Observational Implications of Cosmological Event Horizons

TL;DR

This work analyzes how cosmological event horizons in a late-time accelerating universe constrain our ability to observe inflation. By applying covariant entropy bounds and relating reheating entropy to the final de Sitter horizon, the authors quantify the observable inflationary window, finding that only the last $N \sim 60$ e-folds can ever be probed if the present dark energy scale is $$(10^{-3} eV)^4.$$ They show that inflationary perturbations beyond this window are effectively erased or never reenter the horizon, and that the CMB information will eventually be overwhelmed by cosmological Hawking radiation with a crossover time set by $T_{CMB}(t_T)=T_H$, leading to a bound that tightens to $t_T \sim 60/H_0$ as $w \to -1$. The results imply our current CMB data may be the furthest back in the early universe that we can ever access, reframing the timing of cosmological observations in the context of eternal acceleration.

Abstract

In a universe dominated by a small cosmological constant or by eternal dark energy with equation of state w < -1/3, observers are surrounded by event horizons. The horizons limit how much of the universe the observers can ever access. We argue that this implies a bound N~60 on the number of e-folds of inflation that will ever be observable in our universe if the scale of the dark energy today is ~(10^{-3} eV)^4. This bound is independent of how long inflation lasted, or for how long we continue to observe the sky. The bound arises because the imprints of the inflationary perturbations thermalize during the late acceleration of the universe. They "inflate away" just like the initial inhomogeneities during ordinary inflation. Thus the current CMB data may be looking as far back in the history of the universe as will ever be possible, making our era a most opportune time to study cosmology.

Figures (3)

• Figure 1: Causal patch of an observer in a universe where inflation and reheating are followed by eternal accelerated expansion. The symbols designate: PH and FH - past and future sections of the event horizon, AH - apparent, or Hubble, horizon, RS - reheating surface, and LS - a future oriented light sheet, which intersects both the event horizon and the infinitely inflated future. Black arrows are the worldlines of the entropy released at the end of inflation.
• Figure 2: Evolution of the wavelengths of some typical inflationary perturbations in the causal patch in a universe without (left panel) and with (right panel) event horizons. In the left panel, all fluctuations eventually reenter the Hubble horizon. In the right panel, in the case $a)$, a fluctuation is stretched outside of the Hubble horizon during inflation, remains there for a time, then reenters during a matter dominated era after inflation, and eventually gets expelled out of the horizon once more during the final stage of acceleration. In the case b), the fluctuation could have reentered about now, but the late acceleration pushes it back out. In the case c), the late acceleration prevents the fluctuation from ever reentering the Hubble horizon.
• Figure 3: On the left, evolution of the comoving Hubble scale $a(t) H(t)$ for a universe which inflates, followed by radiation and matter domination; on the right, the same graph for a universe that enters a late-time accelerating phase.