Large-scale structure power spectrum from scalar-tensor gravity

TL;DR

This paper investigates the large-scale structure power spectrum in scalar-tensor gravity, revealing how different $f(R)$ models influence the evolution and features of the matter power spectrum, supporting the equivalence with $f(R)$ theories.

Contribution

It applies a dynamical system approach and $1+3$ covariant formalism to analyze the matter power spectrum in scalar-tensor gravity, extending understanding of $f(R)$ and scalar-tensor equivalence.

Findings

Power spectrum evolves above the scale-invariant line for $1<n<1.3$.

For $n extgreater=1.3$, the spectrum shows oscillations and saturation.

Results align with previous observations and support $f(R)$ and scalar-tensor theory equivalence.

Abstract

This work deals with the computation of the power spectrum of large-scale structure using the dynamical system approach for a multi-fluid universe in scalar-tensor theory of gravity. We use the $1+3$ covariant approach to obtain evolution equations and study the behavior of the matter power spectrum of perturbation equations. The study is based on the equivalence between $f(R)$ theory of gravity and scalar-tensor theory of gravity. We find that, for power-law $(R^{n})$ models, with $1<n<1.3$, we have the power spectrum evolving above general relativistic scale-invariant line. For $n\geq 1.3$, the power spectrum starts with constant amplitude then it experiences oscillations and eventually saturates at finite amplitude. Such behavior is consistent with other observations in the literature. The result supports the ongoing investigations of the equivalence between $f(R)$ and scalar-tensor theory at linear order.