Jerzy Stelmach

Can the Stephani model be an alternative to FRW accelerating models

A class of Stephani cosmological models as a prototype of a non-homogeneous universe is considered. The non-homogeneity can lead to accelerated evolution, which is now observed from the SNe Ia data. Three samples of type Ia supernovae obtained by Perlmutter et al, Tonry et al and Knop et al are taken into account. Different statistical methods (best fits as well as maximum likelihood method) to obtain estimation for the model parameters are used. The Stephani model is considered as an alternative to the ΛCDM model in the explanation of the present acceleration of the universe. The model explains the acceleration of the universe at the same level of accuracy as the ΛCDM model (χ2 statistics are comparable). From the best fit analysis it follows that the Stephani model is characterized by a higher value of density parameter Ωm0 than the ΛCDM model. It is also shown that the model is consistent with the location of CMB peaks.

Observable quantities in cosmological models with strings

The Friedman equation for the universe with arbitrary curvature filled with mutually noninteracting pressureless dust, radiation, cosmological constant, and strings is considered. The explicit solution of the Friedman equation is obtained for specific models. Formulas are derived for luminosity distance, angular diameter, and source counts, which may serve for testing the string-dominated universe. It seems that the most sensitive test, at least from the formal point of view, is the formula for the number of galaxies N(z) corresponding to a given value of the redshift. It is shown that the maximum of N(z) strongly depends on the density of strings, especially if the density is large enough to explain the Omega problem. 47 refs.

Non-homogeneity-driven universe acceleration

A class of spherically symmetric Stephani cosmological models is examined in the context of evolution type. It is assumed that the equation of state at the symmetry centre of the models is barotropic (p(t) = αρ(t)) and the function k(t) playing the role of spatial curvature is proportional to the Stephani version of the Friedmann-Robertson-Lemaitre-Walker scale factor R(t) (k(t) = βR(t)). A classification of the cosmological models is performed depending on different values and signs of parameters α and β. It is shown that for β<0 (hyperbolic geometry) a dust-like (α = 0) cosmological model exhibits accelerated expansion at later stages of evolution. The Hubble and deceleration parameters are defined in the model and it is shown that the deceleration parameter decreases with the distance becoming negative for sufficiently distant galaxies. The redshift-magnitude relation m(z) is calculated and discussed in the context of SnIa observational data. It is noted that the most distant supernovae of type Ia fit quite well to the relation m(z) calculated in the considered model (H0 = 65 km s-1 Mpc-1, Ω0≤0.3) without introducing the cosmological constant. It is also shown that the age of the universe in the model is longer than in the Friedmann model corresponding to the same H0 and Ω0 parameters.

Angular sizes in spherically symmetric Stephani cosmological models

Spherically symmetric Stephani cosmological models are considered in the context of angular sizes of compact as well as expanding objects percepted by an observer placed at the symmetry centre. We assume that the matter filling up Stephani universe satisfies barotropic equation of state at the symmetry centre p(r ≈ 0, t) = αρ(t). Angular sizes of compact objects are examined as a function of parameter α, of energy density parameter Ωα0 and of the redshift z. Small angle anisotropies of microwave background radiation connected with typical density fluctuation of mass corresponding to a galaxy are also calculated in the model. Finally the horizon problem is discussed in detail.

Effect of exotic matter on the angular size of anisotropies of the microwave background

Abstract The influence of exotic forms of matter on the angle subtended by the anisotropies imprinted on the microwave background is investigated. For simplicity only two particular equations of state p = − 1 3 ϱ and p = − 2 3 ϱ for the exotic matter are considered. It appears that the exotic matter enlarges the size of anisotropies. Addition of the positive cosmological constant makes the apparent angular size of the anisotropy much larger.