Probing the scale dependence of non-Gaussianity with spectral distortions of the cosmic microwave background

Abstract

Many inflation models predict that primordial density perturbations have a nonzero three-point correlation function, or bispectrum in Fourier space. Of the several possibilities for this bispectrum, the most commmon is the local-model bispectrum, which can be described as a spatial modulation of the small-scale (largewavenumber) power spectrum by long-wavelength density fluctuations. While the local model predicts this spatial modulation to be scale-independent, many variants have some scale-dependence. Here we note that this scale dependence can be probed with measurements of frequency-spectrum distortions in the cosmic microwave background (CMB), in particular highlighting Compton-y distortions. Dissipation of primordial perturbations with wavenumbers 50 Mpc −1 k 10 4 Mpc −1 give rise to chemical-potential (µ) distortions, while those with wavenumbers 1 Mpc −1 k 50 Mpc −1 give rise to Compton-y distortions. With local-model non-Gaussianity, the distortions induced by this dissipation can be distinguished from those due to other sources via their crosscorrelation with the CMB temperature T . We show that the relative strengths of the µT and yT correlations thus probe the scale-dependence of non-Gaussianity and estimate the magnitude of possible signals relative to sensitivities of future experiments. We discuss the complementarity of these measurements with other probes of squeezed-limit non-Gaussianity.

Cross-correlation between thermal Sunyaev-Zeldovich effect and the integrated Sachs-Wolfe effect

“…[12]. If primordial perturbations are non-Gaussian, the amplitude of small-wavelength power can be modulated by long-wavelength Fourier modes of the density field.…”

“…We now estimate the detectability of the yT crosscorrelation from non-Gaussianity, discussed in Ref. [12]. In that work, the late-time contribution to C yy l and C yT l was neglected, and the detectability of the primordial signal was inferred assuming that detection of y fluctuations was noise-limited.…”

“…[12], there are no existing model-independent constraints on f y nl . We now estimate the detectability of the yT crosscorrelation from non-Gaussianity, discussed in Ref.…”

“…Recent work has shown that primordial non-Gaussianity may lead to a yT cross-correlation which may be used to probe scale-dependent nonGaussianity [12]. The present calculation will be used to explore whether this early-Universe signal can be distinguished from late-time effects that induce a yT correlation.…”

Cosmological constraints fromμEcross correlations

“…For instance, the chemical potential-type distortion to the CMB black body spectrum is estimated as µ " Op10´8q based on the almost scale-invariant and Gaussian primordial curvature perturbations [7,15], and the next generation of space missions is expected to detect this [16,17]. Recently, the anisotropies in the distortions were also discussed in the context of a primordial non-Gaussianity search [18][19][20][21][22][23]. Even though the chemical potentials are the thermodynamic quantities which are realized in each diffusion patch, they can fluctuate according to the primordial 3-and 4-point correlation functions.…”