Bouncing inflation in nonlinear $R^2+R^4$ gravitational model

Abstract

We study a gravitational model with curvature-squared R 2 and curvature-quartic R 4 nonlinearities. The effective scalar degree of freedom φ (scalaron) has a multi-valued potential U (φ) consisting of a number of branches. These branches are fitted with each other in the branching and monotonic points. In the case of four-dimensional space-time, we show that the monotonic points are penetrable for scalaron while in the vicinity of the branching points scalaron has the bouncing behavior and cannot cross these points. Moreover, there are branching points where scalaron bounces an infinite number of times with decreasing amplitude and the Universe asymptotically approaches the de Sitter stage. Such accelerating behavior we call bouncing inflation. For this accelerating expansion there is no need for original potential U (φ) to have a minimum or to check the slow-roll conditions. A necessary condition for such inflation is the existence of the branching points. This is a new type of inflation. We show that bouncing inflation takes place both in the Einstein and Brans-Dicke frames.

Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

“…The bounces preceding the inflationary phase, were proposed in Refs. [243][244][245][718][719][720], and these are known as the "bounce inflation scenario". An interesting proposal that appeared in the literature was the singular bounce [192] in which case a soft Type IV singularity occurs at the bounce point.…”

Viability of the intermediate inflation scenario with F(T) gravity

“…[59,60]. An interesting scenario could be that before the intermediate inflation scenario occurs, a contracting bouncing phase occurs, like in bounce inflation scenarios [61][62][63]. This scenario could be realized in the context of modified gravity, but we defer this project to a future work.…”

A polynomial f(R) inflation model

“…See [15][16][17][18] and [19] for a review. The full dynamics for n = 4 is analyzed in [20] in detail. In this paper we focus on another limit, namely λ n ≪ 1 and the term of R n can be taken as a small correction to the Starobinsky's inflation model.…”