Adam Balcerzak

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.

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.

Gibbons-Hawking boundary terms and junction conditions for higher-order brane gravity models

We derive the most general junction conditions for the fourth-order brane gravity constructed of arbitrary functions of curvature invariants. We reduce these fourth-order theories to second order theories at the expense of introducing new scalar and tensor fields - the scalaron and the tensoron. In order to obtain junction conditions we apply the method of generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. After assuming the continuity of the scalaron and the tensoron on the brane, we recover junction conditions for such general brane universe models previously obtained by different methods. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.

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.

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

Density perturbations in a finite scale factor singularity universe

\Lambda

Randall-Sundrum limit of f(R) brane-world models

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

Critical assessment of some inhomogeneous pressure Stephani models

\Lambda

Off-center Observers Versus Supernovae in Inhomogeneous Pressure Universes

CDM models at large redshift, while the drift for LTB models is always negative. This prediction may perhaps be tested in future telescopes such as European Extremely Large Telescope (EELT), Thirty Meter Telescope (TMT), Giant Magellan Telescope (GMT), and especially, in gravitational wave interferometers DECi-Hertz Interferometer Gravitational Wave Observatory and Big Bang Observer (DECIGO/BBO), which aim at low redshift.