## What is the nature of the Big Bang?

The universe has emerged approximately 13.75 billion years ago in extreme physical conditions callednthe Big Bang. The fundamental theory of the Cosmos, Einstein's general relativity, breaks down in attempts to explain the origin of this peculiar state with which everything has begun. There is, however, a way to extend general relativity in order to account for the singularity by combining it with quantum theory. By applying such extensions to well-known general relativisty models of homogenous but anisotropic universes (so-called Bianchi models), one may try to obtain the singularity resolution and study the real behavior of spacetime at the Planck scale.

## Can we observationally test quantum cosmology?

The domain of quantum cosmology is still behind the range of observational cosmology. In our research, we strive to change this situation. In particular, we perform predictions regarding generation of gravitational waves in the Planck epoch. The obtained spectra of gravitational waves are then compared with the CMB data, allowing to put constraining on some relevant parameters. However, applicability of this method is very sensitive on duration of inflation. Therefore, we also search for some new possible ways of testing physics at the Planck epoch.

## Is the bounce scenario generic in the Horava theory of gravity?

The visualisation of the phase space shows that a bounce is possible, but not generic, in some models of the Horava gravity. Depending on initial conditions the evolution of the Universe may lead, after a period of contraction, to a bounce and then expansion, or to a Big Crunch. There are also interesting solutions which describe some new sort of oscillating universes. In some realistic situations, it is possible to go from one oscillating bouncing solution to another. Further modifications of the theory bring another possibilities.

## Was there signature change at the Planck epoch?

The possibility of signature change, from Lorentzian to Euclidean one, at the Planck epoch was proposed by Hartle and Hawinkg in early eighties. While such possibility is conceptually interesting, mechanism behind the signature change remains mysterious. Our recent results predict such transition as consequence of discreteness of space at the Planck scale. In our model, signature change occurs gradually with increasing energy density. In our current studies we are going to understand nature of the signature change at the microscopic level. We also study impact of the signature change on propagation of cosmological perturbations.