Observational estimates of the initial power spectrum at small scale from Lyman-$lpha$ absorbers

摘要

We present a new method of measuring the power spectrum of initialperturbations to an unprecedently small scale of $sim$ 10$h^{-1}$ kpc. Weapply this method to a sample of 4500 Ly-$lpha$ absorbers and recover thecold dark matter (CDM) like power spectrum at scales $geq 300h^{-1}$kpc with aprecision of $sim$ 10%. However at scales $sim 10 - 300 h^{-1}$kpc themeasured and CDM--like spectra are noticeable different. This result suggests acomplex inflation with generation of excess power at small scales. Themagnitude and reliability of these deviations depend also upon the possibleincompleteness of our sample and poorly understood process of formation of weakabsorbers. Confirmation of the CDM--like shape of the initial power spectrum ordetection of its distortions at small scales are equally important for widelydiscussed problems of physics of the early Universe, galaxy formation, andreheating of the Universe. Our method links the observed mass function ofabsorbers with the correlation function of the initial velocity field andtherefore it avoids the Nyquist restrictions limiting the investigations basedon the smoothed flux or density fields. The physical model of absorbers adopted here asserts that they are formed inthe course of both linear and nonlinear adiabatic or shock compression of darkmatter (DM) and gaseous matter. At scales $geq 1h^{-1}$Mpc all characteristicsof the DM component and, in particular, their redshift distribution are foundto be consistent with theoretical expectations for Gaussian initialperturbations with a CDM--like power spectrum.