Causality and Primordial Tensor Modes

Abstract

We introduce the real space correlation function of $B$-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation. By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings, must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. $\theta \gtrsim 2^{\circ }$. Since ordinary $B$-modes are defined non-locally in terms of the Stokes parameters $Q$ and $U$ and therefore don't have to respect causality, special care is taken to define `causal $\tilde{B}$-modes' for the analysis. We compute the real space $\tilde{B}$-mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves. The correct identification of inflationary tensor modes is crucial since it relates directly to the energy scale of inflation. Wrongly associating tensor modes from causal seeds with inflation would imply an incorrect inference of the energy scale of inflation. We find that the superhorizon $\tilde{B}$-mode signal is above cosmic variance for the angular range $2^{\circ }<\theta <4^{\circ }$ and is therefore in principle detectable. In practice, the signal will be challenging to measure since it requires accurately resolving the recombination peak of the $B$-mode power spectrum. However, a future CMB satellite (CMBPol), with noise level ${\Delta }_P\simeq 1\mu$K-arcmin and sufficient resolution to efficiently correct for lensing-induced $B$-modes, should be able to detect the signal at more than 3$\sigma$ if the tensor-to-scalar ratio isn't smaller than $r\simeq 0.01$.

19 pages, 7 figures

References in corpus (4)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• B-modes from Cosmic Strings
• A Nearly Scale Invariant Spectrum of Gravitational Radiation from Global Phase Transitions
• On the degeneracy between primordial tensor modes and cosmic strings in future CMB data from Planck

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• 3-pt Statistics of Cosmological Stochastic Gravitational Waves
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• Non-Gaussianity from Self-Ordering Scalar Fields
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• Probing the Gravitational Wave Signature from Cosmic Phase Transitions at Different Scales
• Reheating signature in the gravitational wave spectrum from self-ordering scalar fields
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• The Superhorizon Test of Future B-mode Experiments
• Tensor Tilt from Primordial B-modes
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• Impact of particle production during inflation on the CMB detection