The End of Cosmic Growth

TL;DR

This paper explores how cosmic structure growth will cease in the future due to the interplay of gravity and cosmic acceleration, analyzing both general relativity and modified gravity models, and revealing that growth ultimately ends.

Contribution

It provides analytic asymptotic behaviors for cosmic growth under GR and modified gravity, showing that growth generally halts in the universe's future and examining the evolution of the gravitational growth index.

Findings

Growth of large scale structure ends in the future under most models.

The gravitational growth index $$ exhibits a characteristic evolution in GR.

$f(R)$ models show unique asymptotic behavior in growth indices.

Abstract

The growth of large scale structure is a battle between gravitational attraction and cosmic acceleration. We investigate the future behavior of cosmic growth under both general relativity (GR) and modified gravity during prolonged acceleration, deriving analytic asymptotic behaviors and showing that gravity generally loses and growth ends. We also note the `why now' problem is equally striking when viewed in terms of the shut down of growth. For many models inside GR the gravitational growth index $\gamma$ also shows today as a unique time between constant behavior in the past and a higher asymptotic value in the future. Interestingly, while $f(R)$ models depart in this respect dramatically from GR today and in the recent past, their growth indices are identical in the asymptotic future and past.