Nonstationary cosmological models with rotation

Cosmological models containing rotation and expansion have become of great interest since the publication of Birch. In the present paper we obtain a wide class of exact solutions describing an expanding and rotating universe. Sources are taken to be an anisotropic or ideal fluid, a massless scalar field, and a radiation field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 48–51, March, 1988.     

Five-domensional, nonstationary cosmological solutions with rotation

Two nonstationary cosmological solutions of the five-dimensional Einstein equations are found for different metrics. In one case the sources of the gravitational field are an anisotropic fluid and a radiation field, while in the other case they are an anisotropic fluid, a radiation field, and a heat flux. Perm' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 25–28, September, 1997.     

Self-consistent solutions of the semiclassical Einstein equations with cosmological constant

The general solution to the semiclassical backreaction equation is found for conformally invariant free quantum fields in spatially flat homogeneous and isotropic spacetime with Cosmological constant and with no classical source when the ratio of the renormalisation parameters/=9/4. It contains a two-parameter family of bouncing solutions that avoid the singularity. There are several one-parameter families which do not have particle horizons. The stability of these solutions is investigated and it is found that they are stable when and have different signs. However, when both parameters have the same sign the set of stable solutions is restricted by the condition 0 < < 1/9. In both cases these solutions have a final de Sitter stage.     

Spontaneous symmetry breaking in cosmological models with rotation

We study the possibility of spontaneously broken gauge symmetry in the theory of a charged massive or massless scalar field for cosmological models of the Gödel and Ozsvath-Schücking types. We consider the effect of spontaneous symmetry breaking in the construction of a new cosmological solution with rotation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 22–26, February, 1989.The author thanks the participants of the seminars of Prof. A. A. Grib and Prof. D. D. Ivanenko for discussions of the results.     

Bianci-IX cosmological models with rotation in general relativity theory

Bianci-IX metrics have been used to obtain new exact solutions to the GRT equations, which may describe the early stages in the evolution of an expanding and rotating universe.Kaluga Branch, Bauman Moscow State Technical University. M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 9, pp. 122–127, September, 1994.     

Bianchi-II cosmological models with rotation in general relativity theory

We obtain a broad class of new exact solutions in Bianchi-II cosmologies with rotation and expansion. We show that within the framework of general relativity theory, we can construct realistic cosmological models in good agreement with current observational data.N. É. Bauman State Technical University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 54–63, October, 1994.     

Exact solutions in cosmological inflationary models

The exact solutions of the Einstein equations that correspond to a given evolution of the scale factor in the inflationary stage in the development of the universe are considered within the framework of the theory of a self-acting scalar field that interacts minimally with a gravitational field. The form of the potential that ensures a given rate of expansion and the solution for the scalar field are calculated for each type of inflation considered. Some general laws of the relation between the form of potential and the scale factor evolution are analyzed. Moscow State University Branch in Ul'yanovsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 83–88, August, 1996.     

Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization

We consider a PDE system comprising compressible hydrodynamics, flux-limited diffusion radiation transport and chemical ionization kinetics in a cosmologically-expanding universe. Under an operator-split framework, the cosmological hydrodynamics equations are solved through the piecewise parabolic method, as implemented in the Enzo community hydrodynamics code. The remainder of the model, including radiation transport, chemical ionization kinetics, and gas energy feedback, form a stiff coupled PDE system, which we solve using a fully-implicit inexact Newton approach, and which forms the crux of this paper. The inner linear Newton systems are solved using a Schur complement formulation, and employ a multigrid-preconditioned conjugate gradient solver for the inner Schur systems. We describe this approach and provide results on a suite of test problems, demonstrating its accuracy, robustness, and scalability to very large problems.     

Type-D vacuum solutions with cosmological constant

All type-D vacuum (nonnull orbit and null orbit) solutions with are exhibited in canonical coordinates. The nonnull orbit metrics with contain four families of solutions: the static Levi-Cività metrics, the nondivergingD's, the divergingD's, and the diverging and twisting solutions. The null orbit metrics subdivide into two subclasses of solutions: the divergenceless null orbitD's, and the diverging and twisting null orbit solution.     

Inhomogeneous cosmological models with heat flux

We present a general class of inhomogeneous cosmological models filled with non-thermalized perfect fluid by assuming that the background spacetime admits two space-like commuting Killing vectors and has separable metric coefficients. The singularity structure of these models depends on the choice of the parameters and the metric functions. A number of previously known perfect fluid models follow as particular cases of this general class. Physical and geometrical features of these models are studied and the general expression for temperature distribution is given.     

Brans-Dicke models with time-dependent cosmological term

More general solutions than those presented by Bertolami are deduced in the Brans-Dicke cosmology, endowed with a time-dependent cosmological term, for a Robertson-Walker metric and a perfect fluid obeying the perfect gas law of state.     

Self-similar cosmological models

The kinematics and dynamics of self-similar cosmological models are discussed. The degrees of freedom of the solutions of Einstein's equations for different types of models are listed. The relation between kinematic quantities and the classifications of the self-similarity group is examined. All dust local rotational symmetry models have been found.     

Self-consistent asset pricing models

We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alphas and betas of the factor model are unobservable. Self-consistency leads to renormalized betas with zero effective alphas, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value α_i at the origin between an asset i's return and the proxy's return. Self-consistency also introduces “orthogonality” and “normality” conditions linking the betas, alphas (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from January 1990 to February 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the self-consistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the self-consistency condition derives a risk-factor decomposition in the multi-factor case which is identical to the principal component analysis (PCA), thus providing a direct link between model-driven and data-driven constructions of risk factors. This correspondence shows that PCA will therefore suffer from the same limitations as the CAPM and its multi-factor generalization, namely lack of out-of-sample explanatory power and predictability. In the multi-period context, the self-consistency conditions force the betas to be time-dependent with specific constraints.     

Behavior of a bundle of rays forming the image of a source in cosmological models with rotation

Our earlier results regarding the absence of Birch anisotropy in cosmological models with rotation were obtained under the assumption that a bundle of rays forming the image of a source is nonrotating. This appears to be at variance with the rotation of space. The detailed analysis in the present paper of the behavior of rays propagating from a source to an observer shows that the congruence of the rays is, in fact, nonrotating. The doubts expressed by some authors in reference to our conclusions that the Birch effect is not attributable to cosmological rotation are thereby put to rest. Zh. éksp. Teor. Fiz. 114, 769–776 (September 1998)     

Singularity-free cosmological solutions with non-rotating perfect fluids

A conjecture stated by Raychaudhuri which claims that the only physical perfect fluid non-rotating non-singular cosmological models are comprised in the Ruiz–Senovilla and Fernández–Jambrina families is shown to be incorrect. An explicit counterexample is provided and the failure of the argument leading to the result is explicitly pointed out.