Gravitational constant in multiple field gravity

TL;DR

This paper derives an expression for the effective Newton's constant in a broad class of multiple scalar field gravity theories with non-canonical kinetic terms, analyzing its behavior in different frames and energy-momentum conservation.

Contribution

It introduces a general framework for calculating the effective Newton's constant in multi-field gravity models with complex Lagrangians, extending previous single-field results.

Findings

Effective Newton's constant derived for general multi-field Lagrangian

Analysis conducted in both Jordan and Einstein frames

Insights into energy-momentum conservation in these models

Abstract

In the present study, we consider general form of the Lagrangian $ f(R, \phi^{I}, X) $, that is a function of the Ricci scalar, multiple scalar fields and non-canonical kinetic terms. We obtain the effective Newton's constant deep inside the Hubble radius. We use Jordan and Einstein frames, and study the conservation of energy-momentum tensor.