Minimal exponential measure model in the post-Newtonian limit

TL;DR

This paper analyzes the minimal exponential measure (MEMe) gravity model in the post-Newtonian regime, extending the PPN formalism to constrain the model's parameters using gravitational measurements, showing potential for significantly tighter bounds.

Contribution

The paper develops an extended PPN formalism for the MEMe model and demonstrates how precision gravitational measurements can greatly improve parameter constraints.

Findings

The behavior of the MEMe model closely matches general relativity for realistic parameters.

The monopole term of the gravitational potential is calculated within the MEMe framework.

Constraints on the model parameter q can be improved by up to 10 orders of magnitude using precision measurements.

Abstract

We examine the post-Newtonian limit of the minimal exponential measure (MEMe) model presented in [J. C. Feng, S. Carloni, Phys. Rev. D 101, 064002 (2020)] using an extension of the parameterized post-Newtonian (PPN) formalism which is also suitable for other type-I minimally modified Gravity theories. The new PPN expansion is then used to calculate the monopole term of the post-Newtonian gravitational potential and to perform an analysis of circular orbits within spherically symmetric matter distributions. The latter shows that the behavior does not differ significantly from that of general relativity for realistic values of the MEMe model parameter $q$. Instead the former shows that one can use precision measurements of Newton's constant $G$ to improve the constraint on $q$ by up to $10$ orders of magnitude.