Constraining Post-Newtonian Parameters with the Cosmic Microwave Background

Abstract: The Parameterised Post-Newtonian (PPN) approach is the default framework for performing precision tests of gravity in nearby astrophysical systems. In recent works we have extended this approach for cosmological applications, and in this paper we use observations of the anisotropies in the Cosmic Microwave Background to constrain the time variation of the PPN parameters $\alpha$ and $\gamma$ between last scattering and the present day. We find their time-averages over cosmological history should be within $\sim 20\%$ of their values in GR, with $\bar{\alpha}=0.89^{+0.08}_{-0.09}$ and $\bar{\gamma}=0.90^{+0.07}_{-0.08}$ at the $68\%$ confidence level. We also constrain the time derivatives of these parameters, and find that their present-day values should be within a factor of two of the best Solar System constraints. Many of these results have no counter-part from Solar System observations, and are entirely new constraints on the gravitational interaction. In all cases, we find that the data strongly prefer $\bar{\alpha}\simeq \bar{\gamma}$, meaning that observers would typically find local gravitational physics to be compatible with GR, despite considerable variation of $\alpha$ and $\gamma$ being allowed over cosmic history. This study lays the groundwork for future precision tests of gravity that combine observations made over all cosmological and astrophysical scales of length and time.