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Added by
Mariusz Dabrowski P.
Publication date
2005
fields
Physics
and research's language is
English
Authors
Mariusz P. Dabrowski
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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.
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Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.
The effects of a running gravitational coupling and the entropic force on future singularities are considered. Although it is expected that the quantum corrections remove the future singularities or change the singularity type, treating the running gravitational coupling as a function of energy density is found to cause no change in the type of singularity but causes a delay in the time that a singularity occurs. The entropic force is found to replaces the singularity type $II$ by $bar{III}$ ($a=$const., $H=$const., $dot{H} to infty$, $p to infty$, $rho to infty$) which differs from previously known type $III$ and to remove the $w$-singularity. We also consider an effective cosmological model and show that the types $I$ and $II$ are replaced by the singularity type $III$.
We study a metric cubic gravity theory considering odd-parity modes of linear inhomogeneous perturbations on a spatially homogeneous Bianchi type I manifold close to the isotropic de Sitter spacetime. We show that in the regime of small anisotropy, the theory possesses new degrees of freedom compared to General Relativity, whose kinetic energy vanishes in the limit of exact isotropy. From the mass dispersion relation we show that such theory always possesses at least one ghost mode as well as a very short-time-scale (compared to the Hubble time) classical tachyonic (or ghost-tachyonic) instability. In order to confirm our analytic analysis, we also solve the equations of motion numerically and we find that this instability is developed well before a single e-fold of the scale factor. This shows that this gravity theory, as it is, cannot be used to construct viable cosmological models.
The models of cyclic universes and cyclic multiverses based on the alternative gravity theories of varying constants are considered.
Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In such a model it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the energy density would remain unaffected. The particular evolution of the scale factor of the universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era. In this paper we will present the results of our confrontation of one example class of SFS models with the available cosmological data from high redshift supernovae, baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB). We then discuss the viability of the model in question as an alternative to dark energy.
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