Abstract:
$\nu$MSM is a minimal renormalizable extension of the Standard Model by right handed neutrinos. This model explains the neutrino oscillations and provides a candidate for the Dark Matter and a mechanism of baryon number generation in the Early Universe. We discuss here existing constraints on the model and possible consequences for astrophysical and laboratory experiments.

Abstract:
I will discuss the recent LHC and Planck results, which are completely compatible with the Standard Model of particle physics, and the standard cosmological model ($\Lambda$CDM), respectively. It turns out that the extension of the Standard Model is, of course, required, but can be very minimal. I will discuss also what future measurements may be important to test this approach.

Abstract:
The Higgs field of the pure Standard Model can lead to the inflationary expansion of the early Universe if it is non-minimally coupled to gravity. The model predicts Cosmic Microwave Background (CMB) parameters in perfect agreement with the current observations and has implications for the Higgs boson mass. We review the model, its predictions, problems arising with its quantization and some closely related models.

Abstract:
Uranium, Thorium and Potassium-40 abundances in the Earth were calculated in the frame of Hydridic Earth model. Terrestrial heat producton from U, Th and K40 decays was calculated also. We must admit the existance of Earth expansion process to understand the obtained large value of terrestrial heat producton. The geoneutrino detector with volume more than 5 kT (LENA type) must be constructed to definitely separate between Bulk Silicat Earth model and Hydridic Earth model. In second version of the article we assume that K40 concentration distributes in the Earth uniformly.

Abstract:
A method of reducing the problem of the calculation of tree multiparticle cross sections in $\phi^4$ theory to the solution of a singular classical Euclidean boundary value problem is introduced. The solutions are obtained numerically in terms of the decomposition in spherical harmonics, and the corresponding estimates of the tree cross sections at arbitrary energies are found. Numerical analysis agrees with analytical results obtained earlier in the limiting cases of large and small energies.

Abstract:
We analyse the effect of the non-minimal coupling of the form $\xi\phi^2R/2$ on the single field inflation. If the non-minimal coupling is large, it relaxes the constraint on the field self coupling, making it possible to use the Standard Model Higgs field as the inflaton. At the same time, even small non-minimal coupling constant, $\xi\gtrsim10^{-3}$, brings the usual inflaton with quartic potential in agreement with the WMAP5 observations.

Abstract:
We study the phenomenology of a realistic version of the chaotic inflationary model, which can be fully and directly explored in particle physics experiments. The inflaton mixes with the Standard Model Higgs boson via the scalar potential, and no additional scales above the electroweak scale are present in the model. The inflaton-to-Higgs coupling is responsible for both reheating in the Early Universe and the inflaton production in particle collisions. We find the allowed range of the light inflaton mass, 270 MeV<~m_chi<~1.8 GeV, and discuss the ways to find the inflaton. The most promising are two-body kaon and B-meson decays with branching ratios of orders 10^{-9} and 10^{-6}, respectively. The inflaton is unstable with the lifetime 10^{-9}--10^{-10} s. The inflaton decays can be searched for in a beam-target experiment, where, depending on the inflaton mass, from several billions to several tenths of millions inflatons can be produced per year with modern high-intensity beams.

Abstract:
We extend the analysis of \cite{Bezrukov:2008ej} of the Standard Model Higgs inflation accounting for two-loop radiative corrections to the effective potential. As was expected, higher loop effects result in some modification of the interval for allowed Higgs masses m_min

Abstract:
A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A regularization technique is proposed, which enables one to choose physically relevant branches of solutions everywhere in the classically forbidden region and also in the allowed region. At relatively high energy the physical branch describes tunneling via creation of a classical state, close to the top of the barrier. The method is checked against exact solutions of the Schrodinger equation in a quantum mechanical system of two degrees of freedom.

Abstract:
We present three features which can be used to distinguish the R^2-inflation Higgs-inflation from with ongoing, upcoming and planned experiments, assuming no new physics (apart form sterile neutrinos) up to inflationary scale. (i) Slightly different tilt of the scalar perturbation spectrum n_s and ratio r of scalar-to-tensor perturbation amplitudes. (ii) Gravity waves produced within R^2-model by collapsing, merging and evaporating scalaron clumps formed in the post-inflationary Universe. (iii) Different ranges of the possible Standard Model Higgs boson masses, where the electroweak vacuum remains stable while the Universe evolves after inflation. Specifically, in the R^2-model Higgs boson can be as light as 116 GeV. These effects mainly rely on the lower reheating temperature in the R^2-inflation.