Confronting Rainbow-deformed $f(R)$ Gravity with the ACT Data

TL;DR

This paper explores a combined quantum-inspired modification of inflationary cosmology involving gravity's rainbow and $f(R)$ gravity, demonstrating compatibility with ACT observational data and analyzing different $f(R)$ models.

Contribution

It introduces a novel model merging gravity's rainbow effects with $f(R)$ gravity during inflation, showing its consistency with observational data and extending understanding of quantum gravity impacts on early universe.

Findings

The combined gravity's rainbow and $f(R)$ model aligns with ACT data.

Power-law $f(R)$ models are viable without extending slow-roll inflation.

Quantum effects can be imprinted in inflationary dynamics.

Abstract

In this work we examine a theoretical scenario which combines two fundamental theoretical proposals for the early Universe and a possible evolution for the early post-inflationary epoch. Specifically, we assume that the early Universe contains gravity's rainbow effects on the spacetime and the inflationary Lagrangian contains $R^2$ corrections or $f(R)$ gravity corrections in general. In addition we assume that the era beyond the end of inflation until the reheating temperature is reached, is a kination era. Both theories, $R^2$ and gravity's rainbow emerge from a quantum context so their effects should be first checked at the theory which connects the quantum with the classical, hence inflation. Spacetime is four dimensional and the effects of the quantum theory could possibly be imprinted in the inflationary Lagrangian and of course on the spacetime itself. For the gravity's rainbow deformed Starobinsky model, both Lagrangian quantum effects and spacetime quantum effects are combined. As we show the resulting theory is compatible with the ACT data. We also consider power-law $f(R)$ gravity deformations and we show that in this case, the model is viable without the need of extending the slow-roll era of inflation.