Testing time-delayed cosmology

Abstract

Inspired by nonlocal gravity theories, time-delayed cosmology proposes a delayed Friedmann equation that generically predicts an inflationary period with a natural end. The key parameter of this proposal is a time delay that is presumed to be very small in order for the model to evade potential astrophysical constraints. This work subjects this small-delay assumption to a test. We address the question of just how large a time delay can be accommodated within our current cosmological data. In order to do so, we do not restrict the model to the inflationary era and consider its possible operation in the late Universe as well, with an eye for any smoking-gun features that may indicate the presence of a time delay. We study the background evolution predicted by the delayed Friedmann equation and determine the growth of Newtonian perturbations in this delayed background. We show that a surprisingly large late-time cosmic delay is statistically consistent with Hubble expansion rate and growth data. Based on these observables, we also find that the standard $$\varLambda $$ Λ CDM model has no advantage over time-delayed cosmology in terms of the Bayes factor.