Evolution of Structures in Generalized Gravity Theories

TL;DR

This paper explores the evolution of structures in generalized gravity theories by leveraging their conformal equivalence to Einstein's gravity with a scalar field, deriving perturbation equations, and analyzing their asymptotic behavior.

Contribution

It introduces a unified framework for analyzing scalar and tensor perturbations in generalized gravity theories using conformal transformations.

Findings

Derived background and perturbation equations for generalized Einstein's gravity.

Presented asymptotic solutions for perturbations in these theories.

Identified conserved quantities governing large-scale evolution.

Abstract

A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the equations for the background and the perturbations, and the general asymptotic solutions for the perturbations in the generalized Einstein's gravity from the simple results known in the minimally coupled scalar field. Results for the scalar and tensor perturbations can be presented in unified forms. The large scale evolutions for both modes are characterized by corresponding conserved quantities. We also present the normalization condition for canonical quantization.