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

Abstract

We investigate the phenomenological consequences of a modification of the initial state 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 squeezed configuration, allowing for a non-standard initial state produces an exception. Here, we calculate the signature of an initial state modification in single-field slow-roll inflation in both the scale-dependent bias of the large-scale structure (LSS) and mu-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 LSS (as opposed to k^-2 for the local-form). As a non-zero bispectrum in the squeezed configuration correlates a long-wavelength mode with two short-wavelength modes, it induces a correlation between the CMB temperature anisotropy on large scales with the temperature-anisotropy-squared on very small scales; this correlation persists as the small-scale anisotropy-squared is processed into mu-type distortions. While the local-form mu-distortion turns out to be too small to detect in the near future, a modified initial vacuum state enhances the signal by a large factor owing to an extra factor of k_1/k. 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. (Abridged)