The relaxed Einstein equations in the context of a mixed UV-IR modified theory of gravity

Abstract

In this article we will modify the Einstein field equations by promoting Newton’s constant G to a covariant differential operator composed of two terms which operate in different energy regimes (IR and UV). The IR term inside the covariant differential operator acts like a high-pass filter with a macroscopic distance filter scale and effectively degravitates energy sources characterized by wavelengths larger than the filter scale. While this term is predominant for cosmological energy processes it is almost inessential on astrophysical scales where the UV contribution inside leads to much stronger deviations compared to GR. In the context of this particular theory of gravity we work out the effective relaxed Einstein equations, the effective 1.5 post-Newtonian near zone mass for n-body systems as well as the IR and UV modified Schwarzschild metrics. We use these results in the context of the Double Pulsar binary system and observe that we recover, in the limit of vanishing UV-IR modification parameters, the corresponding general relativistic results.