Terrestrial Sagnac delay constraining modified gravity models

TL;DR

This paper investigates how terrestrial Sagnac delay measurements can constrain specific $f(R)$ gravity models, providing an alternative to cosmological and astrophysical tests by analyzing light beam time gaps around Earth's weak gravitational field.

Contribution

It introduces a method to use terrestrial Sagnac delay measurements to constrain $f(R)$ gravity parameters, extending previous astrophysical constraints to weak-field Earth-based experiments.

Findings

Sagnac delay deviations depend on Ricci curvature, mass, and spin.

Constraints on $f(R)$ parameters are comparable to those from strong-field phenomena.

The method offers a terrestrial test for modified gravity theories.

Abstract

Modified gravity theories include $f(\mathbf{R})-$gravity models that are usually constrained by the cosmological evolutionary scenario. However, it has been recently shown that they can also be constrained by the signatures of accretion disk around constant Ricci curvature Kerr-$f(\mathbf{R}_{0})$ stellar sized black holes. Our aim here is to use another experimental fact, viz., the terrestrial Sagnac delay to constrain the parameters of specific $f(\mathbf{R})-$gravity prescriptions. We shall assume that a Kerr-$f(\mathbf{R}_{0})$ solution asymptotically describes Earth's weak gravity near its surface. In this spacetime, we shall study oppositely directed light beams from source/observer moving on non-geodesic and geodesic circular trajectories and calculate the time gap, when the beams re-unite. We obtain the \textit{exact }time gap called Sagnac delay in both cases and expand it to show how the flat space value is corrected by the Ricci curvature, the mass and the spin of the gravitating source. Under the assumption that the magnitude of corrections are of the order of residual uncertainties in the delay measurement, we derive the allowed intervals for Ricci curvature. We conclude that the terrestrial Sagnac delay can be used to constrain the parameters of specific $f(\mathbf{R})$ prescriptions. Despite using the weak field gravity near Earth's surface, it turns out that the model parameter ranges still remain the same as those obtained from the strong field accretion disk phenomenon.