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

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, ϕ_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 ϕ_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.

9 pages, RevTex

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• Cosmological variation of the MOND constant: secular effects on galactic systems
• Nonlocal Metric Realizations of MOND
• Effect of transitions in the Planck mass during inflation on primordial power spectra
• Time evolution of the local gravitational parameters and gravitational wave polarizations in a relativistic MOND theory
• Post-Newtonian parameters in the tensor-vector-scalar theory
• ΛCDM with baryons vs. MOND: the time evolution of the universal acceleration scale in the Magneticum simulations
• Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND
• Elucidating the z-dependence of the MOND acceleration (a_0) within the Scale Invariant Vacuum (SIV) paradigm
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• Comparison of HMG and flat rotation velocities inferred from galaxy-galaxy weak lensing