Time-reparametrization invariance in eternal inflation

Abstract

I address some recently raised issues regarding the time-parametrization dependence in stochastic descriptions of eternal inflation. To clarify the role of the choice of the time gauge, I show examples of gauge-dependent as well as gauge-independent statements about physical observables in eternally inflating spacetimes. In particular, the relative abundance of thermalized and inflating regions is highly gauge-dependent. The unbounded growth of the 3-volume of the inflating regions is found in certain time gauges, such as the proper time or the scale factor gauge. Yet in the same spacetimes there exist time foliations with a finite and monotonically decreasing 3-volume, which I demonstrate by an explicit construction. I also show that there exists no "correct" choice of the time gauge that would yield an unbiased stationary probability distribution for observables in thermalized regions.

version accepted by Phys.Rev.D, minor additions and clarifications suggested by the referee

References in corpus (10)

• From the Big Bang Theory to the Theory of a Stationary Universe
• Stationarity of Inflation and Predictions of Quantum Cosmology
• Making Predictions in Eternally Inflating Universe
• Predictability crisis in inflationary cosmology and its resolution
• Unambiguous probabilities in an eternally inflating universe
• A prescription for probabilities in eternal inflation
• Uncertainties of predictions in models of eternal inflation
• The eternal fractal in the universe
• Langevin Analysis of Eternal Inflation
• On the factor ordering problem in stochastic inflation

Cited by in corpus (17)

• Eternal Symmetree
• Hurdles for Recent Measures in Eternal Inflation
• The Volume of the Universe after Inflation and de Sitter Entropy
• A measure of the multiverse
• Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
• Is Brane Inflation Eternal?
• A volume-weighted measure for eternal inflation
• Measures on transitions for cosmology from eternal inflation
• Self-reproduction in k-inflation
• Reheating-volume measure for random-walk inflation
• Age-dependent decay in the landscape
• Reheating-volume measure in the landscape
• 4-volume cutoff measure of the multiverse
• The grainy multiverse
• Mathematical Issues in Eternal Inflation
• Stochastic Eternal Inflation in a Bianchi Type I Universe
• Eternal inflation near inflection points: a challenge to primordial black hole models