Abstract:
In view of our accelerating universe, one of the outstanding theoretical issues is the absence of a quantum-gravitational description of de Sitter space. Although speculative, an intriguing circumvention may be found in the realm of brane-world scenarios; where the physical universe can be interpreted as a non-critical 3-brane moving in a higher-dimensional, static bulk. In this paper, we focus on the cosmological implications of a positively curved brane world evolving in the background of a ``topological'' anti-de Sitter black hole (i.e, Schwarzschild-like but with an arbitrary horizon topology). We show that the bulk black hole will typically induce either an asymptotically de Sitter ``bounce'' universe or a big bang/big crunch FRW universe, depending on a critical value of mass. Interestingly, the critical mass is only non-vanishing in the case of a spherical horizon geometry. We go on to provide a holographic interpretation of this curiosity.

Abstract:
Ordinary-sterile neutrino oscillations can generate a significant lepton number asymmetry in the early Universe. We study this phenomenon in detail. We show that the dynamics of ordinary-sterile neutrino oscillations in the early Universe can be approximately described by a single integro-differential equation which we derive from both the density matrix and Hamiltonian formalisms. This equation reduces to a relatively simple ordinary first order differential equation if the system is sufficiently smooth (static limit). We study the conditions for which the static limit is an acceptable approximation. We also study the effect of the thermal distribution of neutrino momenta on the generation of lepton number. We apply these results to show that it is possible to evade (by many orders of magnitude) the Big Bang Nucleosynthesis (BBN) bounds on the mixing parameters, $\delta m^2$ and $\sin^2 2\theta_0$, describing ordinary-sterile neutrino oscillations. We show that the large angle or maximal vacuum oscillation solution to the solar neutrino problem does not significantly modify BBN for most of the parameter space of interest, provided that the tau and/or mu neutrinos have masses greater than about 1 eV. We also show that the large angle or maximal ordinary-sterile neutrino oscillation solution to the atmospheric neutrino anomaly does not significantly modify BBN for a range of parameters.

Abstract:
The abundances of anti-protons and protons are considered within momentum-integrated Boltzmann equations describing Little Bangs, i.e., fireballs created in relativistic heavy-ion collisions. Despite of a large anti-proton annihilation cross section we find a small drop of the ratio of anti-protons to protons from 170 MeV (chemical freeze-out temperature) till 100 MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus corroborating the solution of the previously exposed "ani-proton puzzle". In contrast, the Big Bang evolves so slowly that the anti-baryons are kept for a long time in equilibrium resulting in an exceedingly small fraction. The adiabatic path of cosmic matter in the phase diagram of strongly interacting matter is mapped out.

Abstract:
The physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the "big bang", and possibly a "big crunch". However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with "big rips" and "sudden singularities" added to the mix, as well as renewed interest in non-singular cosmological events such as "bounces" and "turnarounds". In this article we present a complete catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, using generalized power series, purely kinematical definitions of these cosmological events are provided in terms of the behaviour of the scale factor a(t). The notion of a "scale-factor singularity'" is defined, and its relation to curvature singularities (polynomial and differential) is explored. Second, dynamical information is extracted by using the Friedmann equations (without assuming even the existence of any equation of state) to place constraints on whether or not the classical energy conditions are satisfied at the cosmological milestones. We use these considerations to derive necessary and sufficient conditions for the existence of cosmological milestones such as bangs, bounces, crunches, rips, sudden singularities, and extremality events. Since the classification is extremely general, the corresponding results are to a high degree model-independent: In particular, we provide a complete characterization of the class of bangs, crunches, and sudden singularities for which the dominant energy condition is satisfied.

Abstract:
Big bang of the Friedmann-Robertson-Walker (FRW)-brane universe is studied. In contrast to the spacelike initial singularity of the usual FRW universe, the initial singularity of the FRW-brane universe is point-like from the viewpoint of causality including gravitational waves propagating in the bulk. Existence of null singularities (seam singuralities) is also shown in the flat and open FRW-brane universe models.

Abstract:
The evolution of strongly interacting matter during the cosmological confinement transition is reviewed. Despite of many proposed relics no specific signal from the rearrangement of quarks and gluons into hadrons has been identified by observations. In contrast to this, several observables in heavy-ion collisions at CERN-SPS energies point to the creation of a matter state near or slightly above deconfinement. We focus here on the analysis of dileptons and direct photons. Similarities and differences of the Big Bang and the Little Bang confinement dynamics are elaborated.

Abstract:
The occurrence of a big smash singularity which ends the universe in a finite time in the future is investigated in the context of superquintessence, i.e. dark energy with effective equation of state parameter w<-1. The simplest model of superquintessence based on a single nonminimally coupled scalar field exhibits big smash solutions which are attractors in phase space.

Abstract:
The usual Einstein's equations is modified as a one parameter family of equations in the framework of rainbow gravity. In this paper we derive the modified Friedmann-Robertson-Walker (FRW) equations when the cosmological evolution of radiation particles is taken into account. In particular, given some specific dispersion relations, the big bounce solutions to the modified FRW equations can be derived. Notably, to obtain a well defined rainbow metric at the moment of the big bounce, we find it seems necessary to introduce a cosmological constant which depends on the energy of probes as well, implying that a universe with a positive cosmological constant more likely undergoes a big bounce at least at this phenomenological level.

Abstract:
It has been claimed in several papers that a phantom energy-dominated universe can undergo a ``big trip'', i.e., tunneling through a wormhole that grows faster than the cosmic substratum due to the accretion of phantom energy, and will reappear on the other mouth of the wormhole. We show that such claims are unfounded and contradict the Einstein equations.

Abstract:
Four lectures on Big Bang cosmology, including microwave background radiation, Big Bang nucleosynthesis, dark matter, inflation, and baryogenesis.