The nature of singularity in multidimensional anisotropic Gauss-Bonnet cosmology with a perfect fluid

We investigate dynamics of (4+1) and (5+1) dimensional flat anisotropic Universe filled by a perfect fluid in the Gauss-Bonnet gravity. An analytical solutions valid for particular values of the equation of state parameter $w=1/3$ have been found. For other values of $w$ structure of cosmological singularity have been studied numerically. We found that for $w > 1/3$ the singularity is isotropic. Several important differences between (4+1) and (5+1) dimensional cases are discussed.Comment: 8 pages, 2 fig

Constraints on inflation in closed universe

We investigate inflation in closed Friedmann-Robertson-Walker universe filled with the scalar field with power-law potential. For a wide range of powers and parameters of the potential we numerically calculated the slow-roll parameters and scalar spectral index at the epoch when present Hubble scale leaves the horizon and at the end of inflation. Also we compare results of our numerical calculations with recent observation data. This allows us to set a constraint on the power of the potential: alpha < (3.5 - 4.5).Comment: 5 pages, 5 figures; extended versio

Алелопатичні прийоми регулювання ґрунтових процесів при довготривалій культурі Syringa vulgaris L.

It was established that application of humus and green-manure (Brassica rapa var. oleifera) of the essential decrease of phytotoxicity of soil collected after long-term cultivation of lilac. It was shown that simultaneous application of humus and green-manure quickens humification processes in soil. The state of pigment system of lilac seedlings depended on biological activity of soil.Встановлено істотне зниження фітотоксичності ґрунту під довготривалою монокультурою бузку при внесенні перегною та сидерата (Brassica rара var. oleifera). Показано, що спільне їх застосування прискорює процеси гуміфікації у фунті. Стан пігментної системи сіянців бузку визначається біологічною активністю ґрунту

Cosmological solutions in Einstein–Gauss–Bonnet gravity with static curved extra dimensions

In this paper we perform systematic investigation of all possible solutions with static compact extra dimensions and expanding three-dimensional subspace (“our Universe”). Unlike previous papers, we consider extra-dimensional subspace to be constant-curvature manifold with both signs of spatial curvature. We provide a scheme how to build solutions in all possible number of extra dimensions and perform stability analysis for the solutions found. Our study suggests that the solutions with negative spatial curvature of extra dimensions are always stable while those with positive curvature are stable for a narrow range of the parameters and the width of this range shrinks with growth of the number of extra dimensions. This explains why in the previous papers we detected compactification in the case of negative curvature but the case of positive curvature remained undiscovered. Another interesting feature which distinguish cases with positive and negative curvatures is that the latter do not coexist with maximally-symmetric solutions (leading to “geometric frustration” of a sort) while the former could – this difference is noted and discussed