Constraints on Large-Scale White Noise in the Cosmic Density Field

We present observational constraints on large-scale white noise (LSWN) in the cosmic density field, a phenomenon predicted to arise from nonlinear mode coupling during cosmological evolution. Building on the theoretical framework of our companion paper, where we demonstrated that nonlinearities inevitably redistribute power from small to large scales through mode mixing, we confront these predictions with current cosmological data. We modify the class Boltzmann code to incorporate a white noise component ${k}_{\mathrm{BH}}/k$ in the primordial power spectrum and perform parameter estimation using current cosmological data. The nondetection of excess power on the largest observable scales places stringent upper bounds: ${k}_{\mathrm{BH}}\ensuremath{\le}1.80\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ at 99% confidence. These constraints imply the primordial power spectrum must deviate from a power law on small scales, perhaps with a sharp cutoff at ${k}_{\mathrm{cut}}\ensuremath{\lesssim}0.03\text{ }\text{ }{\mathrm{pc}}^{\ensuremath{-}1}$ or through running of the spectral index with ${\ensuremath{\alpha}}_{s}\ensuremath{\lesssim}\ensuremath{-}0.019$. Our results demonstrate that LSWN provides a powerful probe of the primordial spectrum at scales orders of magnitude smaller than those directly observable, offering unique constraints on early-universe physics.