Mariusz P. Da̧browski

Exotic‐singularity‐driven dark energy

We discuss various types of exotic (non‐standard) singularities in the Universe: a Big‐Rip (BR or type I), a Sudden Future Singularity (SFS or type II), a Generalized Sudden Future Singularity, a Finite Scale Factor singularity (FSF or type III), a Big‐Separation (BS or type IV) and a w‐singularity. They are characterized by violation of all or some of the energy conditions which results in a blow‐up of all or some of the physical quantities: the scale factor, the energy density, the pressure, and the barotropic index. We relate the emergence of these singularities with physical theories (superstring, brane, higher‐order gravity, loop quantum cosmology). We show how the models involving exotic singularities may serve as dark energy by applying the observational data. In particular, we show that some of these exotic singularities (though being of a weak type according to relativistic definitions) may occur in the near future of the universe.

Null strings in Schwarzschild spacetime

The null string equations of motion and constraints in Schwarzschild spacetime are given. The solutions are those of the null geodesics of general relativity appended by a null string constraint in which the {open_quotes}constants of motion{close_quotes} depend on the world-sheet spatial coordinate. Because of the extended nature of a string, the physical interpretation of the solutions is completely different from the point particle case. In particular, a null string is generally not propagating in a plane through the origin, although each of its individual points is. Some special solutions are obtained and their physical interpretation is given. Especially, the solution for a null string with a constant radial coordinate r moving vertically from the south pole to the north pole around the photon sphere is presented. A general discussion of classical null or tensile strings as compared to massless or massive particles is given. For instance, tensile circular solutions with a constant radial coordinate r do not exist at all. The results are discussed in relation to the previous literature on the subject. {copyright} {ital 1997} {ital The American Physical Society}

Boundary conditions in quantum string cosmology

We discuss in detail how to consistently impose boundary conditions in quantum string cosmology. Since a classical time parameter is absent in quantum gravity, such conditions must be imposed with respect to intrinsic variables. Constructing wave packets for minisuperspace models from different tree-level string effective actions, we explain in particular the meaning of a transition between “pre-big-bang” and “post-big-bang” branches. This leads to a scenario different from previous considerations.

Simple dynamics on the brane

We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models. The simplicity of our formulation in comparison to some earlier studies is expressed in the following: our dynamical system is a 2-dimensional Hamiltonian system, and what is more advantageous, it is free from the degeneracy of critical points so that the system is structurally stable. The phase plane analysis of Randall-Sundrum models with isotropic Friedmann geometry clearly shows that qualitatively we deal with the same types of evolution as in general relativity, although quantitatively there are important differences.

Redshift drift in varying speed of light cosmology

Abstract We derive a redshift drift formula within the framework of varying speed of light (VSL) theory using the specific ansatz for the variability of c ( t ) = c 0 a n ( t ) . We show that negative values of the parameter n, which correspond to diminishing value of the speed of light during the evolution of the universe, effectively rescale dust matter to become little negative pressure matter, and the cosmological constant to became phantom. Positive values of n (growing c ( t ) ) make VSL model to become more like Cold Dark Matter (CDM) model. Observationally, there is a distinction between the VSL model and the ΛCDM model for the admissible values of the parameter n ∼ − 10 − 5 , though it will be rather difficult to detect by planned extremely large telescopes (EELT, TMT, GMT) within their accuracy.

Future state of the universe

Following the observational evidence for cosmic acceleration which may exclude a possibility for the universe to recollapse to a second singularity, we review alternative scenarios of its future evolution. Although the de Sitter asymptotic state is still an option, some other asymptotic states which allow new types of singularities such as Big-Rip (due to a phantom matter) and sudden future singularities are also admissible and are reviewed in detail. The reality of these singularities which comes from the relation to observational characteristics of the universe expansion are also revealed and widely discussed.

Redshift drift in a pressure-gradient cosmology

We derive a redshift drift formula for the spherically symmetric inhomogeneous pressure Stephani universes which are complementary to the spherically symmetric inhomogeneous density Lema\^itre-Tolman-Bondi models. We show that there is a clear difference between redshift drift predictions for these two models as well as between the Stephani models and the standard

Abolishing the maximum tension principle

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Statefinders and observational measurement of superenergy

CDM Friedmann models. The Stephani models have positive drift values at small redshift and behave qualitatively (but not quantitatively) as the

Spacetime averaging of exotic singularity universes

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