arXiv subjects

Mariusz P. Dabrowski

Publications and source records attributed to Mariusz P. Dabrowski.

At least 73 records · Page 4Linked to original sources

arXiv2007

Energy, angular momentum, superenergy and angular supermomentum in conformal frames

We find the rules of the conformal transformation for the energetic quantities such as the Einstein energy-momentum complex, the Bergmann-Thomson angular momentum complex, the superenergy tensor, and the angular supermomentum tensor of gravitation and matter. We show that the conformal transformation rules for the matter parts of both the Einstein complex and the Bergmann-Thomson complex are fairly simple, while the transformation rules for their gravitational parts are more complicated. We also find that the transformational rules of the superenergy tensor of matter and the superenergy tensor of gravity are quite complicated except for the case of a pure gravity. In such a special case the superenergy density as well as the sum of the superenergy density and the matter energy density are invariants of the conformal transformation. Besides, in that case, a conformal invariant is also the Bel-Robinson tensor which is a part of the superenergy tensor. As for the angular supermomentum tensor of gravity - it emerges that its transformational rule even for a pure gravity is quite complicated but this is not the case for the angular supermomentum tensor of matter. Having investigated some technicalities of the conformal transformations, we also find the conformal transformation rule for the curvature invariants and, in particular, for the Gauss-Bonnet invariant in a spacetime of arbitrary dimension.

hep-th↗

arXiv2007

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.

hep-th↗

arXiv2007

How far is it to a sudden future singularity of pressure?

We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden singularity may happen in the very near future (e.g. within ten million years) and its prediction at the present moment of cosmic evolution cannot be distinguished, with current observational data, from the prediction given by the standard quintessence scenario of future evolution. Fortunately, sudden future singularities are characterized by a momentary peak of infinite tidal forces only; there is no geodesic incompletness which means that the evolution of the universe may eventually be continued throughout until another ``more serious'' singularity such as Big-Crunch or Big-Rip.

astro-ph↗

arXiv2007

Phantom Dark Energy and its Cosmological Consequences

I discuss the dark energy characterized by the violation of the null energy condition ($\varrho + p \geq 0$), dubbed phantom. Amazingly, it is admitted by the current astronomical data from supernovae. We discuss both classical and quantum cosmological models with phantom as a source of matter and present the phenomenon called phantom duality.

gr-qc↗

arXiv2007

Big-Rip, Sudden Future, and other exotic singularities in the universe

We discuss exotic singularities in the evolution of the universe motivated by the progress of observations in cosmology. Among them there are: Big-Rip (BR), Sudden Future Singularities (SFS), Generalized Sudden Future Singularities (GSFS), Finite Density Singularities (FD), type III, and type IV singularities. We relate some of these singularities with higher-order characteristics of expansion such as jerk and snap. We also discuss the behaviour of pointlike objects and classical strings on the approach to these singularities.

gr-qc↗

arXiv2006

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.

astro-ph↗

arXiv2006

Quantum phantom cosmology

We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss in particular the behaviour of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the Big Rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the Big-Bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.

hep-th↗

arXiv2006

Strings at future singularities

We discuss the behaviour 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.

hep-th↗

arXiv2006

The conformal status of $ω=-3/2$ Brans-Dicke cosmology

Following recent fit of supernovae data to Brans-Dicke theory which favours the model with $ω= - 3/2$ \cite{fabris} we discuss the status of this special case of Brans-Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit $ω= -3/2$ is consistent only with the vacuum field equations and it makes such a Brans-Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans-Dicke theory with $ω= -3/2$ gives a border between a standard scalar field model and a ghost/phantom model. In this paper we show that in $ω= -3/2$ Brans-Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non-zero spatial curvature except for $k=-1$ case. Further we show that this $k=-1$ case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non-zero spatial curvature models of Kantowski-Sachs type are admissible in $ω= -3/2$ Brans-Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.

hep-th↗

arXiv2005

Phantom Friedmann Cosmologies and Higher-Order Characteristics of Expansion

We discuss a more general class of phantom ($p < -\varrho$) cosmologies with various forms of both phantom ($w < -1$), and standard ($w > -1$) matter. We show that many types of evolution which include both Big-Bang and Big-Rip singularities are admitted and give explicit examples. Among some interesting models, there exist non-singular oscillating (or "bounce") cosmologies, which appear due to a competition between positive and negative pressure of variety of matter content. From the point of view of the current observations the most interesting cosmologies are the ones which start with a Big-Bang and terminate at a Big-Rip. A related consequence of having a possibility of two types of singularities is that there exists an unstable static universe approached by the two asymptotic models - one of them reaches Big-Bang, and another reaches Big-Rip. We also give explicit relations between density parameters $Ω$ and the dynamical characteristics for these generalized phantom models, including higher-order observational characteristics such as jerk and "kerk". Finally, we discuss the observational quantities such as luminosity distance, angular diameter, and source counts, both in series expansion and explicitly, for phantom models. Our series expansion formulas for the luminosity distance and the apparent magnitude go as far as to the fourth-order in redshift $z$ term, which includes explicitly not only the jerk, but also the "kerk" (or "snap") which may serve as an indicator of the curvature of the universe.

