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

TL;DR

This paper investigates a nonlinear gravitational model with $R^2$ and $R^4$ terms, revealing a new bouncing inflation mechanism driven by scalaron dynamics near branching points, independent of traditional slow-roll conditions.

Contribution

It introduces a novel bouncing inflation phenomenon caused by scalaron bouncing at branching points in a nonlinear $R^2+R^4$ gravity model, without requiring a potential minimum or slow-roll.

Findings

Scalaron exhibits bouncing behavior near branching points.

Bouncing scalaron leads to asymptotic de Sitter inflation.

Bouncing inflation occurs in both Einstein and Brans-Dicke frames.

Abstract

We study a gravitational model with curvature-squared $R^2$ and curvature-quartic $R^4$ nonlinearities. The effective scalar degree of freedom $\phi$ (scalaron) has a multi-valued potential $U(\phi)$ 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 $U(\phi)$ 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.