Determining Cosmology for a Nonlocal Realization of MOND

Abstract

We numerically determine the cosmological branch of the free function in a nonlocal metric-based modification of gravity which provides a relativistic generalization of Milgrom's Modified Newtonian Dynamics. We are able to reproduce the $\Lambda$CDM expansion history over virtually all of cosmic history, including the era of radiation domination during Big Bang Nucleosynthesis, the era of matter domination during Recombination, and most of the era of vacuum energy domination. The very late period of $0 \leq z < 0.0880$, during which the model deviates from the $\Lambda$CDM expansion history, is interesting because it causes the current value of the Hubble parameter to be about 4.5\% larger than it would be for the $\Lambda$CDM model. This may resolve the tension between inferences of $H_0$ which are based on data from large redshift and inferences based on Hubble plots.