Cosmological perturbations in conformal gravity II

TL;DR

This paper extends the analysis of cosmological perturbations in conformal gravity, providing the general solutions and showing how fluctuations evolve in conformal Robertson-Walker backgrounds, with implications for early universe cosmology.

Contribution

It presents the complete set of solutions for cosmological perturbations in conformal gravity and demonstrates their construction from flat background solutions, including growth behavior in the early universe.

Findings

Fluctuations around conformal backgrounds can be derived from flat background solutions.

In conformal Robertson-Walker cosmology, early universe fluctuations grow as t^4.

The paper provides a scalar, vector, tensor decomposition of fluctuations in conformal gravity.

Abstract

In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a flat background. For this construction to hold it is not necessary that the perturbative geometry associated with the fluctuations itself be conformal to flat. Using this construction we show that in a conformal Robertson-Walker cosmology early universe fluctuations grow as $t^4$. We present the scalar, vector, tensor decomposition of the fluctuations in the conformal theory, and compare and contrast our work with the analogous treatment of fluctuations in the standard Einstein gravity theory.