ar X iv : a st ro - p h / 03 04 48 4 v 2 9 J ul 2 00 3 Observational estimates of the initial power spectrum at small scale from Lyman - α absorbers

We present a new method of measuring the power spectrum of initial perturbations to an unprecedently small scale of ∼ 10h −1 kpc. We apply this method to a sample of 4500 Ly-α absorbers and recover the cold dark matter (CDM) like power spectrum at scales ≥ 300h −1 kpc with a precision of ∼ 10%. However at scales ∼ 10 − 300h −1 kpc the measured and CDM–like spectra are noticeably different. This result suggests a complex inflation with generation of excess power at small scales. The magnitude and reliability of these deviations depend upon the possible incompleteness of our sample and poorly understood process of formation of weak absorbers. Confirmation of the CDM–like shape of the initial power spectrum or detection of its distortions at small scales are equally important for widely discussed problems of physics of the early Universe, galaxy formation, and reheating of the Universe. We use the Zel'dovich theory of gravitational instability to derive statistical description of the properties of observed structure. Our method links the observed mass function of absorbers with the correlation function of the initial velocity field and therefore it avoids the Nyquist restrictions limiting the investigations based on the smoothed flux or density fields. This approach is in general consistent with numerical simulations of the process of structure formation, describes reasonably well the Large Scale Structure observed in the galaxy distribution at small redshifts and emphasizes the generic similarity of galaxies and absorbers. The physical model of absorbers adopted here asserts that they are formed in the course of both linear and nonlinear adiabatic or shock compression of dark matter (DM) and gaseous matter. It allows us to link the column density and overdensity of DM and gaseous components with observed characteristics of absorbers such as the column density of neutral hydrogen, redshifts and Doppler parameter. At scales ≥ 1h −1 Mpc all characteristics of the DM component and, in particular, their redshift distribution are found to be consistent with theoretical expectations for Gaussian initial perturbations with a CDM–like power spectrum.