The amplitude of mass density fluctuations at z approximate to 3.25 from the Ly alpha forest of Q1422+231

The real-space optical-depth distribution along the line of sight to the QS O Q1422+231 is recovered from two HIRES spectra using a modified version of the inversion method proposed by Nusser & Haehnelt. The first two moments of the truncated optical-depth distribution are used to constrain the densi ty-fluctuation amplitude of the intergalactic medium (IGM) assuming that th e IGM is photoionized by a metagalactic UV background and obeys a temperatu re-density relation. The fluctuation amplitude and the power-law index alph a of the relation between gas and neutral hydrogen (H I) density are degene rate. The rms of the IGM density at z approximate to 3.25 estimated from th e first spectrum is sigma = root exp[(1.8 +/- 0.27)(2)alpha(2)] - 1, with 1 .56 < alpha < 2 for plausible reionization histories. This corresponds to 0 .9 less than or similar to sigma less than or similar to 2.1 with sigma(alp ha = 1.7) = 1.44 +/- 0.3. The values obtained from the second spectrum are higher by approximate to 20 per cent. If the IGM density traces the dark ma tter (DM) as suggested by numerical simulations we have measured the fluctu ation amplitude of the DM density at an effective Jeans scale of a few 100 kpc. For cold dark matter (CDM)-like power spectra the amplitude of dark ma tter fluctuations on these small scales depends on the cosmological density parameter Omega. For power spectra normalized to reproduce the space densi ty of present-day clusters and with a slope parameter of Gamma = 0.21 consi stent with the observed galaxy power spectrum, the inferred Omega can be ex pressed as: Omega = 0.61(alpha/1.7)(1.3)(x(J)/0.62)(-0.6) for a flat univer se, and Omega = 0.91(alpha/1.7)(1.3)(x(J)/0.62)(-0.7) for a lambda = 0 univ erse. x(J) is the effective Jeans scale in (comoving) h(-1) Mpc. Based on a suite of detailed mock spectra the 1 sigma error is approximate to 25 per cent. The estimates increase with increasing Gamma. For the second spectrum we obtain 15 per cent lower values.