Slow-roll Regime Research Articles

Palatini [formula omitted]: A new framework for inflationary attractors

Palatini F(R) gravity proved to be a powerful tool in order to realize asymptotically flat inflaton potentials. Unfortunately, it also inevitably implies higher-order inflaton kinetic terms in the Einstein frame that might jeopardize the evolution of the system out of the slow-roll regime. We prove that a F(R+X) gravity, where X is the inflaton kinetic term, solves the issue. Moreover, when F is a quadratic function such a choice easily leads to a new class of inflationary attractors, fractional attractors, that generalizes the already well-known polynomial α-attractors.

Beyond (and back to) Palatini quadratic gravity and inflation

We study single-field slow-roll inflation embedded in Palatini F(R) gravity where F(R) grows faster than R 2. Surprisingly, the consistency of the theory requires the Jordan frame inflaton potential to be unbounded from below. Even more surprisingly, this corresponds to an Einstein frame inflaton potential bounded from below and positive definite. We prove that for all such Palatini F(R)'s, there exists a universal strong coupling limit corresponding to a quadratic F(R) with the wrong sign for the linear term and a cosmological constant in the Jordan frame. In such a limit, the tensor-to-scalar ratio r does not depend on the original inflaton potential, while the scalar spectral index ns does. Unfortunately, the system is ill-defined out of the slow-roll regime. A possible way out is to upgrade to a F(R,X) model, with X the Jordan frame inflaton kinetic term. Such a modification essentially leaves the inflationary predictions unaffected.

Higgs inflation model with non-minimal coupling in hybrid Palatini approach

In this paper, we propose a hybrid metric Palatini approach in which the Palatini scalar curvature is non minimally coupled to the scalar field. We derive Einstein's field equations, i.e., the equations of motion of the scalar field. Furthermore, the background and perturbative parameters are obtained by means of Friedmann equations in the slow roll regime. The analysis of cosmological perturbations allowed us to obtain the main inflationary parameters, e.g., the scalar spectral index and tensor to scalar ratio r. From this perspective, as an application of our analysis, we consider the Higgs field with quartic potential, which plays the inflaton role, and show that predictions of Higgs hybrid inflation are in good agreement with recent observational data [Astron. Astrophys. 641, 61 (2020)].

Eternal inflation and collapse theories

The eternal inflation problem continues to be considered one of standard's cosmology most serious shortcomings. This arises when one considers the effects of “quantum fluctuations” on the zero mode of inflaton field during a Hubble time in the inflationary epoch.In the slow-roll regime it is quite clear that such quantum fluctuations could dwarf the classical rolling down of the inflaton, and with overwhelming probability this prevents inflation from ever ending. When one recognizes that quantum fluctuations can not be taken as synonymous of stochastic fluctuations, but rather intrinsic levels of indefiniteness in the quantities in question, one concludes that the eternal inflation problem simply does not exist. However, the same argument would serve to invalidate the account for the generation of the primordial seeds of cosmic structure as has been amply discussed elsewhere [1,2,3]. In order to do address that issue, one must explain the breaking of homogeneity and isotropy of the situation prevailing during the early inflationary epoch (at both the quantum and classical levels of the description). For that one needs to rely on some additional element, beyond those present in the traditional treatments. The so called spontaneous collapse theories offer a viable candidate for that element, namely the stochastic and spontaneous state reduction characteristic of those proposals possesses the basic features to break those symmetries. In fact, a version of the CSL theory adapted to the cosmological context has been shown to offer a satisfactory account for the origin the seeds of cosmic structure with an adequate power spectrum [2], and will serve as the basis of our analysis. However, once such stochastic collapse is introduced into the theoretical framework the eternal inflation problem has the potential reappear.In this manuscript we explore those issues in detail and discuss an avenue that seems to allow for a satisfactory account for the generation of the primordial inhomogeneities and anisotropies while freeing the theory from the eternal inflation problem.

Mimicking two field inflationary features with a single field

It is well known that damped superimposed oscillations at large scales in the primordial power spectrum can be generated in both single field and two field models. In single field inflationary models, these features typically arise due to deviations from the slow roll regime. On the other hand, in two field models, these features are generated due to a turn in the background trajectory in the field space. In this work, we demonstrate that both single field and two field models can produce identical features at large scales in the primordial power spectrum. To achieve this, we utilize the generalized slow roll approximation and successfully reconstruct single field models based on the featured power spectrum typically generated in two field models. To validate our methodology, we numerically calculate the power spectrum from the reconstructed potential and find a remarkable agreement with the power spectrum which is obtained from the two field model.

