# Implications of a frame dependent gravitational effective action for perturbations on the Robertson-Walker Metric

## TL;DR

This paper explores how a frame-dependent gravitational effective action influences scalar perturbations in cosmology, showing no change to gravitational wave propagation but potential observable effects on scalar fluctuations.

## Contribution

It demonstrates that a specific frame-dependent effective action modifies scalar perturbation equations without affecting tensor modes or gravitational waves.

## Key findings

- Scalar perturbation equations include Hubble scale modifications.
- Tensor and vector perturbations remain unchanged.
- No propagating wave solutions for scalar modifications.

## Abstract

In earlier work we showed that a frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson-Walker (RW) spacetimes. Here we study the implications of this effective action for small fluctuations around a spatially flat RW background geometry. The equations for the conserving extension of the modified stress-energy tensor can be integrated in closed form, and involve only the metric perturbation $h_{00}$. Hence the equations for tensor and vector perturbations are unmodified, but there are Hubble scale additions to the scalar perturbation equations, which nonetheless admit no propagating wave solutions. Consequently, there are no modifications to standard gravitational wave propagation theory, but there may be observable implications for cosmology. We give a self-contained discussion, including an analysis of the restricted class of gauge transformations that act when a frame dependent effective action is present.