Are Scalar and Tensor Deviations Related in Modified Gravity?

TL;DR

This paper investigates whether scalar and tensor deviations in modified gravity are related, finding they are instantaneously independent but globally connected, with implications for combining cosmic structure and gravitational wave observations.

Contribution

The study analytically and numerically demonstrates the independence of scalar and tensor deviations in covariant Galileon gravity, highlighting their global relation and observational complementarity.

Findings

Scalar and tensor deviations can be independent at a given time.

Deviations are globally related if one persists over a period.

Results suggest combined surveys can better constrain modified gravity.

Abstract

Modified gravity theories on cosmic scales have three key deviations from general relativity. They can cause cosmic acceleration without a physical, highly negative pressure fluid, can cause a gravitational slip between the two metric potentials, and can cause gravitational waves to propagate differently, e.g. with a speed different from the speed of light. We examine whether the deviations in the metric potentials as observable through modified Poisson equations for scalar density perturbations are related to or independent from deviations in the tensor gravitational waves. We show analytically they are independent instantaneously in covariant Galileon gravity -- e.g. at some time one of them can have the general relativity value while the other deviates -- though related globally -- if one deviates over a finite period, the other at some point shows a deviation. We present expressions for the early time and late time de Sitter limits, and numerically illustrate their full evolution. This in(ter)dependence of the scalar and tensor deviations highlights complementarity between cosmic structure surveys and future gravitational wave measurements.