The Early-time Cosmology with Stiff Era from Modified Gravity

TL;DR

This paper explores incorporating a stiff era into early universe cosmology within $F(R)$ gravity, analyzing its effects on inflation, baryogenesis, and gravitational waves, and proposing models consistent with standard cosmology.

Contribution

It introduces a novel $F(R)$ gravity model that includes a stiff era following inflation, linking it to baryogenesis and gravitational wave predictions.

Findings

Stiff era can coexist with standard cosmology phases.

Baryon-to-entropy ratio constrains $F(R)$) models.

Primordial gravitational waves provide additional constraints.

Abstract

In this work, we shall incorporate a stiff era in the Universe's evolution in the context of $F(R)$ gravity. After deriving the vacuum $F(R)$ gravity, which may realize a stiff evolution, we combine the stiff $F(R)$ gravity with an $R^2$ model, and we construct a qualitative model for the inflationary and stiff era, with the latter commencing after the end of the inflationary era. We assume that the baryogenesis occurs during the stiff era, and we calculate the baryon to entropy ratio, which effectively constraints the functional form of the stiff $F(R)$ gravity. Further constraints on the stiff $F(R)$ gravity may come from the primordial gravitational waves, and particularly their scalar mode, which is characteristic of the $F(R)$ gravity theory. The stiff era presence does not contradict the standard cosmology era, namely, inflation, and the radiation-matter domination eras. Furthermore, we investigate which $F(R)$ gravity may realize a dust and stiff matter dominated Einstein-Hilbert evolution.