Probing modified gravity theories with the Sandage-Loeb test

TL;DR

This study evaluates how future Sandage-Loeb test measurements can significantly improve constraints on modified gravity theories, especially when combined with existing cosmological data, by breaking parameter degeneracies.

Contribution

It demonstrates that the Sandage-Loeb test can effectively break degeneracies in modified gravity models and provide complementary constraints beyond current observational methods.

Findings

Sandage-Loeb test improves constraints when combined with CMB data.

It breaks degeneracies between model parameters.

Provides unique parameter bounds for $f(R)$ gravity.

Abstract

In this paper, we quantify the ability of a future measurement of the Sandage-Loeb test signal from the Cosmic-Dynamic-Experiment-like spectrograph to constrain some popular modified gravity theories including DGP brane-world scenario, $f(R)$ modified gravity and $f(T)$ gravity theory. We find that the Sandage-Loeb test measurements are able to break degeneracies between model parameters markedly and thus greatly improve cosmological constraints for all concerned modified gravity theories when combined with the latest observations of CMB--shift parameter. However, they yield almost the same degeneracy directions between model parameters as that from the distance ratio data derived from the latest observations of the cosmic microwave background and baryonic acoustic oscillations (CMB/BAO). Moreover, for the $f(R)$ modified gravity, the Sandage-Loeb test could provide completely different bounded regions in model parameters space as compared to CMB/BAO and thus supplement strong complementary constraints.