Abstract:
In this lecture first I present a brief genesis of the ideas on the electroweak baryogenesis and then I focus on a mechanism in which the source of $CP$ violation is a $CP$-violating field condensate which could occur, for example, in multi-higgs extensions of the Standard Model. In the limit of a thick bubble wall one finds a classical force acting on particles proportional to the mass squared and the $CP$ violating phase. One can study this force in the fluid approximation in which the effects of transport and particle decays can be taken into account. A novelty in this talk is generalization of the problem to the relativistic velocity. There is a regime in which the final formula for the baryon asymmetry has a rather simple form.

Abstract:
Baryon asymmetry can be generated at the first order electroweak phase transition, provided there is a CP violation on the bubble wall. In this report we discuss the role of leptons and quarks in the `non-local' baryogenesis mechanism.

Abstract:
I review my recent work with Brian Greene and Thomas Roos. First I discuss the effect of a negative cross-coupling on the inflaton decay in two scalar field theories. Our main finding is a new effect, the negative coupling instability, which leads to explosive particle production and very fast inflaton decay. Then I discuss the consequences of this instability for grandunified baryogenesis models. The novel aspect of this review is an intuitive explanation of the negative coupling instability, using field trajectories in the configuration space.

Abstract:
In this study we examine post-inflationary cosmologies dominated by a scalar field with the equation of state: p_phi=w_phi rho_phi (0 leq w_phi leq 1) in order to facilitate baryogenesis at the electroweak scale. We take a more conventional approach from one in Ref. 1 [Joyce, Prokopec] and assume that the Universe reheats by the scalar field decay before the nucleosynthesis epoch, and find a larger expansion rate at the electroweak scale than the one obtained in Ref. 1. The decaying field models suffer however from an entropy release that dilutes the baryon number produced at the electroweak scale. This dilution is minimized when the kinetic scalar field mode dominates (w_phi = 1), singling it out as the preferred cosmology with regard to baryogenesis. We study both cases, the electroweak transition with an expansion driven departure from equilibrium, and a first order phase transition. We show that in the former case with some tuning one can produce the amount of matter consistent with observation. In the latter case the expansion rate at the electroweak scale may be almost as large as the symmetric phase sphaleron rate, so that even the electroweak models with a relatively weak first order phase transition can be viable for baryogenesis.

Abstract:
In this talk I discuss models in which a homogeneous scalar field is used to modify standard cosmology above the nucleosynthesis scale to provide an explanation for the observed matter-antimatter asymmetry of the Universe.

Abstract:
We consider several gauge invariant higher dimensional operators that couple gravity, gauge fields and scalar or fermionic fields and thus break conformal invariance. In particular, we consider terms that break conformal invariance by the photon coupling to heavy and light fermions. While the coupling to heavy fermions typically do not induce significant magnetic fields, the coupling to light fermions may produce observable magnetic fields when there are a few hundred light fermions. Next we consider Planck scale modifications of the kinetic gauge terms of the form f(phi) F_{mu nu} F^{mu nu} and h(psi) F_{mu nu} \~F^{mu nu}, where f and h are functions of scalar and pseudoscalar fields phi, psi, and F_{mu nu}, ~F^{mu nu} are the gauge field strength and its dual, respectively. For a suitable choice of f sufficiently strong magnetic fields may be produced in inflation to be potentially observable today. The pseudoscalar coupling may lead to birefringence in inflation, but no observable magnetic field amplification. Finally, we show that the photon coupling to metric perturbations produces by far too weak fields to be of cosmological interest.

Abstract:
We consider an O(N) symmetric scalar field model in the mean field (Hartree) approximation and show that the symmetry can be broken in de Sitter space. We find that the phase transition can be of first order, and that its strength depends non-analytically on the parameters of the model. We also show that the would-be Goldstone bosons acquire a mass, effectively becoming pseudo-Goldstone bosons, thus breaking the O(N) symmetry. Our results imply that topological defects can form during inflation.

Abstract:
It is well known that string theories naturally compactify on anti-de Sitter spaces, and yet cosmological observations show no evidence of a negative cosmological constant in the early Universe's evolution. In this letter we present two simple nonlocal modifications of the standard Friedmann cosmology that can lead to observationally viable cosmologies with an initial (negative) cosmological constant. The nonlocal operators we include are toy models for the quantum cosmological backreaction. In Model I an initial quasiperiodic oscillatory epoch is followed by inflation and a late time matter era, representing a dark matter candidate. The backreaction in Model II quickly compensates the negative cosmological term such that the Ricci curvature scalar rapidly approaches zero, and the Universe ends up in a late time radiation era.

Abstract:
After a short review of electroweak scale baryogenesis, we consider the dynamics of chiral fermions coupled to a complex scalar field through the standard Yukawa interaction term at a strongly first order electroweak phase transition. By performing a systematic gradient expansion we can use this simple model to study electroweak scale baryogenesis. We show that the dominant sources for electroweak baryogenesis appear at linear order in the Planck constant h-bar. We provide explicit expressions for the sources both in the flow term and in the collision term of the relevant kinetic Boltzmann equation. Finally, we indicate how the kinetic equation sources appear in the fluid transport equations used for baryogenesis calculations.

Abstract:
We argue that, when coupled to Einstein's theory of gravity, the Yukawa theory may solve the cosmological constant problem in the following sense: The radiative corrections of fermions generate an effective potential for the scalar field, such that the effective cosmological term Lambda_eff is dynamically driven to zero. Thence, for any initial positive cosmological constant Lambda_0, Lambda_eff = 0 is an attractor of the semiclassical Einstein theory coupled to fermionic and scalar matter fields. When the initial cosmological term is negative, Lambda_eff=Lambda_0 does not change. Next we argue that the dark energy of the Universe may be explained by a GUT scale fermion with a mass, m = 4.3 * 10^15 (Lambda_0/10^13GeV)^(1/2) GeV. Finally, we comment on how the inflationary paradigm, BEH mechanism and phase transitions in the early Universe get modified in the light of our findings.