Microwave background radiation anisotropy from scalar field gradients

Analytic calculations of the cosmological density fluctuations and microwave background radiation anisotropies induced by gradients in a topologically trivial scalar field are presented. This anlaytic solution should provide a good test for numerical simulations of microwave anisotropy from scalar fields. To the extent that these results generalize to other scalar field models and configurations, they imply that (1) MBR measurements limit large-scale primordial variations greater than about 5×{}10¹⁶ GeV within our horizon, (2) the total scalar field variation is a fair predictor of the magnitude of the MBR anisotropy, but is only accurate to within a factor of about three, (3) scalar fields as well as other models of seeded perturbations produce a few times more anisotropy ΔTT for a given density fluctuation δρρ (on the same scale) than do primordial adiabatic perturbations, (4) models of scalar field seeds which produce a scale-invariant spectrum of perturbations seem to require galaxies to be more clustered than the mass on small scales, and (5) scalar fields do not "tilt" the Universe.