Fourth order gravity and experimental constraints on Eddington parameters

TL;DR

This paper explores the parametrized post-Newtonian (PPN) limits of higher-order gravity theories, demonstrating that certain polynomial $f(R)$ models align with experimental constraints and general relativity.

Contribution

It generalizes the PPN-limit formulation for scalar-tensor and fourth-order gravity theories using $f(R)$ derivatives, identifying models compatible with experimental data.

Findings

Certain third-order polynomial $f(R)$) theories are compatible with PPN constraints.

Deviations from General Relativity in these models agree with experimental data.

The approach extends the understanding of gravity theories beyond Einstein's framework.

Abstract

PPN-limit of higher order theories of gravity represents a still controversial matter of debate and no definitive answer has been provided, up to now, about this issue. By exploiting the analogy between scalar-tensor and fourth-order theories of gravity, one can generalize the PPN-limit formulation. By using the definition of the PPN-parameters $\gamma$ and $\beta$ in term of the $f(R)$ derivatives, we show that a family of third-order polynomial theories, in the Ricci scalar $R$, turns out to be compatible with the PPN-limit and the deviation from General Relativity theoretically predicted agree with experimental data.