Spectral distortions from the dissipation of tensor perturbations

Abstract

Spectral distortions of the cosmic microwave background (CMB) may become a powerful probe of primordial perturbations at small scales. Existing studies of spectral distortions focus almost exclusively on primordial scalar metric perturbations. Similarly, vector and tensor perturbations should source CMB spectral distortions. In this paper, we give general expressions for the effective heating rate caused by these types of perturbations, including previously neglected contributions from polarization states and higher multipoles. We then focus our discussion on the dissipation of tensors, showing that for nearly scale invariant tensor power spectra, the overall distortion is some six orders of magnitudes smaller than from the damping of adiabatic scalar modes. We find simple analytic expressions describing the effective heating rate from tensors using a quasi-tight coupling approximation. In contrast to adiabatic modes, tensors cause heating without additional photon diffusion and thus over a wider range of scales, as recently pointed out by Ota et al. (2014). Our results are in broad agreement with their conclusions, but we find that small-scale modes beyond k 2 × 10 4 Mpc −1 cannot be neglected, leading to a larger distortion, especially for very blue tensor power spectra. At small scales, also the effect of neutrino damping on the tensor amplitude needs to be included.

Blue-tilted tensor spectrum and thermal history of the Universe

“…The spectral index of the primordial GW spectrum can change at some frequency. Therefore, #1 There are more ways to obtain upper bounds on the amount of the stochastic GWs, such as dark radiation constraints from the CMB [28,29], CMB µ distortion [30,31], helioseismology [32], precision Doppler tracking from the Cassini spacecraft [33], orbital monitoring of binary systems [34], torsion-bar antennas [35], seismic spectrum from the Earth [36], synchronous recycling interferometers [37], crosscorrelation measurement between the Explorer and Nautilus cryogenic resonant bar detectors [38], and Global Positioning System (GPS) satellite [39].…”

Mixed inflaton and spectator field models: CMB constraints and μ distortion

“…#6 In fact, the tensor mode can also generate µ distortion [39,40]. However, the distortion can be comparable to the one generated by the scalar mode only when the tensor spectral index is blue-tilted [39,40].…”

“…However, the distortion can be comparable to the one generated by the scalar mode only when the tensor spectral index is blue-tilted [39,40]. Therefore here we neglect such a contribution and hence the tensor-to-scalar ratio is here irrelevant for calculating the value of µ. larger µ corresponds to the one with larger n s , as seen from the right panel of Fig.…”

Cosmological constraints fromμEcross correlations

“…On the other hand, there is an essential difficulty for the further improvement of the observable ranges in the CMB anisotropy experiments since Silk damping erases fluctuations on angular scales smaller than Op1˝q. In this sense, the CMB spectral deformation induced by Silk damping can be a complementary approach to the small scale physics [4][5][6][7][8][9][10][11][12][13][14]. This is because such distortions are sourced from second order effects of temperature perturbations which dissipated due to Silk damping.…”