$\mathcal{R}^2$ effectively from Inflation to Dark Energy

TL;DR

This paper explores how a simple modified gravity model with an $ ext{R}^2$ term can connect early universe inflation to late-time dark energy, using astrophysical and laboratory constraints.

Contribution

It establishes a natural relation between the $ ext{R}^2$ coefficient and the cosmological constant, linking high-energy physics to cosmological evolution.

Findings

The $ ext{R}^2$ coefficient is constrained by astrophysical data.

Renormalization of $c$ correlates inflationary energy with dark energy.

The $ ext{R}^2$ term may unify inflation and dark energy phenomena.

Abstract

We consider the single-parameter $\mathcal{R}+ c\mathcal{R}^2$ gravitational action and use constraints from astrophysics and the laboratory to derive a natural relation between the coefficient $c$ and the value of the cosmological constant. We find that the renormalisation of $c$ from the energy of the inflationary phase to the infrared, where the acceleration of the expansion of the Universe takes place, is correlated with the evolution of the vacuum energy. Our results suggest that the coefficient of the $\mathcal{R}^2$ term may provide an unexpected bridge between high-energy physics and cosmological phenomena such as inflation and dark energy.