The primordial matter power spectrum on sub-galactic scales

Abstract

The primordial matter power spectrum quantifies fluctuations in the distribution of dark matter immediately following inflation. Over cosmic time, over-dense regions of the primordial density field grow and collapse into dark matter halos, whose abundance and density profiles retain memory of the initial conditions. By analyzing the image magnifications in eleven strongly-lensed and quadruply-imaged quasars, we infer the abundance and concentrations of low-mass halos, and cast the measurement in terms of the amplitude of the primordial matter power spectrum. We anchor the power spectrum on large scales, isolating the effect of small-scale deviations from the $\Lambda$CDM prediction. Assuming an analytic model for the power spectrum and accounting for several sources of potential systematic uncertainty, including three different models for the halo mass function, we obtain correlated inferences of $\log_{10}\left(P / P_{\Lambda \rm{CDM}}\right)$, the power spectrum amplitude relative to the predictions of the concordance cosmological model, of $0.0_{-0.4}^{+0.5}$, $0.1_{-0.6}^{+0.7}$, and $0.2_{-0.9}^{+1.0}$ at k = 10, 25 and 50 $\rm{Mpc^{-1}}$ at $68 \%$ confidence, consistent with cold dark matter and single-field slow-roll inflation.