Matter Power spectrum (Matteo Viel)

The Ly-alpha forest provides a powerful way to measure the dark matter distribution at scales and redshifts not probed by other observables. Neutral hydrogen in the IGM is a tracer of baryonic matter fluctuations and, at scales above the Jeans length (roughly 1 comoving Mpc at z = 3), of the underlying dark matter distribution. Building on early insights from semi-analytical models and hydrodynamical simulations, Croft et al. (1998) proposed a method to measure the linear dark matter power spectrum from the Ly-alpha forest flux power spectrum. Since then the field has developed rapidly. Several new methods to derive the linear matter power spectrum have been proposed (e.g. Gnedin & Hamilton 2002) and measurements of the matter power spectrum from the Ly-alpha forest have been fully incorporated into cosmological measurements by the WMAP team (Wilkinson Microwave Anisotropy Probe, e.g. Spergel et al. 2003) for better parameter constraints. Most work in this field has been based on two data sets (Fig. 1): 1) the Sloan Digital Sky Survey (SDSS) QSO sample consists of thousands of low-resolution (R ~ 2000), low S/N~5 spectra, enabling the recovery of the flux power spectrum over z = 2.2- 4.2 with rather small statistical errors; 2) the UVES/VLT sample consists of about 25 QSO spectra at high resolution (R~45000) and high S/N~80 at z~2. The latter provides a measurement of the flux power spectrum with larger statistical errors due to the small size of the data set, but the high quality of the data facilitates important insights into instrumental and astrophysical systematic uncertainties. McDonald et al. (2006) and Kim et al. (2004) have measured the forest flux power spectrum, based on the SDSS sample and the UVES/VLT sample, respectively. The results from the two groups are in good overall agreement, but detailed comparisons show quantitative differences. In the light of the ~0.6% statistical errors (overall amplitude and slope of flux power at z = 3 and at a given scale) of the SDSS data, it is therefore very important to understand the systematic uncertainties at the same level of accuracy in order to take full advantage of the Ly-alpha forest data. As the accuracy of data sets has improved the first hints of systematic biases have emerged. The values of the amplitude of density fluctuations measured from Ly forest data, while in agreement between different groups, are larger than those obtained from the cosmic microwave background. This tension at the 2 sigma level in the measured amplitude of the matter power spectrum allows to constrain cosmological parameters as for example the neutrino mass fraction and the running of the spectral index. At present, the tightest constraints in terms of neutrinos are derived from a combination of Ly-alpha data and WMAP data and also inflationary models are strongly constrained by measuring the running of the spectral index at the forest scales (Seljak et al. 2006). It is thereby fundamental to understand whether the tension between the matter power derived from IGM data and other large scale structure probes is due to systematic errors that have not been accounted for or is real and can constrain fundamental properties of the Universe.

Exploring the z > 3.5 regime with a sample like the one proposed here will result in a precise measurement of the matter clustering at epochs that are closer to the linear regime than previous samples (Kim et al. 2004, Croft et al. 2002): the power spectrum, being only midly affected by non-linear evolution, will thus more closely resemble the primordial one. The prospects and motivation for further improved measurements of the matter power spectrum from Ly forest data are thus excellent.
The power spectrum measurement at high redshift will also put constraints on the thermal state of the IGM at an epoch which is close to a possible He ii reionization. Viel, et al. (2009, MNRAS, 399, L39) have shown that the ux probability distribution function as derived from UVES/VLT spectra is in tension with the ux power spectrum as measured from the SDSS and, in particular, the derived IGM temperature is signicantly dierent at the 2 level. This suggests that there is an unknown systematic eect which has still to be properly modelled and understood. By accurately determining the IGM temperature at z > 3:5 we will be able to trace the early stages of He ii reionization by measuring the photoionization heating from QSOs (e.g., McQuinn et al. 2009, MNRAS, 694, 842; Becker et al. 2011, MNRAS, 410, 1096). A completely new mechanism of heating of the IGM has also been proposed, which is done by Blazars through plasma instabilities (Puchwein et al. 2011, MNRAS submitted, arXiv:1107.3837). This eect would cause a dierent redshift evolution of the IGM thermal state, impacting several ux statistics in ways that are distinct from He ii reionization.