Electron-positron plasma is of interest in many fields of physics and astrophysics, e.g. in the early universe, active galactic nuclei, the center of our Galaxy, compact astrophysical objects such as hypothetical quark stars, neutron stars and gamma-ray bursts sources. It is also relevant for the physics of ultraintense lasers and thermonuclear reactions. We study physical properties of dense and hot electron-positron plasmas. In particular, we are interested in the issues of its creation and relaxation, its kinetic properties and hydrodynamic description, baryon load and radiation from such plasmas.

Astrophysical observations, in particular of transient sources such as gamma-ray bursts, provide motivation for theoretical analysis of physical conditions taking place in nonequilibrium optically thick relativistic plasma. There are substantial differences between the ion-electron plasma and electron-positron plasma. Firstly, the former is collisionless in the wide range of parameters, while collisions are often essential in the latter. Secondly, when collisions are important relevant interactions in the former case are Coulomb scattering of particles which are usually described by the classical Rutherford cross-section. In contrast, interactions in the pair plasma are described by quantum cross-sections even if the plasma itself can be still treated as classical one. We study thermalization process, relevant reactions, timescales and effects of baryon load, quantum degeneracy and initial conditions on this process. We develop a numerical code which solves relativistic Boltzmann equations with collision integrals computed directly from QED matrix elements.

Recent observations, especially by the Fermi satellite, point out the importance of the thermal component in time resolved spectra of gamma-ray bursts. This fact revives strong interest in photospheric emission from relativistic outflows. Early studies already suggested that the observed spectrum of photospheric emission from relativistically moving objects differs in shape from the Planck spectrum. However, this component appears to be subdominant in many GRBs and the origin of the dominant component is highly debated. We focus on spectral and timing characteristics of the photospheric emission from the relativistic outflows of finite duration. Physical effects which make the photospheric emission spectrum different from the black body spectrum are studied.

Limits on propagation of ultra high energy particles in the Universe are set up by their interactions with cosmic background of photons and neutrinos. We study the mean free path and the energy loss length for ultra high energy photons, protons and neutrinos by taking into account cosmic evolution of these backgrounds. For photons the relevant processes are the Breit-Wheeler process, the double pair production process as well as the photon-photon scattering process. For protons the relevant reactions are the photopion production and the Bethe-Heitler process.

The origin of the Universe and its early evolution are not accessible to direct observations. From the theoretical viewpoint, cosmological singularity appears to be inevitable within General Relativity theory, and it marks a breakdown of the theory. The idea that our expanding universe was preceded by a contracting phase is an attractive alternative to this picture. Within Loop Quantum Gravity, a leading nonperturbative background independent approach to quantize gravity, we study initial conditions for expanding universe. In particular, the issue of the generality of initial conditions which could lead to successful inflation, is investigated.