Studies on the Large-Scale Structure of the Universe

We have decided to try to have almost self-contained chapters, in each of which there is presented a specific framework together with our contribution to the particular area and to its discussion, because we got interested in several different, albeit related, projects (some of which, not fully exploited, are not presented here). Also, a large part of the work which won't show up directly is the large number of computer codes which have been developed. Numerical work played a very significant part in the present work, although as a tool and not as an end for future applications, as often happens in numerical theses. Hence we will not usually give the details of the computer programs, but only their principles when they are useful. Nevertheless we remark that it often took endless hours to produce a single figure or a single number which is buried in the text. We have organized the presentation of material according to the cosmological 'clock' (i.e. for different values of the redshift, z ): we will discuss first events which refer to an almost primordial epoch (i.e. to the last scattering surface of the Cosmic Microwave Background (CMB), with a redshift, for the effect which is of concern to us, of z r-..1 103 ), then we pass on to intermediate epochs, those of possible formation of galaxies and clusters of galaxies ( z r-..1 0(1) ), and we will end with a discussion concerned with superclusters (SC) at very recent epochs ( z ~ 1 ). Of the following chapters, two (Chap. II and Chap. III) are concerned in detail with the study of possible Large-Scale (LS) fluctuations of the CMB. This topic is of paramount importance to the whole field and to cosmology at large, and indeed these two chapters constitute the core of our thesis' work. In Chap. II we first discuss the effect we will be concerned with (the SachsWolfe effect) and then develop a new formalism which takes into account, in an exact way, the fact that different experiments get different results even if they are measuring the same fluctuation, because of different sizes of the experimental beams used. This point, which might seem to be trivial, has important consequences. We then present the first meaningful comparison between present results on the LS anisotropies of the CMB. In Chap. III we pursue further the study of LS CMB anisotropies and implement and enlarge the formalism. We first give a discussion of the effect of the beamsize on observations of possible cosmological hotspots. Then we discuss the results of a recent experiment, and also clarify the validity range of the new results we obtain by a direct application of the results of Chap. II to the data, through a Likelihood Ratio method. We continue with a discussion of how to derive meaningful confidence levels on upper limits for cosmic density fluctuations, from experimental upper limits on CMB LS fluctuations that are quoted in the literature. Then, through Monte-Carlo simulations of different realizations of the CMB last scattering surface, we obtain upper limits on the amplitude of density fluctuations (for the scale invariant spectrum) which are almost one order of magnitude more stringent than those obtainable from the limits on the quadrupole component of the temperature :fluctuations. We conclude the Chapter with a discussion of effects which could have caused a recently reported 'bump' in the CMB sky. In Chap. IV we show the impact that different perturbation spectra, obtained in 'hybrid' models, have on the mass-multiplicity function, evaluated with the Press-Schechter formalism and with approximate formulre for the peak number density. We then discuss the possible effect of an increase of the amplitude of the galaxy spatial two-point correlation as a function of the limiting intrinsic luminosity of the sample. An explanation of this effect is tentatively given m terms of the theory of biased galaxy formation. In Chap. V we present and discuss present catalogues of clusters of galaxies and then concentrate on an analysis of the .most recent available one. We discuss the problems of distance estimates through apparent magnitudes, and then derive a relationship with which we obtain distance and density estimates for this new catalogue. We also discuss percolation algorithms including the one we devised and have applied to this recent data. We then pass on to discuss the problem of LS peculiar velocities, which is one of the 'hottest topics' at the moment in this field, and review recent results and methodologies which try to get estimates for the value of 0 0 • We close the chapter and the thesis with a discussion of the most interesting SC we found by our analysis. The interest comes from the fact that this SC is close to us (on a cosmological scale) and is in a very particular position. Being close, this SC can be studied more easily than others which are much further away, and therefore be a source of a wealth of cosmological information. On the other hand, not only is its radial distance of interest, but also its direction: this SC could in fact be mostly responsible for the observed peculiar velocity of our Local Group (LG) of galaxies.