General Slow-Roll Inflation in f(R) Gravity under the Palatini Approach

Sabit Bekov,Diego Sáez-Chillón Gómez,Kairat Myrzakulov,Ratbay Myrzakulov

doi:10.3390/sym12121958

Sabit Bekov, Diego Sáez-Chillón Gómez + Show 2 more

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https://doi.org/10.3390/sym12121958

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Abstract

Slow-roll inflation is analyzed in the context of modified gravity within the Palatini formalism. As shown in the literature, inflation in this framework requires the presence of non-traceless matter; otherwise, it does not occur just as a consequence of the nonlinear gravitational terms of the action. Nevertheless, by including a single scalar field that plays the role of the inflaton, slow-roll inflation can be performed in these theories, where the equations lead to an effective potential that modifies the dynamics. We obtain the general slow-roll parameters and analyze a simple model to illustrate the differences introduced by the gravitational terms under the Palatini approach, and the modifications on the spectral index and the tensor to scalar ratio predicted by the model.

Highlights

IntroductionGeneral Relativity and other theories constructed from scalar invariants of the Riemann and Ricci tensors assume a metric compatible connection, the so-called Levi–Civita connection, which states that
General Relativity and other theories constructed from scalar invariants of the Riemann and Ricci tensors assume a metric compatible connection, the so-called Levi–Civita connection, which states that∇λ gμν = 0 and the gravitational action is constructed in terms of such connection and its derivatives.one may consider both objects in principle as independent fields at the level of the action and applying the variational principle to obtain the field equations for both, this is the so-calledPalatini approach
We aim to obtain the general slow-roll condition with an arbitrary f (R) action in the Palatini formalism with the presence of a scalar field that plays the role of the inflaton that slow rolls, i.e., its kinetic term is very small in comparison to its potential at the beginning of inflation

Summary

Introduction

General Relativity and other theories constructed from scalar invariants of the Riemann and Ricci tensors assume a metric compatible connection, the so-called Levi–Civita connection, which states that. Ricci tensor is constructed in terms of an arbitrary connection, the theory does not lead to General. The so-called Palatini f (R) gravity, where R = gμν Rμν (Γ) with Γ a independent field, has been widely analyzed in the literature. The modifications on the energy conditions have been studied in [22], and the possible violations of the local gravity tests have been analyzed with the post-Newtonian approach applied to this type of theories [23], as well as the stellar structure [24] and the junction conditions [25], where significant and interesting differences are found. In a more analytic context, the variational principle [26], the Cauchy problem [27] and Birkhoff’s theorem have been explored [28]; in addition, a possible mapping among solutions in GR and these theories are given in [29]

Objectives

Conclusion