In this thesis, the density fluctuations are assumed to be *ab initio* at the
period of recombination ( ), when radiation and matter decoupled, but a
short overview of some of the theories for the genesis and generation of density
fluctuations in the very early Universe will be given in this section.

Prior to about 1980, astrophysicists were mostly interested in finding the initial conditions at high redshift that would result in the structures we observe today. During the 1980s, a remarkable flow of ideas from other parts of physics, especially from particle physics, led to a deeper understanding of the very early Universe ( s), some which were more speculative than others. The grand unified theories (GUTs) are an example of this.

One theory has become rather accepted among astrophysicist, namely the inflationary model, which was first proposed by Guth, but has later been modified. The word ``inflation'' is supposed to indicate a rapid exponential expansion, where the energy needed originates from vacuum. This may sound very suspect, but if the Universe is being super-cooled through a phase transition, we will get a situation where vacuum obtains energy. One speculates that in this inflationary phase the expansion was driven by a scalar field, and that quantum fluctuations in this field were stretched beyond the horizon scale by the rapid expansion. After the completion of inflation, we first have a situation of a nearly-homogeneous distribution of matter and radiation, followed by a period of about years where radiation dominated, ended with the decoupling of radiation and matter at . A number of inflationary theories have been proposed, most of them without any connection to particle physic theories. The consequence of this state of affairs is that it seems very unlikely that the existence of an inflationary period in the early Universe will ever be disproved.

What was the nature of the primeval density fluctuations? The adiabatic mode of fluctuations is generally considered the prime candidate for seeding large-scale structure. In this model the local number density of photons is proportional to the number density of baryons and dark matter particles, that is, we have a cosmic fluid where radiation and matter are perturbed together. The resultant energy density perturbations generates a non-vanishing curvature fluctuation and gravitational potential. This is why the adiabatic perturbations also are referred to as curvature perturbations. In cosmologies with inflation, adiabatic perturbations emerge naturally, but not inevitably. To have a complete model, we must specify how the density fluctuations vary with position. In the case of inflation, it is reasonable to assume them to be Gaussian and scale-invariant.

The primeval density inhomogeneities could also have been entropy perturbations. In this model the energy density is constant, but there is a local variation in the ratio of photon to baryon and dark matter particle number. The constant energy density results in an equality between the local spatial curvature and the global curvature of the Universe. For this reason, these perturbations are also called isocurvature. At present there is no natural-looking picture of the origin of such perturbations; it fits badly with the inflationary model.

An alternative model for the source of the primeval density fluctuations are cosmic strings or global monopoles, or textures. These are topological defects from the symmetry-breaking phase transition at the end of the grand unification epoch. This model has very few parameters and hence is more appealing then the inflationary scenarios, but in this thesis the confidence is placed in the latter.

Mon Jul 5 02:59:28 MET DST 1999