Cyclic cosmology from Lagrange-multiplier modified gravity

TL;DR

This paper explores cyclic, singularity-free cosmological models within Lagrange-multiplier modified gravity frameworks, including scalar-field and $f(R)$ theories, analyzing their background evolution and stability of perturbations.

Contribution

It introduces reconstructed potentials and functions in Lagrange-multiplier modified gravity to achieve cyclic cosmologies and studies their perturbation stability.

Findings

Cyclicity achieved with simple potentials in scalar-field models.

Stable perturbation behavior across the bounce in both scenarios.

Existence of oscillation modes indicating dynamical degrees of freedom in $f(R)$ models.

Abstract

We investigate cyclic and singularity-free evolutions in a universe governed by Lagrange-multiplier modified gravity, either in scalar-field cosmology, as well as in $f(R)$ one. In the scalar case, cyclicity can be induced by a suitably reconstructed simple potential, and the matter content of the universe can be successfully incorporated. In the case of $f(R)$-gravity, cyclicity can be induced by a suitable reconstructed second function $f_2(R)$ of a very simple form, however the matter evolution cannot be analytically handled. Furthermore, we study the evolution of cosmological perturbations for the two scenarios. For the scalar case the system possesses no wavelike modes due to a dust-like sound speed, while for the $f(R)$ case there exist an oscillation mode of perturbations which indicates a dynamical degree of freedom. Both scenarios allow for stable parameter spaces of cosmological perturbations through the bouncing point.