Quantum Evolution of the Bianchi Type I Model

The behaviour of the flat anisotropic model of the Universe with a scalar field is explored within the framework of quantum cosmology. The principal moment of the account of an anisotropy is the presence either negative potential barrier or positive repelling wall. In the first case occur the above barrier reflection of the wave function of the Universe, in the second one there is bounce off a potential wall. The further evolution of the Universe represents an exponential inflating with fast losses of an anisotropy and approach to the standard cosmological scenario.Comment: Latex, 18 pages, 5 figure

Homogeneous Solutions of Quadratic Gravity

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. In this work we present the 3+1 decomposition for the zero vorticity case for arbitrary spatially homogenous spaces. We specialize for the particular Bianchi $I$ diagonal case. The 3- curvature can be understood as a generalized potential, and the Bianchi $I$ case is a limiting case where this potential is negligible to the dynamics. The spirit should be analogous, in some sense to the BKL solution. In this sense, a better understanding of the Bianchi $I$ case could shed some light into the general Bianchi case.Comment: talk presented in the 8th Friedmann Seminar, 30 May - 03 June 2011, Rio de Janeiro, Brazi

The Power of General Relativity

We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to $R^{1+\delta}$. This scale-free extension reduces to general relativity when $\delta \to 0$. In order to constrain generalisations of general relativity of this power class we analyse the behaviour of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires $\delta >0$ or $\delta <-1/4$. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound $-0.017<\delta <0.0012.$ We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter--radiation equality will be shifted by $\sim 1$ for a value of $\delta \sim 0.0005.$ We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound $\delta =2.7\pm 4.5\times 10^{-19}$ assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound $0\leq \delta <7.2\times 10^{-19}$ on theories of this type.Comment: 26 pages and 5 figures. Published versio

Disappearing cosmological constant in f(R) gravity

For higher-derivative f(R) gravity where R is the Ricci scalar, a class of models is proposed which produce viable cosmology different from the LambdaCDM one at recent times and satisfy cosmological, Solar system and laboratory tests. These models have both flat and de Sitter space-times as particular solutions in the absence of matter. Thus, a cosmological constant is zero in flat space-time, but appears effectively in a curved one for sufficiently large R. A 'smoking gun' for these models would be small discrepancy in values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed which is connected with possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe.Comment: 8 pages, footnote clarified, grammatical typo corrected, references added, final version to be published in JETP

Isotropic Loop Quantum Cosmology

Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical effects the classical singularity is absent in those models in the sense that the evolution does not break down there, contrary to the classical situation where space-time is inextendible. This effect is generic and does not depend on matter violating energy conditions, but it does depend on the factor ordering of the Hamiltonian constraint. Furthermore, it is shown that loop quantum cosmology reproduces standard quantum cosmology and hence (e.g., via WKB approximation) to classical behavior in the large volume regime where the discreteness of space is insignificant. Finally, an explicit solution to the Euclidean vacuum constraint is discussed which is the unique solution with semiclassical behavior representing quantum Euclidean space.Comment: 30 page

A Cosmological Theory without Singularities

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.Comment: 25 pages, 11 figures (available as hard copies from the authors), uses phyzzx, BROWN-HET-89

Emergent Universe with Exotic Matter

A general framework for an emergent universe scenario has been given which makes use of an equation of state. The general features of the model have also been studied and possible primordial composition of the universe have been suggested.Comment: 11 pages, no fi