Initial conditions, Discreteness and non-linear structure formation in cosmology

In this lecture we address three different but related aspects of the initial continuous fluctuation field in standard cosmological models. Firstly we discuss the properties of the so-called Harrison-Zeldovich like spectra. This power spectrum is a fundamental feature of all current standard cosmological models. In a simple classification of all stationary stochastic processes into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with $P(0)=0$, belong. In statistical physics language they are well described as glass-like. Secondly, the initial continuous density field with such small amplitude correlated Gaussian fluctuations must be discretised in order to set up the initial particle distribution used in gravitational N-body simulations. We discuss the main issues related to the effects of discretisation, particularly concerning the effect of particle induced fluctuations on the statistical properties of the initial conditions and on the dynamical evolution of gravitational clustering.Comment: 28 pages, 1 figure, to appear in Proceedings of 9th Course on Astrofundamental Physics, International School D. Chalonge, Kluwer, eds N.G. Sanchez and Y.M. Pariiski, uses crckapb.st pages, 3 figure, ro appear in Proceedings of 9th Course on Astrofundamental Physics, International School D. Chalonge, Kluwer, Eds. N.G. Sanchez and Y.M. Pariiski, uses crckapb.st

The Glass-like Universe: Real-space correlation properties of standard cosmological models

After reviewing the basic relevant properties of stationary stochastic processes (SSP), defining basic terms and quantities, we discuss the properties of the so-called Harrison-Zeldovich like spectra. These correlations, usually characterized exclusively in k-space (i.e. in terms of power spectra P(k)), are a fundamental feature of all current standard cosmological models. Examining them in real space we note their characteristics to be a {\it negative} power law tail \xi(r) \sim - r^{-4} and a {\it sub-poissonian} normalised variance in spheres \sigma^2(R) \sim R^{-4} \ln R. We note in particular that this latter behaviour is at the limit of the most rapid decay (\sim R^{-4}) of this quantity possible for any stochastic distribution (continuous or discrete). This very particular characteristic is usually obscured in cosmology by the use of Gaussian spheres. In a simple classification of all SSP into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with P(0)=0, belong. In statistical physics language they are well described as glass-like. They do not have either ``scale-invariant'' features, in the sense of critical phenomena, nor fractal properties. We illustrate their properties with some simple examples, in particular that of a ``shuffled'' lattice.Comment: 20 pages, 3 postscript figures, corrected some typos and minor changes to match the accepted version in Physical Review

The detectability of baryonic acoustic oscillations in future galaxy surveys

We assess the detectability of baryonic acoustic oscillation (BAO) in the power spectrum of galaxies using ultralarge volume N-body simulations of the hierarchical clustering of dark matter and semi-analytical modelling of galaxy formation. A step-by-step illustration is given of the various effects (non-linear fluctuation growth, peculiar motions, non-linear and scale-dependent bias) which systematically change the form of the galaxy power spectrum on large scales from the simple prediction of linear perturbation theory. Using a new method to extract the scale of the oscillations, we nevertheless find that the BAO approach gives an unbiased estimate of the sound horizon scale. Sampling variance remains the dominant source of error despite the huge volume of our simulation box (=2.41 h−3 Gpc3). We use our results to forecast the accuracy with which forthcoming surveys will be able to measure the sound horizon scale, s, and, hence constrain the dark energy equation of state parameter, w (with simplifying assumptions and without marginalizing over the other cosmological parameters). Pan-STARRS could potentially yield a measurement with an accuracy of Δs/s= 0.5–0.7 per cent (corresponding to Δw≈ 2–3 per cent), which is competitive with the proposed WFMOS survey (Δs/s= 1 per cent Δw≈ 4 per cent). Achieving Δw≤ 1 per cent using BAO alone is beyond any currently commissioned project and will require an all-sky spectroscopic survey, such as would be undertaken by the SPACE mission concept under proposal to ESA