Newton's constant in f(R,R_{\mu \nu}R^{\mu \nu},\Box R) theories of gravity and constraints from BBN

TL;DR

This paper investigates modifications to gravity involving higher order and nonlocal terms, deriving an effective Newtonian constant and using BBN and local constraints to test the viability of these theories.

Contribution

It derives an effective Newtonian constant in complex gravity theories and applies BBN and local constraints to evaluate their viability.

Findings

Constraints on the effective Newtonian constant from BBN.

Limits on the $ox R$ correction from primordial nucleosynthesis.

Viability assessments of modified gravity models based on observational bounds.

Abstract

We consider corrections to the Einstein-Hilbert action which contain both higher order and nonlocal terms. We derive an effective Newtonian gravitational constant applicable at the weak field limit and use the primordial nucleosynthesis (BBN) bound and the local gravity constraints on $G_{eff}$ in order to test the viability of several cases of our general Lagrangian. We will also provide a BBN constrain on the $\Box R$ gravitational correction.