Can the degeneracies in the gravity sector be broken?

TL;DR

This paper investigates whether current and future growth rate measurements can distinguish modified gravity theories from the standard mbda CDM model, finding that significant improvements are needed for discrimination.

Contribution

The authors explicitly construct $f(R)$, $f(G)$, and $f(T)$ gravity models that replicate mbda CDM at the background level and analyze the observational data needed to differentiate them.

Findings

Current growth rate data cannot break the degeneracy.

A threefold improvement in data quality is required for discrimination.

Euclid-like surveys could achieve the necessary data precision.

Abstract

It has been long known that by appropriately modifying gravity one can always reproduce the expansion history of any dark energy model, e.g. the $\Lambda$CDM. This degeneracy cannot be broken with geometric probes like the Type Ia supernovae, the cosmic microwave background or the baryon acoustic oscillations since they are based on the measurement of distances and scales and therefore require the expansion history $H(z)$, so one may only hope to break this degeneracy by using dynamic probes like the growth rate data that track the matter density perturbations. We demonstrate that breaking this degeneracy is not currently possible by explicitly constructing $f(R)$, $f(G)$ and $f(T)$ theories that mimic exactly the $\Lambda$CDM model at the background level and confronting them against the latest observational cosmological data. We also determine the necessary improvement in the growth rate data in order to discriminate these theories from $\Lambda$CDM. We found that at least a threefold improvement is necessary, something which will be possible with a survey like Euclid.