Cosmological dispersion, the corrected redshift formula, and large-scale structure.

Abstract

We calculate the exact frequency redshift for both massless and massive scalar fields coupled to gravity in Friedmann-Robertson-Walker backgrounds. The exact redshift expression factorizes and is proportional to the naive Doppler shift times a term representing diffractive effects. These diffractive or dispersive corrections can be large for field modes with wavelengths on the order of the horizon size. The corresponding mode amplitudes undergo amplification or deamplification, with respect to conformally coupled scalars, depending on the value of the coupling to gravity. Implications for cosmological density perturbations are discussed.