Constraining theories of gravity by GINGER experiment

Salvatore Capozziello,Giorgio Carelli,Giuseppe Terreni,Donatella Ciampini,Nicolò Beverini,Umberto Giacomelli,Raffaele Velotta,Francesco Bajardi,Andrea Basti,Enrico Maccioni,Angela D V Di Virgilio,Paolo Marsili,Antonello Ortolan,Alberto Porzio,Carlo Altucci,Francesco Fuso,Andrea Simonelli

doi:10.1140/epjp/s13360-021-01373-4

Abstract

The debate on gravity theories to extend or modify general relativity is very active today because of the issues related to ultraviolet and infrared behavior of Einstein’s theory. In the first case, we have to address the quantum gravity problem. In the latter, dark matter and dark energy, governing the large-scale structure and the cosmological evolution, seem to escape from any final fundamental theory and detection. The state of the art is that, up to now, no final theory, capable of explaining gravitational interaction at any scale, has been formulated. In this perspective, many research efforts are devoted to test theories of gravity by space-based experiments. Here, we propose straightforward tests by the GINGER experiment, which, being Earth based, requires little modeling of external perturbation, allowing a thorough analysis of the systematics, crucial for experiments where sensitivity breakthrough is required. Specifically, we want to show that it is possible to constrain parameters of gravity theories, like scalar–tensor or Horava–Lifshitz gravity, by considering their post-Newtonian limits matched with experimental data. In particular, we use the Lense–Thirring measurements provided by GINGER to find out relations among the parameters of theories and finally compare the results with those provided by LARES and Gravity Probe B satellites.

Highlights

We use the Lense–Thirring measurements provided by GINGER to find out relations among the parameters of theories and compare the results with those provided by LARES and Gravity Probe B satellites
We propose to constrain theories of gravity exploiting the expected sensitivity on relativistic precessions of the GINGER (Gyroscopes IN General Relativity) experiment
From Eq (44), we obtain that the effective gravitational constant of Horava–Lifshitz gravity is related to the Newtonian constant through the numerical relation

Summary

Introduction

We shall take into account metric theories, whose action includes curvature invariants and scalar fields Another theory which we are going to test is the Horava–Lifshitz gravity which we shall describe below. As mentioned in Introduction, modified theories of gravity aim to relax some assumption of GR, as well as that of second-order field equations or symmetric connections, while extended theories retain the fundamental assumptions of GR but take into account further ingredients into the gravitational actions like curvature invariants and scalar fields. As an example of alternative theory to GR, we consider the Horava–Lifshitz gravity, proposed by Horava in [63] It has been formulated as an effective quantum gravity approach not requiring the Lorentz invariance at fundamental ultraviolet scales. A a gauge field depending on spatial coordinates and time

The Kerr solution and the Lense–Thirring precession

The PPN formalism in higher-order scalar–tensor gravity

The PPN formalism in Horava–Lifshitz Gravity

G H L M sin α sin θ R

Findings

Discussion and conclusions