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

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, vertical bar a(2)vertical bar < 1.33 x 10(12) 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 vertical bar a(2)vertical bar greater than or similar to 10(17) m(2) and vertical bar a(2)vertical bar less than or similar to 1.2 x 10(18) m(2) respectively and it is complementary to the stringent ones provided by lab based experiments, like the Eot-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).