hep-th↗

arXiv2005

Statefinders, higher-order energy conditions and sudden future singularities

We link observational parameters such as the deceleration parameter, the jerk, the kerk (snap) and higher-order derivatives of the scale factor, called statefinders, to the conditions which allow to develop sudden future singularities of pressure with finite energy density. In this context, and within the framework of Friedmann cosmology, we also propose higher-order energy conditions which relate time derivatives of the energy density and pressure which may be useful in general relativity.

gr-qc↗

arXiv2004

Observable Quantities in Cosmological Models with Strings

The Friedman equation for the universe with arbitrary curvature $(k = 0, \pm 1)$, filled with mutually noninteracting pressureless dust, radiation, cosmological constant, and strings is considered. We assume the string domination scenario for the evolution of the latter component. Moreover, we discuss the simplest possibility for the scaling of the string energy density: $\varrho \propto R^{-2}$. For such models we write down the explicit solution of the Friedman equation. We realize that corresponding cosmological models do not essentially differ from those without strings. We find an analytic formula for the radial coordinate $χ$ of a galaxy with a redshift z and express it in terms of astronomical parameters. This relation is then used for the derivation of the astrophysical formulas such as 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. We show that the maximum of $N(z)$ strongly depends on the density of strings, especially if the density is large enough to explain the $Ω$ problem. Other tests are also proposed.

astro-ph↗

arXiv2004

Conformal relativity versus Brans-Dicke and superstring theories

Conformal relativity theory which is also known as Hoyle-Narlikar theory has recently been given some new interest. It is an extended relativity theory which is invariant with respect to conformal transformations of the metric. In this paper we show how conformal relativity is related to the Brans-Dicke theory and to the low-energy-effective superstring theory. We show that conformal relativity action is equaivalent to a transformed Brans-Dicke action for Brans-Dicke parameter $ω= -3/2$ in contrast to a reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to a Brans-Dicke action with Brans-Dicke parameter $ω= -1$. In fact, Brans-Dicke parameter $ω=-3/2$ gives a border between a standard scalar field evolution and a ghost. We also present basic cosmological solutions of conformal relativity in both Einstein and string frames. The Eintein limit for flat conformal cosmology solutions is unique and it is flat Minkowski space. This requires the scalar field/mass evolution instead of the scale factor evolution in order to explain cosmological redshift. It is interesting that like in ekpyrotic/cyclic models, a possible transition through a singularity in conformal cosmology in the string frame takes place in the weak coupling regime.

hep-th↗

arXiv2004

Energy-momentum and angular momentum of Goedel universes

We discuss the Einstein energy-momentum complex and the Bergmann-Thomson angular momentum complex in general relativity and calculate them for space-time homogeneous Goedel universes. The calculations are performed for a dust acausal model and for a scalar-field causal model. It is shown that the Einstein pseudotensor is traceless, not symmetric, the gravitational energy is "density" is negative and the gravitational Poynting vector vanishes. Significantly, the total (gravitational and matter) energy "density" fro the acausal model is zero while for the casual model it is negative.The Bergmann-Thomson angular momentum complex does not vanish for both Gödel models.

gr-qc↗

arXiv2003

Phantom cosmologies

We discuss a class of phantom ($p < - \varrho$) cosmological models. Except for phantom we admit various forms of standard types of matter and discuss the problem of singularities for these cosmologies. The singularities are different from those of standard matter cosmology since they appear for infinite values of the scale factor. We also find an interesting relation between the phantom models and standard matter models which is like the duality symmetry of string cosmology.

hep-th↗

arXiv2002

Brane universes tested by supernovae

We discuss observational constrains coming from supernovae Ia \cite{Perlmutter99} imposed on the behaviour of the Randall-Sundrum models. In the case of dust matter on the brane, the difference between the best-fit general relativistic model with a $Λ$-term \cite{Perlmutter99} and the best-fit brane models becomes detectable for redshifts $z > 0.6$. It is interesting that brane models predict brighter galaxies for such redshifts which is in agreement with the measurement of the $z = 1.7$ supernova \cite{Riess01} and with the New Data from the High Z Supernovae Search Team \cite{schmit02}. We also demonstrate that the fit to supernovae data can also be obtained, if we admit the "super-negative" dark energy $p = - (4/3) \varrho$ on the brane, where the dark energy in a way mimics the influence of the cosmological constant. It also appears that the dark energy enlarges the age of the universe 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.

astro-ph↗

arXiv2002

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.

hep-th↗

arXiv2002

Null string evolution in black hole and cosmological spacetimes

We discuss the problem of the motion of classical strings in some black hole and cosmological spacetimes. In particular, the null string limit (zero tension) of tensile strings is considered. We present some new exact string solutions in Reissner-Nordström black hole background as well as in the Einstein Static Universe and in the Einstein-Schwarzschild (a black hole in the Einstein Static Universe) spacetime. These solutions can give some insight into a general nature of propagation of strings (cosmic and fundamental) in curved backgrounds.

hep-th↗