The CMB and the measure of the multiverse

TL;DR

This paper compares how different measures in eternal inflation affect predictions of CMB perturbations, finding that while measures influence certain predictions, these effects are within cosmic variance, thus supporting standard inflationary results.

Contribution

It demonstrates the impact of measure choice on CMB predictions in eternal inflation and shows these effects are within cosmic variance, validating standard inflationary predictions.

Findings

Different measures predict distinct monopole and 3-point function contributions.

Effects of measure choice are within cosmic variance limits.

Standard inflationary predictions remain valid despite measure dependence.

Abstract

In the context of eternal inflation, cosmological predictions depend on the choice of measure to regulate the diverging spacetime volume. The spectrum of inflationary perturbations is no exception, as we demonstrate by comparing the predictions of the fat geodesic and causal patch measures. To highlight the effect of the measure---as opposed to any effects related to a possible landscape of vacua---we take the cosmological model, including the model of inflation, to be fixed. We also condition on the average CMB temperature accompanying the measurement. Both measures predict a 1-point expectation value for the gauge-invariant Newtonian potential, which takes the form of a (scale-dependent) monopole, in addition to a related contribution to the 3-point correlation function, with the detailed form of these quantities differing between the measures. However, for both measures both effects are well within cosmic variance. Our results make clear the theoretical relevance of the measure, and at the same time validate the standard inflationary predictions in the context of eternal inflation.