Constraints on the non-minimally coupled Witten-O'Raifeartaigh inflation

We investigate the impact of a non-minimal coupling of the scalar field with gravity in inflationary models, where a small coupling is allowed. As a concrete example, we consider the Witten-O'Raifeartaigh model, where, in line with other models, the presence of a coupling strength ξ can recover concordance of the inflationary parameters with cosmic microwave background (CMB) constraints, provided by the Planck collaboration. We go beyond the slow-roll regime and investigate the impact in the description of CMB anisotropies by performing a statistical analysis of the model with the most recent Planck + Baryon Acoustic Oscillations (BAO) data to seek for any indication of a non-zero coupling by data within the model. We find that not only the presence of a non-minimal coupling is seen, but the model has a slight statistical preference when compared with the standard ΛCDM one. We also discuss the results on the minimally-coupled model, which in general, favours the simple setting where the associated mass scale is equal to the reduced Planck mass Mp while being, in general, disfavored concerning the standard model.

Quantum-gravitational corrections to the power spectrum for a closed universe

We study the quantum-gravitational corrections to the power spectrum of a gauge-invariant inflationary scalar perturbations in a closed model of a universe. We consider canonical quantum gravity as an approach to quantizing gravity. This leads to the Wheeler-DeWitt equation, which has been studied by applying a semiclassical Born–Oppenheimer type of approximation. At the corresponding orders of approximation, we recover both the uncorrected and quantum-gravitationally corrected Schrödinger equations for the perturbation modes from which we calculate the quantum-gravitational corrections to the power spectrum in the slow-roll regime. The results are compared to the power spectra for the flat model of the universe.

Inflationary entanglement

We investigate the entanglement due to geometric corrections in particle creation during inflation. To do so, we propose a single-field inflationary scenario, nonminimally coupled to the scalar curvature of spacetime. We require particle production to be purely geometric, setting to zero the Bogoliubov coefficients and computing the $S$ matrix associated with spacetime perturbations, which are traced back to inflaton fluctuations. The corresponding particle density leads to a nonzero entanglement entropy whose effects are investigated at primordial time of Universe evolution. The possibility of modeling our particle candidate in terms of dark matter is discussed. The classical backreaction of inhomogeneities on the homogeneous dynamical background degrees of freedom is also studied and quantified in the slow-roll regime.

Quantum cosmology, eternal inflation, and swampland conjectures

In light of the recent swampland conjectures, we explore quantum cosmology and eternal inflation beyond the slow roll regime. We consider a model of a closed universe with a scalar field ϕ in the framework of tunneling approach to quantum cosmology. The scalar field potential is assumed to have a maximum at ϕ = 0 and can be approximated in its vicinity as V(ϕ)≈ 3H 2 - 1/2m 2 ϕ 2. Using the instanton method, we find that for m < 2H the dominant nucleation channel for the universe is tunneling to a homogeneous, spherical de Sitter space. For larger values of m/H, the most probable tunneling is to an inhomogeneous closed universe with a domain wall wrapped around its equator. We determine the quantum state of the field ϕ in the nucleated universe by solving the Wheeler-DeWitt equation with tunneling boundary conditions. Our results agree with earlier work which assumed a slow-roll regime m ≪ H. We finally show that spherical universes nucleating with m < 2H undergo stochastic eternal inflation with inflating regions forming a fractal of dimension d > 2. For larger values of m the field ϕ is unstable with respect to formation of domain walls and cannot be described by a perturbative stochastic approach.

Discordances in Cosmology and the Violation of Slow-Roll Inflationary Dynamics.

We identify examples of single field inflationary trajectories beyond the slow-roll regime that improve the fit to Planck 2018 data compared to a baseline Λ cold dark matter model with power law form of primordial spectrum and at the same time alleviate existing tensions between different datasets in the estimate of cosmological parameters such as H_{0} and S_{8}. A damped oscillation in the first Hubble flow function-or equivalently a feature in the potential-and the corresponding localized oscillations in the primordial power spectrum partially mimic the improvement in the fit of Planck data due to A_{L} or Ω_{K}. Compared to the baseline model, this model can lead simultaneously to a larger value of H_{0} and a smaller value of S_{8}, a trend that can be enhanced when the most recent SH0ES measurement for H_{0} is combined with Planck and BICEP-Keck 2018 data. Large scale structure data and more precise cosmic microwave background polarization measurements will further provide critical tests of this intermediate fast-roll phase.

