Chaotic inflation in modified gravitational theories

General Relativity and Gravitation, 2014

The European Physical Journal C, 2019

We study chaotic inflation with a Galileon-like self-interaction $$G(\phi ,X)\Box \phi $$G(ϕ,X)□ϕ, where $$G(\phi ,X)\propto X^{n}$$G(ϕ,X)∝Xn. General conditions required for successful inflation are deduced and discussed from the background and cosmological perturbations under slow-roll approximation. Interestingly, it is found that in the regime where the Galileon term dominates over the standard kinetic term, the tensor-to-scalar ratio becomes significantly suppressed in comparison to the standard expression in General Relativity (GR). Particularly, we find the allowed range in the space of parameters characterizing the chaotic quadratic and quartic inflation models by considering the current observational data of Planck from the $$n_{\mathcal {S}}-r$$nS-r plane. Finally, we discuss about the issue if the Galileon term is dominant by the end of inflation, this can affect the field oscillation during reheating.

International Journal of Modern Physics A, 2021

We apply the “systematic” first-order cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is nonminimally coupled to gravity within both the “Metric” and “Palatini” formulations. Accommodating Planck 2018 data with a length scale [Formula: see text] larger than Planck length [Formula: see text] requires amending the model. First, we assume [Formula: see text] gravity where we show that an [Formula: see text]-term within Palatini formulation is able to make the model viable. All along the discussions, we elucidate the origin of the difference between the “Metric” and “Palatini” formalisms, and also highlight the terms dropped when applying the shortcut “potential formulae method,” unlike the “systematic method,” for the observable parameters. Second, another variant of the model, represented by a two-exponentials potential, fits also the data with [Formula: see text].

Journal of the Physical Society of Japan

The main goal of this article is to explore a model with inflation inspired by Galileon inflaton field and how this model is modified by introducing a generalized coupling form Gð; XÞ ¼ À 2pþ1 X q M 6q , in the action. The analytical solutions of the inflaton field and corresponding potential are obtained under slow-roll approximation using specific evolution of the isotropic scale factor, i.e., intermediate, logamediate and exponential. Consistency of the predictions of the model with observations is being done by computing the scalar-tensor power spectra, the scalar spectral index, its running as well as the tensor-scalar ratio. For all the three models with inflation, we constrain the involved model parameters for which its predictions lie inside the allowed region from Planck 2015 data. L ¼ Kð; XÞ À Gð; XÞ□ þ fðÞR: One can see the Refs. 13, 17, 21, and 29 for a classical work on the topic of Galileon inspired inflation.

