# Late-times asymptotic equation of state for a class of nonlocal theories of gravity

## TL;DR

This paper studies the late-time behavior of a class of nonlocal gravity theories, showing they tend to mimic a cosmological constant with a diverging Hubble rate, differing from standard models.

## Contribution

It demonstrates that most nonlocal gravity models asymptotically approach an equation of state of -1 and exhibit a diverging Hubble rate, expanding understanding of their late-time cosmological behavior.

## Key findings

- Effective equation of state approaches -1 at late times
- Hubble factor diverges monotonically in these models
- Behavior is consistent across models with vanishing initial conditions

## Abstract

We investigate the behavior of the asymptotic late-times effective equation of state for a class of nonlocal theories of gravity. These theories modify the Einstein-Hilbert Lagrangian introducing terms containing negative powers of the d'Alembert operator acting on the Ricci scalar. We find that imposing vanishing initial conditions for the nonlocal content during the radiation-dominated epoch implies the same asymptotic late-times behavior for most of these models. In terms of the effective equation of state of the universe, we find that asymptotically $\omega_{ \rm eff} \rightarrow -1$, approaching the value given by a cosmological constant. On the other hand, unlike in the case of $\Lambda$CDM, the Hubble factor is a monotonic growing function that diverges asymptotically. We argue that this behavior is not a coincidence and discuss under which conditions this is to be expected in these nonlocal models.