Higher-order extension of Starobinsky inflation: Initial conditions, slow-roll regime, and reheating phase

The most current observational data corroborate the Starobinsky model as one of the strongest candidates in the description of an inflationary regime. Motivated by such success, extensions of the Starobinsky model have been increasingly recurrent in the literature. The theoretical justification for this is well grounded: higher-order gravities arise in high-energy physics in the search for the ultraviolet completeness of general relativity. In this paper, we propose to investigate the inflation due to the extension of the Starobinsky model characterized by the inclusion of the ${R}^{3}$ term. We make a complete analysis of the potential and phase space of the model, where we observe the existence of three regions with distinct dynamics for the scalar field. We can establish restrictive limits for the number of $e$-folds through a study of the reheating and by considering the usual couplings of the standard matter fields and gravity. Thereby, we duly confront our model with the observational data from Planck, BICEP3/Keck, and BAO. Finally, we discuss how the inclusion of the cubic term restricts the initial conditions necessary for the occurrence of a physical inflation.

Effective potential of scalar-tensor gravity with quartic self-interaction of scalar field

One-loop effective potential of scalar-tensor gravity with a quartic scalar field self-interaction is evaluated up to first post-Minkowskian order. The potential develops an instability in the strong field regime which is expected from an effective theory. Depending on model parameters the instability region can be exponentially far in a strong field region. Possible applications of the model for inflationary scenarios are highlighted. It is shown that the model can enter the slow-roll regime with a certain set of parameters.

Inflation from inhomogeneous polarized Gowdy model

We study polarized Gowdy cosmologies on the three torus coupled to a massive scalar field. The phase space of the model admits a simple splitting between homogeneous and inhomogeneous sectors after a suitable gauge fixing. The presence of the mass term of the scalar field breaks the linearity of the equations of motion of the inhomogeneous fields. We discuss regimes of physical interest in which we recover a linear dynamics of these nonperturbative inhomogeneities, despite the metric is fully inhomogeneous at early times. We expand the inhomogeneous fields in Fourier modes and express them at all times as linear combinations of a basis of orthonormal complex solutions to the equations of motion, with coefficients that turn out to be an infinite collection of constants of motion. We argue that the resulting model can describe a nonperturbative inhomogeneous early Universe dominated by the kinetic energy of an inflaton at early times that can eventually reach a slow-roll regime with a nearly exponential expansion at late times that isotropices and homogenizes the geometry.

Model independent prediction of the spectral index of primordial quantum fluctuations

One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for cosmological scalar perturbations. This tilt is understood as a consequence of a quasi de Sitter classical equation of state describing the inflationary dark energy dominated era. Here, following previous work, we find a departure of scale invariance for the quantum Fisher information associated to de Sitter vacuum for scalar quantum spectator modes. This gives rise to a purely quantum cosmological tilt with a well defined dependence on energy scale. This quantum tilt is imprinted, in a scale dependent energy uncertainty for the spectator modes. The effective quasi de Sitter description of this model independent energy uncertainty uniquely sets the effective quasi de Sitter parameters (i.e., the small deviation from the cosmological constant equation of state) at all energy scales. In particular, in the slow-roll regime characterized by an almost constant ϵ, the quantum Fisher — model independent — prediction for the spectral index is n s = 0.9672. Moreover, the energy scale dependence of the quantum cosmological tilt implies the existence of a cosmological phase transition at energies higher than the CMB scale and of the order of 1 Mpc-1 where the tilt goes from red into blue. This strongly suggest the existence of a pre-inflationary phase where the effective scalaron contributes to the spectral index as normal relativistic matter and where the corresponding growth of the power spectrum can result in dark matter in the form of small mass primordial black holes. The source and features of the quantum cosmological tilt leading to these predictions are determined by the entanglement features of the de Sitter α- vacuum states.

Deviation from Slow-Roll Regime in the EGB Inflationary Models with r ∼ Ne−1

We consider Einstein–Gauss–Bonnet (EGB) inflationary models using the effective potential approach. We present evolution equations in the slow-roll regime using the effective potential and the tensor-to-scalar ratio. The choice of the effective potential is related to an expression of the spectral index in terms of e-folding number Ne. The satisfaction of the slow-roll regime is mostly related to the form of the tensor-to-scalar ratio r. The case of r∼1/Ne2 leads to a generalization of α-attractors inflationary parameters to Einstein–Gauss–Bonnet gravity with exponential effective potential. Moreover, the cosmological attractors include models with r∼1/Ne. And we check the satisfaction of the slow-roll regime during inflation for models with r∼1/Ne.

