-roll inflation and the subsequent reheating phase in the FLRW space-time. Based on astrophysical data, we estimate the Universe reheating temperature.
In this paper, we study a constant-roll inflationary model in the presence of a noncommutative parameter with a homogeneous scalar field minimally coupled to gravity. The specific noncommutative inflation conditions proposed new consequences. On the other hand, we use anisotropic conditions and find new anisotropic constant-roll solutions with respect to noncommutative parameter. Also, we will plot some figures with respect to the specific values of the corresponding parameter and the swampland criteria which is raised from the exact potential obtained from the constant-roll condition. Finally…
We study a single field inflationary model modified by a non-minimal coupling term between the Ricci scalar $R$ and the scalar field $φ$ in the context of constant-roll inflation. The first-order formalism is used to analyse the constant-roll inflation instead of the standard methods used in the literature. In principle, the formalism considers two functions of the scalar field, $W=W(φ)$ and $Z=Z(φ)$, which lead to the reduction of the equations of motion to first-order differential equations. The approach can be applied to a wide range of cosmological situations since it directly relates the …
