The Search For Primordial Tensor Modes

TL;DR

The paper analyzes the prospects for detecting tensor modes from inflation via CMB polarization and space-based gravitational-wave detectors. It connects tensor amplitudes to slow-roll parameters with $r ≈ 16 \epsilon$, $n_s - 1 ≈ 2\eta - 4\epsilon$, and $n_T ≈ -2\epsilon$, and emphasizes B-mode polarization as a direct inflation probe. It assesses current and future experimental capabilities (WMAP/Planck, Clover/QUIET, BBO/DECIGO) and discusses the observational challenges posed by lensing and foregrounds. It argues that detecting tensor modes at $r \sim 10^{-2}$ would strongly constrain high-field inflation, while pursuing $r \sim 10^{-4}$ offers modest payoff unless accompanied by end-of-inflation signatures such as cosmic strings or non-Gaussianities, guiding where to focus next-generation efforts.

Abstract

We review the prospects for detecting tensor modes generated during inflation by CMB polarization experiments and by searching for a stochastic gravitational wave background with laser interferometers in space. We tackle the following two questions: (i) what does inflation predict for the tensor fluctuations? (ii) is it really worth building experiments that can cover only a small range of tensor amplitudes?

Figures (7)

• Figure 1: Temperature and polarization power spectra for the concordance $焃$CDM model. The current (indirect) upper limit of seljak leads to an upper limit on rms polarization anisotropy of $\hbox{$\; \buildrel < \over \sim \;$} 0.35 \mu{\rm K}$. For comparison, the rms signals for the $T$ and $E$ anisotropies are given. Lensing of $E$ modes by intervening matter leads to small scale $B$ modeszaldarriaga2 as shown. The dashed line the white-noise level for an experiment with a sensitivity to $B$-modes of $r \sim 10^{-2}$.
• Figure 2: The left hand panel shows forecasts for the $\pm 1\sigma$ errors on the electric polarization power spectrum $C_l^E$ from WMAP after 4 years of observation. (Forecasts for the Boomerang (2003) experiment, labelled B2K, are also plotted). The right hand panel shows forecasts for Planck. For WMAP and B2K, flat band powers are estimated with $焁 l = 150$ (with finer resolution on large scales for WMAP in the inset). For Planck, flat band powers are estimated with $焁 \ell =20$ in the main plot and with $焁 \ell=2$ in the inset. (Figures computed by A, Challinor, reproduced from bluebook).
• Figure 3: Forecasts for the $\pm 1\sigma$ errors on the magnetic polarization power spectrum $C_l^B$ from Planck. Above $l \sim 150$ the primary spectrum is swamped by weak gravitational lensing of the $E$-modeszaldarriaga2 (Figure computed by A. Challinor, reproduced from bluebook).
• Figure 4: The expected errors from Clover on the $B$-mode power spectrum. The upper panel has tensor-scalar ratio $r=0.36$ ( cf. equation \ref{['niceobs1']}), the middle panel is for $r=0.15$ and the lower panel is for $r=0.011$. The smaller (magenta) error boxes are the contribution from instrument noise and the larger (blue) boxes also include sample variance, include the contribution from weak lensing. (Figure computed by A. Challinor).
• Figure 5: Plots of gravitational wave spectrum $\omega_{\rm gw}$ against tensor-scalar ratio $r$ for a large number of models evolved with the inflationary flow equations. Square (red) points indicate models satisfying the observational constraints on $n_s$ and $dn_s/d\ln k$ given by (\ref{['niceobs2']}). The solid line shows the bound given by Equation (\ref{['upper']}).