International Journal of Modern Physics, 2009

Inflation is today a part of the Standard Model of the Universe supported by the cosmic microwave background (CMB) and large scale structure (LSS) datasets. Inflation solves the horizon and flatness problems and naturally generates density fluctuations that seed LSS and CMB anisotropies, and tensor perturbations (primordial gravitational waves). Inflation theory is based on a scalar field ϕ (the inflaton) whose potential is fairly flat leading to a slow-roll evolution. This review focuses on the following new aspects of inflation. We present the effective theory of inflation à la Ginsburg-Landau in which the inflaton potential is a polynomial in the field ϕ and has the universal form , where w = O(1), M ≪ M P l is the scale of inflation and N ∼ 60 is the number of efolds since the cosmologically relevant modes exit the horizon till inflation ends. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings become naturally small as powers of the ratio (M/M P l ) 2 . The spectral index and the ratio of tensor/scalar fluctuations are ns -1 = O(1/N ), r = O(1/N ) while the running index turns to be dns/d ln k = O(1/N 2 ) and therefore can be neglected. The energy scale of inflation M ∼ 0.7 × 10 16 GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov Chains (MCMC) analysis of the available CMB+LSS data (including WMAP5) with fourth degree trinomial potentials showed: (a) the spontaneous breaking of the ϕ → -ϕ symmetry of the inflaton potential. (b) a lower bound for r in new inflation: r > 0.023 (95% CL) and r > 0.046 (68% CL). (c) The preferred inflation potential is a double well, even function of the field with a moderate quartic coupling yielding as most probable values: ns ≃ 0.964, r ≃ 0.051. This value for r is within reach of forthcoming CMB observations. The present data in the effective theory of inflation clearly prefer new inflation. Study of higher degree inflaton potentials show that terms of degree higher than four do not affect the fit in a significant way. In addition, horizon exit happens for ϕ/[ √ N M P l ] ∼ 0.9 making higher order terms in the potential w negligible. We summarize the physical effects of generic initial conditions (different from Bunch-Davies) on the scalar and tensor perturbations during slow-roll and introduce the transfer function D(k) which encodes the observable initial conditions effects on the power spectra. These effects are more prominent in the low CMB multipoles: a change in the initial conditions during slow roll can account for the observed CMB quadrupole suppression. Slowroll inflation is generically preceded by a short fast-roll stage. Bunch-Davies initial conditions are the natural initial conditions for the fast-roll perturbations. During fast-roll, the potential in the wave equations of curvature and tensor perturbations is purely attractive and leads to a suppression of the curvature and tensor CMB quadrupoles. A MCMC analysis of the WMAP+SDSS data including fast-roll shows that the quadrupole mode exits the horizon about 0.2 efold before fastroll ends and its amplitude gets suppressed. In addition, fast-roll fixes the initial inflation redshift to be zinit = 0.9 × 10 56 and the total number of efolds of inflation to be Ntot ≃ 64. Fast-roll fits the TT, the TE and the EE modes well reproducing the quadrupole supression. A thorough study of the quantum loop corrections reveals that they are very small and controlled by powers of (H/M P l ) 2 ∼ 10 -9 , a conclusion that validates the reliability of the effective theory of inflation. The present review shows how powerful is the Ginsburg-Landau effective theory of inflation in predicting observables that are being or will soon be contrasted to observations. Contents I. Introduction to the Effective Theory of Inflation A. Overview and present status of inflation B. The Standard Cosmological Model C. The Horizon and Flatness problems in non-inflationary cosmology and their inflationary resolution. 1. The horizon problem 2. The flatness problem 3. The solution to the horizon problem in inflation 4. The solution to the flatness problem in inflation 5. The Entropy of the Universe 6. The Age of the Universe D. Inflationary Dynamics in the Effective Theory of Inflation 1. Inflation and Inflaton field dynamics 2. Slow-roll, the Universal Form of the Inflaton Potential and the Energy Scale of Inflation 3. Inflationary Dynamics: Homogeneous Inflaton 4. Fixing the Total Number of Inflation e-folds from Fast-Roll and the CMB Quadrupole suppression E. Gauge invariant Scalar and Tensor Fluctuations 1. Scalar Curvature Perturbations 2. Tensor Perturbations 3. Initial conditions 4. The power spectrum of adiabatic scalar and tensor perturbations 5. The energy scale of inflation and the quasi-scale invariance during inflation. II. Theoretical predictions, MCMC data analysis, early fast-roll stage and CMB quadrupole suppression. A. Ginsburg-Landau polynomial realizations of the Inflaton Potential 1. Binomial inflaton potentials for chaotic inflation 2. Binomial inflaton potentials for new inflation 3. Contrasting the results of new and chaotic binomial inflation. B. Trinomial Chaotic Inflation: Spectral index, amplitude ratio, running index and limiting cases 1. The small asymmetry regime: -1 < h ≤ 0. 2. The flat potential limit h → -1 + 3. The singular limit z = 1 and then h → -1 + yields the Harrison-Zeldovich spectrum 4. The high asymmetry h < -1 regime. C. Trinomial New Inflation: Spectral index, amplitude ratio, running index and limiting cases 1. The weak coupling limit y → 0 2. The strong coupling limit y → ∞ 3. The extremely asymmetric limit |h| → ∞ 4. Regions of n s and r covered by New Inflation and by Chaotic Inflation. D. The Monte Carlo Markov Chain Method of Data Analysis 1. CMB, LSS and Inflation within a MCMC analysis. 2. MCMC results for Trinomial New Inflation. 3. MCMC results for Chaotic Trinomial Inflation. E. Higher degree terms in inflaton potentials 1. Family of models 2. Broken Symmetry models. 3. Field reconstruction for new inflation 4. Chaotic inflation models. 5. Field reconstruction for chaotic inflation 6. Conclusions