Parametrization for the Scale Dependent Growth in Modified Gravity

TL;DR

This paper introduces a scale-dependent analytic approximation for the linear growth of density perturbations in Scalar-Tensor cosmologies, improving accuracy over traditional scale-independent models on large subhorizon scales.

Contribution

It presents a novel scale-dependent approximation that accounts for relativistic corrections, enhancing the modeling of perturbation growth in modified gravity theories.

Findings

The approximation significantly improves growth predictions on large subhorizon scales.

It demonstrates consistency across different gauges, validating the approach.

Compared to exact numerical solutions, the approximation offers better accuracy than standard models.

Abstract

We propose a scale dependent analytic approximation to the exact linear growth of density perturbations in Scalar-Tensor (ST) cosmologies. In particular, we show that on large subhorizon scales, in the Newtonian gauge, the usual scale independent subhorizon growth equation does not describe the growth of perturbations accurately, as a result of scale-dependent relativistic corrections to the Poisson equation. A comparison with exact linear numerical analysis indicates that our approximation is a significant improvement over the standard subhorizon scale independent result on large subhorizon scales. A comparison with the corresponding results in the Synchronous gauge demonstrates the validity and consistency of our analysis.