# Modified Gravity Away from a $\Lambda$CDM Background

## TL;DR

This paper investigates how modified gravity theories, specifically No Slip Gravity, affect cosmic expansion and structure formation, providing new computational tools and constraints based on current observational data.

## Contribution

It introduces a generalized background in No Slip Gravity, explores its effects on cosmological observables, and releases an updated code for further research.

## Key findings

- Maximum Planck mass running |α_M| ≲ 0.03
- Viable positive ISW cross-correlation from modified gravity
- Enhanced gravitational freedom in non-ΛCDM backgrounds

## Abstract

Within the effective field theory approach to cosmic acceleration, the background expansion can be specified separately from the gravitational modifications. We explore the impact of modified gravity in a background different from a cosmological constant plus cold dark matter ($\Lambda$CDM) on the stability and cosmological observables, including covariance between gravity and expansion parameters. In No Slip Gravity the more general background allows more gravitational freedom, including both positive and negative Planck mass running. We examine the effects on cosmic structure growth, as well as showing that a viable positive integrated Sachs-Wolfe effect crosscorrelation easily arises from this modified gravity theory. Using current data we constrain parameters with a Monte Carlo analysis, finding a maximum running $|\alpha_M|\lesssim 0.03$. We provide the modified {\tt hi\_class} code publicly on GitHub, now enabling computation and inclusion of the redshift space distortion observable $f\sigma_8$ as well as the No Slip Gravity modifications.