## Final Report Summary - MCMCLYMAN (Markov chain Monte Carlo reconstruction of the large-scale structure with the Lyman alpha forest)

The main goal of this project is the characterisation of the cosmological large-scale structure (LSS) on different scales from the measurement of quasar absorption spectra tracing the intergalactic medium (IGM) through the Lya forest.

In the current cosmological picture structures in the Universe are believed to have grown from tiny fluctuations through gravitational clustering. Nonlinear processes of structure formation destroy the information about the origin of our Universe. This information is encoded in the large scales in which structures are close to the linear regime. Oscillations of the baryon-photon plasma in the early universe, known as baryon acoustic ascillations (BAO), imprint a distinct signature on the clustering of matter. The BAOs set a characteristic scale that is measurable as an oscillatory pattern in the power spectrum of the LSS and can be used to extract cosmological parameters. The analysis of the LSS is thus one of the major tasks in cosmology.

As we look at the distribution of matter at large distances (redshifts 2-6) we are observing structures in the past light cone. This enables us to get a picture of the Universe at a particularly interesting epoch in which structures were younger remaining closer to the linear regime and galaxies were actively forming. Using the luminous distribution of galaxies as large- scale tracers becomes extremely expensive as larger volumes need to be surveyed. The neutral hydrogen of the IGM represents an appealing alternative. However, extremely luminous sources are required to radiate the IGM and make it visible to us. Such objects are called quasars and are believed to be galaxies with an active galactic nucleus.

The ultraviolet radiation emitted by a quasar suffers resonant Lya scattering as it propagates through the intergalactic neutral hydrogen. In this process, photons are removed from the line-of-sight resulting in an attenuation of the source flux, the so-called Gunn-Peterson effect. The measurement of multiple quasar absorption sight-line spectra traces the LSS. The explicit relationship between the underlying matter field and the observed flux of a quasar spectrum is very complex.

We have developed a novel one-dimensional (1D) technique to recover the nonlinear density field from Lya data which does not require the knowledge on the equation of state, the thermal history or the ionization level of the IGM (S.Gallerani F.S.Kitaura and A.Ferrara 2010). The strong correlation we found between the flux and the matter density enabled us to establish a statistical one-to-one relation between the probability density of the flux and the one of matter. This approach reduces all the assumptions to the knowledge of the matter statistics which is well constrained by N-body simulations. It permits us to deal with strongly skewed matter probability density functions (PDFs) which apply at small scales (~20 kpc). We could also show that the impact on the matter field reconstruction due to peculiar motions cancels out on scales larger than ~10 Mpc.

In parallel, we also developed a novel Bayesian three-dimensional (3D) non-Gaussian reconstruction technique which permits us to accurately solve for incompleteness due to the sparse distribution of quasar spectra. In a first step, the matter statistics from observations was investigated (F.S.Kitaura et al, 2009) and the adequate statistical non-Gaussian model was worked out and compared against N-body simulations (F.S. Kitaura, J. Jasche and B. Metcalf, 2010). Then, the Hamiltonian Markov chain Monte Carlo technique was developed to sample from such a non-Gaussian statistical model (J. Jasche and F.S. Kitaura, 2010; F.S. Kitaura, 2010). Moreover, we extended the Bayesian approach to extract the BAOs from the reconstructed LSS (F.S. Kitaura, S.Gallerani and A.Ferrara 2010). Our work provides a completely new state-of-the-art analysis of the intergalactic structure structure on small- and on large-scales.

In the current cosmological picture structures in the Universe are believed to have grown from tiny fluctuations through gravitational clustering. Nonlinear processes of structure formation destroy the information about the origin of our Universe. This information is encoded in the large scales in which structures are close to the linear regime. Oscillations of the baryon-photon plasma in the early universe, known as baryon acoustic ascillations (BAO), imprint a distinct signature on the clustering of matter. The BAOs set a characteristic scale that is measurable as an oscillatory pattern in the power spectrum of the LSS and can be used to extract cosmological parameters. The analysis of the LSS is thus one of the major tasks in cosmology.

As we look at the distribution of matter at large distances (redshifts 2-6) we are observing structures in the past light cone. This enables us to get a picture of the Universe at a particularly interesting epoch in which structures were younger remaining closer to the linear regime and galaxies were actively forming. Using the luminous distribution of galaxies as large- scale tracers becomes extremely expensive as larger volumes need to be surveyed. The neutral hydrogen of the IGM represents an appealing alternative. However, extremely luminous sources are required to radiate the IGM and make it visible to us. Such objects are called quasars and are believed to be galaxies with an active galactic nucleus.

The ultraviolet radiation emitted by a quasar suffers resonant Lya scattering as it propagates through the intergalactic neutral hydrogen. In this process, photons are removed from the line-of-sight resulting in an attenuation of the source flux, the so-called Gunn-Peterson effect. The measurement of multiple quasar absorption sight-line spectra traces the LSS. The explicit relationship between the underlying matter field and the observed flux of a quasar spectrum is very complex.

We have developed a novel one-dimensional (1D) technique to recover the nonlinear density field from Lya data which does not require the knowledge on the equation of state, the thermal history or the ionization level of the IGM (S.Gallerani F.S.Kitaura and A.Ferrara 2010). The strong correlation we found between the flux and the matter density enabled us to establish a statistical one-to-one relation between the probability density of the flux and the one of matter. This approach reduces all the assumptions to the knowledge of the matter statistics which is well constrained by N-body simulations. It permits us to deal with strongly skewed matter probability density functions (PDFs) which apply at small scales (~20 kpc). We could also show that the impact on the matter field reconstruction due to peculiar motions cancels out on scales larger than ~10 Mpc.

In parallel, we also developed a novel Bayesian three-dimensional (3D) non-Gaussian reconstruction technique which permits us to accurately solve for incompleteness due to the sparse distribution of quasar spectra. In a first step, the matter statistics from observations was investigated (F.S.Kitaura et al, 2009) and the adequate statistical non-Gaussian model was worked out and compared against N-body simulations (F.S. Kitaura, J. Jasche and B. Metcalf, 2010). Then, the Hamiltonian Markov chain Monte Carlo technique was developed to sample from such a non-Gaussian statistical model (J. Jasche and F.S. Kitaura, 2010; F.S. Kitaura, 2010). Moreover, we extended the Bayesian approach to extract the BAOs from the reconstructed LSS (F.S. Kitaura, S.Gallerani and A.Ferrara 2010). Our work provides a completely new state-of-the-art analysis of the intergalactic structure structure on small- and on large-scales.