On the order reduction

In this work we present an extension of the technique of the order reduction to higher perturbative approximations in an iterative fashion. The intention is also to analyze more carefully the conditions for the validity of the order reduction technique. With this in mind, a few simple situations in which the iterative order reduction converges analytically to the exact solutions are presented as examples. It is discovered that the order reduction as a perturbative iterative technique does not converge in the weak coupling limit as most of the known perturbative schemes, at least when applied to these examples. Also, considering these specific examples, the convergence of the order reduction occurs in strong coupling regimes. As a more realistic case, the order reduction is applied to Starobinsky’s inflationary model is presented. It is verified that the method converges to the inflationary solution in the slow-roll regime.

Cosmological evolution of ultralight axionlike scalar fields

We examine the cosmological evolution of ultralight axionlike (ULA) scalar fields with potentials of the form $V(\phi) = m^2 f^2[1 - \cos(\phi/f)]^n$, with particular emphasis on the deviation in their behavior from the corresponding small$-\phi$ power-law approximations to these potentials: $V(\phi) \propto \phi^{2n}$. We show that in the slow-roll regime, when $\dot \phi^2/2 \ll V(\phi)$, the full ULA potentials yield a more interesting range of possibilities for quintessence than do the corresponding power law approximations. For rapidly oscillating scalar fields, we derive the equation of state parameter and oscillation frequency for the ULA potentials and show how they deviate from the corresponding power-law values. We derive an analytic expression for the equation of state parameter that better approximates the ULA value than does the pure power-law approximation.

Nonminimal Higgs inflation within holographic cosmology

We derive a Higgs inflationary model in the context of holographic cosmology, where we consider a universe filled with a Higgs field non-minimally coupled to gravity in a slow-roll regime. The amplitude of density (scalar) perturbations is calculated. In this regard, we show that the background and perturbative parameters characterising the inflationary era are related to the standard one through corrections terms. We found that for the e-fold number $N\sim 58$, the spectral index,$n_{r}$, and the tensor-to-scalar ratio,$r$, values are $0.965$ and $0.021$, respectively, which are in agreement with 2018 Planck observational data. However, as soon as we move from $N\sim 58$, the model is ruled out by the current data.

No slow-roll inflation à la generalized Chaplygin gas in general relativity

The Generalized Chaplygin Gas (GCG) model is characterized by the equation of state P = −A ρ−α, where A>0 and α < 1. The model has been extensively studied due to its interesting properties and applicability in several contexts, from late-time acceleration to primordial inflation. Nonetheless we show that the inflationary slow-roll regime cannot be satisfied by most of the parameter space of the GCG model when General Relativity (GR) is considered. In particular, although the model has been applied to inflation with 0 < α < 1, we show that for −1 < α ≤ 1 there is no expansion of the Universe but an accelerated contraction. For α ≤ −5/3, the second slow-roll parameter ηH is larger than unity, so there is no sustained period of inflation. Only for α very close to -1 the model produces enough e-folds, thus greatly reducing its parameter space. Moreover, we show that the model is ruled out by the Planck 2018 results. Finally, we extend our analysis to the Generalized Chaplygin-Jacobi Gas (GCJG) model. We find that the introduction of a new parameter does not change the previous results. We thus conclude that the violation of the slow-roll conditions is a generic feature of the GCG and GCJG models during inflation when GR is considered and that the models are ruled out by the Planck 2018 results.

Generating primordial features at large scales in two field models of inflation

We investigate the generation of features at large scales in the primordial power spectrum (PPS) when inflation is driven by two scalar fields. In canonical single field models of inflation, these features are often generated due to deviations from the slow-roll regime. While deviations from slow-roll can be naturally achieved in two field models due to a sharp turn in the trajectory in the field space, features at the largest scales of the types suggested by CMB temperature anisotropies are more difficult to achieve in models involving two canonical scalar fields due to the presence of isocurvature fluctuations. We show instead that a coupling between the kinetic terms of the scalar fields can easily produce such features. We discuss models whose theoretical predictions are consistent with current observations and highlight the implications of our results.