Constrain the linear scalar perturbation theory of Cotton gravity

TL;DR

This paper tests Cotton gravity against cosmological data, deriving its scalar perturbation theory and constraining its parameters, finding no significant deviation from the standard $\\Lambda$CDM model.

Contribution

It develops the linear scalar perturbation theory for Cotton gravity and constrains its parameters using cosmological observations, a novel approach in this gravity model.

Findings

Parameter $\beta$ constrained to near zero with tight confidence intervals.

No significant deviation from $\Lambda$CDM observed in linear perturbations.

Cotton gravity remains consistent with current cosmological data.

Abstract

We perform a cosmological test of Cotton gravity, which describes gravity by cotton tensor. We assume in Cotton gravity the background evolution is the same as the flat FLRW background. We derive the cosmological perturbation theory of the scalar mode at the linear level, where the difference from the $\Lambda$CDM model is characterized by the parameter $\beta$. We incorporate Cotton gravity with a neutrino model and perform a Monte Carlo Markov Chain (MCMC) analysis using data from the Cosmic Microwave Background (CMB) and Sloan Digital Sky Survey (SDSS). The analysis constrains parameter $\beta=-0.00008^{+0.00080}_{-0.00104}$ at the 1-$\sigma$ confidence level. We conclude that currently, there is no obvious deviation between Cotton gravity and the $\Lambda$CDM model in the linear cosmological perturbation level for observations.