Scale-dependent bias of galaxies andμ-type distortion of the cosmic microwave background spectrum from single-field inflation with a modified initial state

We investigate the phenomenological consequences of a modification of the initial state of quantum fluctuations of a single inflationary field. While single-field inflation with the standard Bunch-Davies initial vacuum state does not generally produce a measurable three-point function (bispectrum) in the so-called squeezed triangle configuration (where one wave number, k, is much smaller than the other two, kk₁k₂), allowing for a nonstandard initial state produces an exception. Here, we calculate the signature of an initial state modification in single-field slow-roll inflation as it would appear in both the scale-dependent bias of the large-scale structure and -type distortion in the black-body spectrum of the cosmic microwave background (CMB). We parametrize the initial state modifications and identify certain choices of parameters as natural, though we also note some fine-tuned choices that can yield a larger bispectrum. In both cases, we observe a distinctive k^-3 signature in large-scale structure (as opposed to the k^-2 of the so-called local-form bispectrum). As a nonzero bispectrum in the squeezed configuration correlates one long-wavelength mode with two short-wavelength modes, it induces a correlation between the CMB temperature anisotropy observed on large scales with the temperature-anisotropy-squared on very small scales; this correlation persists as the small-scale anisotropy-squared is processed into the -type distortion of the black-body spectrum. While the correlation induced by the local-form bispectrum turns out to be too small to detect in near future, a modified initial vacuum state enhances the signal by a large factor owing to an extra factor of k₁/k compared to the local form. For example, a proposed absolutely-calibrated experiment, PIXIE, is expected to detect this correlation with a signal-to-noise ratio greater than 10, for an occupation number of about 0. 5 in the observable modes. Relatively-calibrated experiments such as Planck and LiteBIRD should also be able to measure this effect, provided that the relative calibration between different frequencies meets the required precision. Our study suggests that the CMB anisotropy, the distortion of the CMB black-body spectrum, and the large-scale structure of the Universe offer new ways to probe the initial state of quantum fluctuations.