Tomasz Stachowiak

Exact solutions for a big bounce in loop quantum cosmology

In this paper we study the flat (k=0) cosmological Friedmann-Robertson-Walker model with holonomy corrections of loop quantum gravity. The considered universe contains a massless scalar field and the cosmological constant {lambda}. We find analytical solutions for this model in different configurations and investigate its dynamical behavior in the whole phase space. Such an approach might be significant e.g. as a phenomenological reference for a further, fully quantum treatment. We show the explicit influence of {lambda} on the qualitative and quantitative character of solutions. Even in the case of positive {lambda} the oscillating solutions without the initial and final singularity appear as a generic case for some quantization schemes.

Full spectrum of the Rabi model

It is shown that in the Rabi model, for an integer value of the spectral parameter x, in addition to the finite number of the classical Judd states there exist infinitely many possible eigenstates. These eigenstates exist if the parameters of the problem are zeros of a certain transcendental function; in other words, there are infinitely many possible choices of parameters for which integer x belongs to the spectrum. Moreover, it is shown that the classical Judd eigenstates appear as degenerate cases of the confluent Heun function.

Towards testing interacting cosmology by distant supernovae

We investigate the possibility of testing cosmological models with interaction between dark matter and the dark energy sector. We assume the standard Friedmann-Robertson-Walker (FRW) model while the so called the energy conservation condition is interpreted locally in terms of energy transfer. We analyze two forms of the dark energy sector: the cosmological constant and the phantom field. We find a simple exact solution of the models in which energy transfer is described by a Cardassian like term in the relation of

Global integrability of cosmological scalar fields

{H}^{2}(z)

Analytical method of spectra calculations in the Bargmann representation

, where

Exact solutions in bouncing cosmology

H

VORTEX IN AXION CONDENSATE AS A DARK MATTER HALO

is Hubbles function and

An exactly solvable system from quantum optics

z

Nonexistence of the final first integral in the Zipoy-Voorhees space-time

is redshift. The considered models have two additional parameters

A differential algorithm for the Lyapunov spectrum

({\ensuremath{\Omega}}_{\mathrm{int}},n)