Speaker
Description
We derive a formula for the post-Newtonian parameter $\gamma$ in $f(R)$ gravity in a straightforward manner without using a scalar-tensor representation or the transformation to the Einstein frame.
The post-Newtonian parameters, defined in the parametrized post-Newtonian formalism, have been used in placing observational constraints on modified theories of gravity with local gravity tests.
In $f(R)$ gravity, it has been shown that $\gamma \approx 1/2$ for the case of light mass of the field $\partial_{R} f$, which is manifestly inconsistent with the constraint $|\gamma -1| \leq 10^{-4}$ obtained from local gravity tests.
For the case that the effective mass of the field $\partial_{R} f$ becomes large in the solar-system scale, the effect of the gravity modification would be suppressed due to the chameleon mechanism, and the observational constraint could be satisfied.
An explicit formula for the parameter $\gamma$, however, has not been obtained for that case.
In our approach, we employ a cosmological post-Newtonian approximation, and carefully make an order-of-magnitude estimate of each term in the field equations for the derivation.
This approximation enables us to treat local-scale high-density regions, in which the chameleon mechanism would take place.
Our results update the previously known ones and provide more stringent constraints from local gravity tests than before.
