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We investigate the phenomenological consequences of a modification of theinitial state of a single inflationary field. While single-field inflation withthe standard Bunch-Davies initial vacuum state does not generally produce ameasurable three-point function (bispectrum) in the squeezed configuration,allowing for a non-standard initial state produces an exception. Here, wecalculate the signature of an initial state modification in single-fieldslow-roll inflation in both the scale-dependent bias of the large-scalestructure (LSS) and mu-type distortion in the black-body spectrum of the cosmicmicrowave background (CMB). We parametrize the initial state modifications andidentify certain choices of parameters as natural, though we also note somefine-tuned choices that can yield a larger bispectrum. In both cases, weobserve a distinctive k^-3 signature in LSS (as opposed to k^-2 for thelocal-form). As a non-zero bispectrum in the squeezed configuration correlatesa long-wavelength mode with two short-wavelength modes, it induces acorrelation between the CMB temperature anisotropy on large scales with thetemperature-anisotropy-squared on very small scales; this correlation persistsas 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 thenear future, a modified initial vacuum state enhances the signal by a largefactor owing to an extra factor of k_1/k. For example, a proposedabsolutely-calibrated experiment, PIXIE, is expected to detect this correlationwith a signal-to-noise ratio greater than 10, for an occupation number of about0.5 in the observable modes. Relatively calibrated experiments such as Planckand LiteBIRD should also be able to measure this effect, provided that therelative calibration between different frequencies meets the requiredprecision. (Abridged)

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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