Mariusz P. Dabrowski

Inhomogenized sudden future singularities

We find that sudden future singularities may also appear in spatially inhomogeneous Stephani models of the universe. They are temporal pressure singularities and may appear independently of the spatial finite density singularities already known to exist in these models. It is shown that the main advantage of the homogeneous sudden future singularities which is the fulfillment of the strong and weak energy conditions may not be the case for inhomogeneous models.

Strings at future singularities

We discuss the behavior of strings propagating in spacetimes which allow future singularities of either a sudden future or a Big-Rip type. We show that in general the invariant string size remains finite at sudden future singularities while it grows to infinity at a Big-Rip. This claim is based on the discussion of both the tensile and null strings. In conclusion, strings may survive a sudden future singularity, but not a Big-Rip where they are infinitely stretched.

Superenergy and supermomentum of Gödel universes

We review the canonical superenergy tensor and the canonical angular supermomentum tensor in general relativity and calculate them for spacetime homogeneous Godel universes to show that both of these tensors do not, in general, vanish. We consider both an original dust-filled pressureless acausal Godel model of 1949 and a scalar-field-filled causal Godel model of Reboucas and Tiomno. For the acausal model, the nonvanishing components of superenergy of matter are different from those of gravitation. The angular supermomentum tensors of matter and gravitation do not vanish either which simply reflects the fact that the Godel universe rotates. However, the axial (totally antisymmetric) and vectorial parts of supermomentum tensors vanish. It is interesting that superenergetic quantities are sensitive to causality in a way that superenergy density gS00 of gravitation in the acausal model is positive, while superenergy density gS00 in the causal model is negative. That means superenergetic quantities might serve as criteria of causality in cosmology and prove useful.

Oscillating Friedman Cosmology

Abstract The non-singular, oscillating Friedman cosmology within the framework of General Relativity is considered. The general oscillatory solution is given and the conditions for its existence are discussed. It is shown that the wall-like-matter and the small, but negative cosmological constant are required for oscillations. The oscillations can, in principle, be deep enough to allow standard hot universe processes like recombination and nucleosynthesis. It is shown that wall-like-matter and string-like-matter can be interpreted as scalar fields with some potentials. This may give another candidate for the dark matter which may be compatible with observational data. For an exact elementary oscillatory solution it is shown that the associated scalar fields potentials are oscillating as well.

Brane f(R) gravity cosmologies

By the application of the generalized Israel junction conditions we derive cosmological equations for the fourth-order f(R) brane gravity and study their cosmological solutions. We show that there exists a nonstatic solution which describes a four-dimensional de Sitter (dS{sub 4}) brane embedded in a five-dimensional anti-de Sitter (AdS{sub 5}) bulk for a vanishing Weyl tensor contribution. On the other hand, for the case of a nonvanishing Weyl tensor contribution, there exists a static brane solution only. We claim that in order to get some more general nonstatic f(R) brane configurations, one needs to admit a dynamical matter energy-momentum tensor in the bulk rather than just a bulk cosmological constant.

Generalized Israel junction conditions for a fourth-order brane world

We discuss a general fourth-order theory of gravity on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.

BRANE UNIVERSES TESTED AGAINST ASTRONOMICAL DATA

We discuss observational constrains coming from supernovae imposed on the behaviour of the Randall–Sundrum models. We test the models using the Perlmutter SNIa data as well as the new Knop and Tonry/Barris samples. The data indicates that, under the assumption that we admit zero pressure dust matter on the brane, the cosmological constant is still needed to explain current observations. We estimate the model parameters using the best-fitting procedure and the likelihood method. The observations from supernovae give a large value of the density parameter for brane matter Ωλ,0≃0.01 as the best fit. For high redshifts z>1.2, the difference between the brane model and the ΛCDM (Perlmutter) model becomes detectable observationally. From the maximum likelihood method we obtained the favored value of Ωλ,0=0.004±0.016 for Ωk,0=0 and Ωm,0=0.3. This gives the limit Ωλ,0<0.02 at 1σ level. While the model with brane effects is preferred by the supernovae type Ia data, the model without brane fluid is still statistically admissible. We also discuss how fit depends on restrictions of the sample, especially with respect to redshift criteria. We also pointed out the property of sensitive dependence of results with respect to the choice of ℳ parameter. For comparison the limit on brane effects which comes from CMB anisotropies and BBN is also obtained. The uncertainty in the location of the first peak gives a stronger limit Ωλ,0<1.0×10-12, whereas from BBN we obtain that Ωλ,0<1.0×10-27. However, both very strict limits are obtained with the assumption that brane effects do not change the physics in the pre-recombination era, while the SNIa limit is model independent. We demonstrate that the fit to supernovae data can also be obtained if we admit the phantom matter p=-(4/3)ϱ on the brane, where this matter mimics the influence of the cosmological constant. We show that phantom matter enlarges the age of the universe on the brane which is demanded in cosmology. Finally, we propose to check for dark radiation and brane tension by the application of the angular diameter of galaxies minimum value test.

A Redshift-Magnitude Relation for Non-Uniform Pressure Universes

A redshift-magnitude relation for the two exact non-uniform pressure spherically symmetric Stephani universes is presented. The Kristian-Sachs method expanding the relativistic quantities in series is used, but only first order terms in redshift z are considered. The numerical results are given both for centrally placed and non-centrally placed observers. In the former case the redshiftmagnitude relation does not depend on the direction in the sky and the Friedman limit can be easily performed. It appears that the effect of spatial dependence of pressure is similar to the effect of the deceleration parameter in Friedman models. In the latter case the angular dependence of the relation is important. This may serve as another possible explanation of the noncompatibility of the theoretical curve of the redshift-magnitude relation with observations for large redshift objects in the Friedman universe. On the other hand comparing the magnitudes of equal redshifts objects in different directions in the sky one can test the reliability of these models.

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.

Quantum Tunneling Effect in Oscillating Friedmann Cosmology

It is shown that the tunneling effect in quantum cosmology is possible not only at the very beginning or the very end of the evolution, but also at the moment of maximum expansion of the universe. A positive curvature expanding Friedmann universe changes its state of evolution spontaneously and completely, {\it without} any changes in the matter content, avoiding recollapse, and falling into oscillations between the nonzero values of the scale factor. On the other hand, an oscillating nonsingular universe can tunnel spontaneously to a recollapsing regime. The probability of such kind of tunneling is given explicitly. It is inversely related to the amount of nonrelativistic matter (dust), and grows from a certain fixed value to unity if the negative cosmological constant approaches zero.