Non-Gaussian statistics and structure formation with cosmic strings

Most of this thesis concerns the search for new statistics for cosmic microwave background (CMB) and large-scale structure observations, which can discriminate between the two main classes of models of structure formation, inflation and topological defects. One of the statistics we study is the kurtosis of spatial gradient maps of the CMB. Using an analytical model for the string network we find that it is a good statistic to distinguish between the cosmic string model and inflationary models of structure formation. The difference between the stringy and inflationary value for the kurtosis is inversely proportional to the angular resolution and to the number of strings per Hubble volume of the strings' scaling solution. If strings are indeed responsible for CMB anisotropies then experiments with resolutions of a couple of arcminutes or smaller could determine it using this statistic. We also look at the probability distribution for large-scale peculiar velocities due to cosmic strings, and show that it is Gaussian to good accuracy, in agreement with the observational results from the 1.9 Jy IRAS survey. Using the normalization of parameters of the cosmic string model from CMB measurements, we show that these peculiar velocity measurements are consistent with the cosmic string model provided that long strings have some small-scale structure.; We study several topics in structure formation with cosmic strings, among them the formation of high redshift objects in the cosmic string plus hot dark matter (HDM) model. Recent observations of high redshift objects put stringent constraints on theories where some of the dark matter is hot. We study the accretion of HDM onto moving cosmic string loops, using a modification of the Zeldovich approximation adapted to HDM. We find that for realistic values of a parameter which determines the number density of loops in the scaling solution, the number density of high redshift objects massive enough to be capable of hosting quasars satisfies the constraints coming from observations of the abundance of quasars at redshifts of about 3.