Recent investigations revealed that the explosive decay of the inflaton field takes place in the first stage of reheating due to the effect of parametric resonance (Kofman et al., 1994). One of surprising possibilities of the non-thermal fluctuations (created particles) during preheating is the symmetry restoration which may lead to the formation of topological defects (Kofman et al., 1996; Tkachev, 1996).

Recently it has been reported that there may be a discrepancy between big bang nucleosynthesis theory and observations (BBN crisis) (Hata et al., 1995). One way to solve the discrepancy might be to adopt some modifications of standard physics used in SBBN (Kawasaki et al, 1997). We show that BBN predictions agree with the primordial abundances of light elements, 4He, D, 3He and 7Li inferred from the observational data if the electron neutrino has a net chemical potential ξve due to lepton asymmetry (Kohri et al., 1997). We study BBN with the effects of the neutrino degeneracy in details using Monte Carlo simulation and make a likelihood analysis using the most recent data. We estimate that (95% C.L.) and (95% C.L.) adopting the presolar Deuterium abundance as the primordial values. If we adopted the low D abundance which is obtained by the observation of the high redshift QSO absorption systems, (95% C.L.) and The estimated chemical potential of ve is about 10−5 eV which is much smaller than experiments can detect (≃ 1 eV). In other words, BBN gives the most stringent constraint on the chemical potential of ve.

The degree of sound speed reduction is estimated during the coexistence epoch of quark-gluon and hadron phases in the first-order QCD phase transition[1]. The sound speed in a mixture is obtained by simply replacing the energy density with the mean value in the usual formula[2]. Since the adiabatic condition is nothing but the second law of thermodynamics which is useless for the purpose of calculating the sound speed qualitatively, we adopt the conservation of the quality which is the energy fraction of the high-energy phase[2]. This is appropriate because the transition of the phases through bubble nucleation is totally suppressed at the coexistence temperature and the expansion speed of bubbles is so small that energy transfer through bubble expansion or contraction is also expected to be negligible during sound-wave propagation. Using the bag model, the numerical value of the minimum sound speed can be calculated as where the uncertainty comes from the selection of the number of relativistic quark species. Thus we can say that the quark-hadron phase transition has no drastic effect on the development of cosmological density perturbations.

In a FRW Universe a massless nonminimally coupled scalar field satisfies the Klein-Gordon equation.

Since the real Universe is clumpy and inhomogeneous even at rather large scale such as 100 Mpc, we may wonder whether the isotropic and homogeneous Friedmann model is valid when we compare some cosmological parameters with the observed values. The observed Hubble parameter H0 or the density parameter Ω0 might be deviated from the theoretically expected ones from the Friedmann model. In fact, the density parameter Ω0 seems to vary depending on the observational methods and the distance scales. Furthermore, our Universe seems to possess a fractal property in the galaxy distributions at least at scale up to 10 Mpc.

It is well known that standard Big-Bang cosmology suffers from certain problems, e.g. singularity, horizon, flatness, … In the present work it is claimed that the appearence of some of these problems is due to two main assumptions. The first is the assumption that the 4-dimentional Riemannian (RIE)-geometry gives a complete description of the cosmic space-time. The second is the assumption that the material distribution in the universe is described by a phenomenological (PH)-matter tensor. It is shown that, by relaxing these two assumptions, some of the problems of the standard Big-Bang cosmology could be avoided. The following table summarises some results in favour of the above claim. The absolute parallelism (AP)-geometry is used to construct some of the theories mentioned in the table.