We reanalyze the nonlocal gravity model of Deser and Woodard, which was proposed to account for the current phase of cosmic acceleration. We show that the growth of perturbations predicted by this nonlocal gravity model when its background evolution is fixed by some particular non-Lambda-cold-dark-matter ($\mathrm{\Lambda }\mathrm{CDM}$) models can be substantially lower than when its background is fixed by $\mathrm{\Lambda }\mathrm{CDM}$. This can be seen when we consider the background expansion by a dark energy model with a slightly less negative equation of state with respect to cosmological constant. Our results hint towards a fact that the choice of the background expansion can play a crucial role in how this nonlocal gravity model can fit the growth history data. While the growth data might show better consistency to general relativity (GR) models (among the background models we studied so far), it seems the nonlocal gravity model studied in this work is able to show comparable consistency to the growth data as well. Showing this consistency can be considered as a significant result since this model can stand as a distinguishable alternative to the standard model of cosmology.

• Received 25 September 2016

DOI:https://doi.org/10.1103/PhysRevD.95.064061