Some aspects of modified theory of gravity in Palatini formalism unveiled

TL;DR

This paper examines the modified Palatini gravity theory, revealing limitations in explaining early universe cosmology and correcting misconceptions about symmetry analysis related to the scalar field's kinetic term.

Contribution

It clarifies the issues with Palatini formalism in early universe cosmology and corrects previous misinterpretations regarding Noether symmetry analysis.

Findings

Palatini f(R) gravity acts as dark energy in late-time acceleration.

The formalism is inadequate for early universe cosmology.

Corrected symmetry analysis reveals new insights.

Abstract

Under conformal transformation, f(R) theory of gravity in Palatini formalism leads to a Brans-Dicke type of scalar-tensor equivalent theory with a wrong sign in the effective kinetic energy term. This means, the effective scalar acts as the dark energy and so late-time cosmic acceleration in matter-dominated era is accountable. However, we unveil some aspects of Palatini formalism, which clearly reveals the fact that the formalism is not suitable to explain the cosmological evolution of the early universe with $f(\mathfrak{R})$ gravity alone. Additionally, it is noticed that some authors, in an attempt to explore Noether symmetry of the theory changed the sign of the kinetic term and hence obtained the wrong answer. Here, we make the correction and unmask a very interesting aspect of symmetry analysis.