Ghost-free $F(R)$ bigravity and accelerating cosmology

TL;DR

This paper introduces a ghost-free $F(R)$ bigravity model that allows for flexible cosmological evolution, including acceleration scenarios like phantom, quintessence, and $ ext{ extLambda}$CDM, through a new scalar-based formulation.

Contribution

It develops a ghost-free $F(R)$ bigravity framework using auxiliary scalars, simplifying the formulation and enabling detailed cosmological reconstruction.

Findings

Successfully reconstructs various accelerating cosmologies.

Demonstrates the model's ability to realize arbitrary universe evolutions.

Provides explicit examples of phantom, quintessence, and $ ext{ extLambda}$CDM$ acceleration.

Abstract

We propose a bigravity analogue of the $F(R)$ gravity. Our construction is based on recent ghost-free massive bigravity where additional scalar fields are added and the corresponding conformal transformation is implemented. It turns out that $F(R)$ bigravity is easier to formulate in terms of the auxiliary scalars as the explicit presentation in terms of $F(R)$ is quite cumbersome. The consistent cosmological reconstruction scheme of $F(R)$ bigravity is developed in detail, showing the possibility to realize nearly arbitrary physical universe evolution with consistent solution for second metric. The examples of accelerating universe which includes phantom, quintessence and $\Lambda$CDM acceleration are worked out in detail and their physical properties are briefly discussed.