Inflationary Super-Hubble Waves and the Size of the Universe

TL;DR

This paper explores how inflationary super-Hubble waves, influenced by the scalar spectral index, affect large-scale cosmic observations and the estimated size of the universe, providing new constraints on inflationary models.

Contribution

It demonstrates how the spectral index impacts super-Hubble waves and the universe's size estimates, linking inflationary theory with observational data.

Findings

The universe's homogeneous patch is at least 87 times larger than the visible universe.

The spectral index determines the sign change in the temperature correlation function.

Size estimates can constrain inflationary model parameters.

Abstract

The effect of the scalar spectral index on inflationary super-Hubble waves is to amplify/damp large wavelengths according to whether the spectrum is red ($n_{s}<1$) or blue ($n_{s}>1$). As a consequence, the large-scale temperature correlation function will unavoidably change sign at some angle if our spectrum is red, while it will always be positive if it is blue. We show that this inflationary filtering property also affects our estimates of the size of the homogeneous patch of the universe through the Grishchuk-Zel'dovich effect. Using the recent quadrupole measurement of ESA's Planck mission, we find that the homogeneous patch of universe is at least 87 times bigger than our visible universe if we accept Planck's best fit value $n_{s}=0.9624$. An independent estimation of the size of the universe could be used to independently constrain $n_{s}$, thus narrowing the space of inflationary models.