Do Newton's G and Milgrom's a_0 vary with cosmological epoch ?

TL;DR

This paper investigates whether Newton's gravitational constant G and Milgrom's acceleration scale a_0 vary over cosmological time using TeVeS theory, finding G is constant and a_0 varies very slowly, aligning with observational data.

Contribution

It provides a detailed calculation of G_N and a_0 dependence on TeVeS parameters and cosmological scalar field, showing G_N is constant and a_0 varies minimally over time.

Findings

G_N remains constant in atomic units, consistent with empirical limits.

a_0 depends on the scalar field and varies slowly, imperceptible back to redshift unity.

Variation of a_0 occurs on timescales much longer than the Hubble time.

Abstract

In the scalar tensor gravitational theories Newton's constant G_N evolves in the expanding universe. Likewise, it has been speculated that the acceleration scale a_0 in Milgrom's modified Newtonian dynamics (MOND) is tied to the scale of the cosmos, and must thus evolve. With the advent of relativistic implementations of the modified dynamics, one can address the issue of variability of the two gravitational ''constants'' with some confidence. Using TeVeS, the Tensor-Vector-Scalar gravitational theory, as an implementation of MOND, we calculate the dependence of G_N and a_0 on the TeVeS parameters and the coeval cosmological value of its scalar field, \phi_c. We find that G_N, when expressed in atomic units, is strictly nonevolving, a result fully consistent with recent empirical limits on the variation of G_N. By contrast, we find that a_0 depends on \phi_c and may thus vary with cosmological epoch. However, for the brand of TeVeS which seems most promising, a_0 variation occurs on a timescale much longer than Hubble's, and should be imperceptible back to redshift unity or even beyond it. This is consistent with emergent data on the rotation curves of disk galaxies at significants redshifts.