A limit on the detectability of the energy scale of inflation

TL;DR

It is shown that the polarization of the cosmic microwave background can be used to detect gravity waves from inflation if the energy scale of inflation is above 2x10(15) GeV.

Abstract

We show that the polarization of the cosmic microwave background can be used to detect gravity waves from inflation if the energy scale of inflation is above 3.2 times 10^15 GeV. These gravity waves generate polarization patterns with a curl, whereas (to first order in perturbation theory) density perturbations do not. The limiting ``noise'' arises from the second--order generation of curl from density perturbations, or rather residuals from its subtraction. We calculate optimal sky coverage and detectability limits as a function of detector sensitivity and observing time.

Figures (3)

• Figure 1: Angular power spectra. Solid lines are for temperature anisotropies due to scalar perturbations, $C_{Tl}^S$ and tensor perturbations, $C_{Tl}^T$ with $r=10^{-3}$. Dashed lines are for the E modes from scalar perturbations, $C_{El}^S$ and the B modes from tensor perturbations, $C_{Bl}^T$. The dotted lines are for the lensing--induced scalar B-modes, $C_{Bl}^S$ before (above) and after (below) the cleaning that can be done by a perfect experiment.
• Figure 2: Angular power spectrum of projected gravitational potential, $\phi$ (solid curve) and the power spectrum of the residuals of different reconstruction procedures: minimum variance for "reference" experiment (long dashes), Wiener filter for the reference experiment (short dashes) and Wiener filter for a noiseless experiment (dotted line).
• Figure 3: Achievable detectability limit as a function of total detector array sensitivity, $s$ and observing time $t$, assuming optimal sky coverage (lower curve) and 1/3 of optimal sky coverage (upper curve). Detectability limit assuming three times optimal sky coverage overlaps the upper curve when optimal sky coverage is less than 1/3.