Structure formation in $f(R)$ gravity: A distinguishing probe between the dark energy and modified gravity

TL;DR

This paper investigates large-scale structure formation in $f(R)$ gravity within the Palatini formalism, comparing it to dark energy models to identify potential observational differences and methods for distinguishing these theories.

Contribution

It introduces a reconstruction method for universe dynamics and structure formation indicators in $f(R)$ gravity, highlighting differences from dark energy models and comparing Palatini and metric formalisms.

Findings

Modified gravity and dark energy models predict slightly different large-scale structures.

Growth index in modified gravity is scale-dependent, unlike in dark energy models.

Large SNIa datasets can help reconstruct $f(R)$ gravity and test cosmic acceleration.

Abstract

In this work, we study the large scale structure formation in the modified gravity in the framework of Palatini formalism and compare the results with the equivalent smooth dark energy models as a tool to distinguish between these models. Through the inverse method, we reconstruct the dynamics of universe, modified gravity action and the structure formation indicators like the screened mass function and gravitational slip parameter. Consequently, we extract the matter density power spectrum for these two models in the linear regime and show that the modified gravity and dark energy models predictions are slightly different from each other at large scales. It is also shown that the growth index in the modified gravity unlike to the dark energy models is a scale dependent parameter. We also compare the results with those from the modified gravity in the metric formalism. The modification on the structure formation can also change the CMB spectrum at large scales however due to the cosmic variance it is hard to detect this signature. We show that a large number of SNIa data in the order of 2000 will enable us to reconstruct the modified gravity action with a suitable confidence level and test the cosmic acceleration models by the structure formation.