The gyroscopic frequency of metric $f(R)$ and generalised Brans-Dicke theories: constraints from Gravity Probe-B

Abstract

We confront the predicted gyroscopic precession (in particular the geodetic precession) from metric $f(R)$ theory with the data provided by the mission, Gravity Probe--B. We find the constraint, $|a_2|<1.33\times 10^{12}{\mathrm{m}}^2$, where $a_2$ is the coefficient assessing the strength of the lowest order correction to the Einstein--Hilbert action for a metric $f(R)$ theory with $f$ analytic. This constraint improves over astrophysical bounds provided by massive black holes and planetary precession which are $|a_2|\gtrsim 10^{17}{\mathrm{m}}^2$ and $|a_2|\lesssim 1.2\times 10^{18}{\mathrm{m}}^2$ respectively and it is complementary to the stringent ones provided by lab based experiments, like the Eöt--Wash experiment. We also investigate the modification of our result for gyroscopic precession if the oblateness of Earth is taken into account by considering the quadrupole moment of Earth. Finally, we provide a generalisation of our result for the gyroscopic precession in the context of Brans--Dicke theories with a potential (recovering the previously derived results in the appropriate limits).

arXiv admin note: text overlap with arXiv:1903.10059

References in corpus (14)

• Gaia Data Release 1. Summary of the astrometric, photometric, and survey properties
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Dark Energy after GW170817 and GRB170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Metric-affine f(R) theories of gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• The Newtonian Limit of F(R) gravity
• On the 1/c Expansion of f(R) Gravity
• Massive gravitational waves from the R^2 theory of gravity: production and response of interferometers
• Covariant Effective Action for Loop Quantum Cosmology from Order Reduction
• Gravitoelectromagnetism in metric f(R) and Brans-Dicke theories with a potential

Cited by in corpus (1)

• Multipole analysis on gyroscopic precession in $f(R)$ gravity with irreducible Cartesian tensors