Constraints on scalar-tensor theories of gravity from observations

TL;DR

This paper investigates how observations of the universe's expansion and structure growth can constrain scalar-tensor theories of gravity, potentially ruling out or confirming their viability in explaining cosmic acceleration.

Contribution

It demonstrates that the growth index parameter's evolution is crucial for distinguishing scalar-tensor gravity models from dark energy models using observational data.

Findings

Linear density perturbations tightly constrain scalar-tensor theories.

Models with Z(φ)=1 exhibit convex evolution shapes.

Future observations can potentially rule out or confirm viable scalar-tensor models.

Abstract

In spite of their original discrepancy, both dark energy and modified theory of gravity can be parameterized by the effective equation of state (EOS) $\omega$ for the expansion history of the Universe. A useful model independent approach to the EOS of them can be given by so-called Chevallier-Polarski-Linder (CPL) parametrization where two parameters of it ($\omega_{0}$ and $\omega_{a}$) can be constrained by the geometrical observations which suffer from degeneracies between models. The linear growth of large scale structure is usually used to remove these degeneracies. This growth can be described by the growth index parameter $\gamma$ and it can be parameterized by $\gamma_{0} + \gamma_{a} (1 - a)$ in general. We use the scalar-tensor theories of gravity (STG) and show that the discernment between models is possible only when $\gamma_a$ is not negligible. We show that the linear density perturbation of the matter component as a function of redshift severely constrains the viable subclasses of STG in terms of $\omega$ and $\gamma$. From this method, we can rule out or prove the viable STG in future observations. When we use $Z(\phi) =1$, $F$ shows the convex shape of evolution in a viable STG model. The viable STG models with $Z(\phi) = 1$ are not distinguishable from dark energy models when we strongly limit the solar system constraint.