Zoltán Keresztes

Tachyon cosmology, supernovae data, and the big brake singularity

We compare the existing observational data on type Ia supernovae with the evolutions of the Universe predicted by a one-parameter family of tachyon models which we have introduced recently [Phys. Rev. D 69, 123512 (2004)]. Among the set of the trajectories of the model which are compatible with the data there is a consistent subset for which the Universe ends up in a new type of soft cosmological singularity dubbed big brake. This opens up yet another scenario for the future history of the Universe besides the one predicted by the standard {lambda}CDM model.

Galactic rotation curves in brane world models

In the brane world scenario the four-dimensional effective Einstein equation has extra source terms, which arise from the embedding of the three-brane in the bulk. These non-local effects, generated by the free gravitational field of the bulk, may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic centre, which is usually explained by postulating the existence of the dark matter. In the present paper we consider the asymptotic behaviour of the galactic rotation curves in the brane world models, and compare the theoretical results with observations of both high surface brightness and low surface brightness galaxies. For the chosen sample of galaxies we determine first the baryonic parameters by fitting the photometric data to the adopted galaxy model; then we test the hypothesis of the Weyl fluid acting as dark matter on the chosen sample of spiral galaxies by fitting the tangential velocity equation of the combined baryonic-Weyl model to the rotation curves. We give an analytical expression for the rotational velocity of a test particle on a stable circular orbit in the exterior region to a galaxy, with Weyl fluid contributions included. The model parameter ranges for which the χ2 test provides agreement (within 1σ confidence level) with observations on the velocity fields of the chosen galaxy sample are then determined. There is a good agreement between the theoretical predictions and observations, showing that extra-dimensional models can be effectively used as a viable alternative to the standard dark matter paradigm.

Covariant gravitational dynamics in 3+1+1 dimensions

We develop a 3+1+1 covariant formalism with cosmological and astrophysical applications. First we give the evolution and constraint equations both on the brane and off-brane in terms of 3-space covariant kinematical, gravito-electro-magnetic (Weyl) and matter variables. We discuss the junction conditions across the brane in terms of the new variables. Then we establish a closure condition for the equations on the brane. We also establish the connection of this formalism with isotropic and anisotropic cosmological brane-worlds. Finally we derive a new brane solution in the framework of our formalism: the tidal charged Taub-NUT-(A)dS brane, which obeys the closure condition.

Will the tachyonic Universe survive the Big Brake

We investigate a Friedmann universe filled with a tachyon scalar field, which behaved as dustlike matter in the past, while it is able to accelerate the expansion rate of the Universe at late times. The comparison with type Ia supernovae (SNIa) data allows for evolutions driving the Universe into a Big Brake. Some of the evolutions leading to a Big Brake exhibit a large variation of the equation of state parameter at low redshifts, which is potentially observable with future data, though hardly detectable with present SNIa data. The soft Big Brake singularity occurs at finite values of the scale factor, vanishing energy density and Hubble parameter, but diverging deceleration and infinite pressure. We show that the geodesics can be continued through the Big Brake and that our model universe will recollapse eventually in a Big Crunch. Although the time to the Big Brake strongly depends on the present values of the tachyonic field and of its time derivative, the time from the Big Brake to the Big Crunch represents a kind of invariant time scale for all field parameters allowed by SNIa.

Paradox of soft singularity crossing and its resolution by distributional cosmological quantities

A cosmological model of a flat Friedmann universe filled with a mixture of anti-Chaplygin gas and dust-like matter exhibits a future soft singularity, where the pressure of the anti-Chaplygin gas diverges (while its energy density is finite). Despite infinite tidal forces the geodesics pass through the singularity. Due to the dust component, the Hubble parameter has a non-zero value at the encounter with the singularity, therefore the dust implies further expansion. With continued expansion however, the energy density and the pressure of the anti-Chaplygin gas would become ill-defined, hence from the point of view of the anti-Chaplygin gas only a contraction is allowed. Paradoxically, the universe in this cosmological model would have to expand and contract simultaneously. This obviosly could not happen. We solve the paradox by redefining the anti-Chaplygin gas in a distributional sense. Then a contraction could follow the expansion phase at the singularity at the price of a jump in the Hubble parameter. Although such an abrupt change is not common in any cosmological evolution, we explicitly show that the set of Friedmann, Raychaudhuri and continuity equations are all obeyed both at the singularity and in its vicinity. We also prove that the Israel junction conditions are obeyed through the singular spatial hypersurface. In particular we enounce and prove a more general form of the Lanczos equation.

Second-order light deflection by tidal charged black holes on the brane

We derive the deflection angle of light rays passing near a black hole with mass m and tidal charge q, confined to a generalized Randall–Sundrum brane with co-dimension 1. We employ the weak lensing approach, up to the second order in perturbation theory by two distinct methods. First we adopt a Lagrangian approach and derive the deflection angle from the analysis of the geodesic equations. Then we adopt a Hamiltonian approach and we recover the same result from the analysis of the eikonal. With this we re-establish the unicity of the result as given by the two methods. Our results in turn implies a more rigorous constraint on the tidal charge from solar system measurements, than derived before.

Combined cosmological tests of a bivalent tachyonic dark energy scalar field model

A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter (

Irradiated asymmetric Friedmann branes

\Omega _{b}h^{2}=0.022161

The luminosity-redshift relation in brane-worlds: I. Analytical results

, where the Hubble constant is fixed as

The luminosity-redshift relation in brane-worlds: II. Confrontation with experimental data

h=0.706