Bounding the Hubble flow in terms of the w parameter

The last decade has seen increasing efforts to circumscribe and bound the cosmological Hubble flow in terms of model-independent constraints on the cosmological fluid - such as, for instance, the classical energy conditions of general relativity. Quite a bit can certainly be said in this regard, but much more refined bounds can be obtained by placing more precise constraints (either theoretical or observational) on the cosmological fluid. In particular, the use of the w-parameter (w=p/rho) has become increasingly common as a surrogate for trying to say something about the cosmological equation of state. Herein we explore the extent to which a constraint on the w-parameter leads to useful and nontrivial constraints on the Hubble flow, in terms of constraints on density rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological distances d(z), and lookback time T(z). In contrast to other partial results in the literature, we carry out the computations for arbitrary values of the space curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.Comment: 15 page

Accelerating expansion and change of signature

We show that some types of sudden singularities admit a natural explanation in terms of regular changes of signature on brane-worlds in AdS$_{5}$. The present accelerated expansion of the Universe and its possible ending at a sudden singularity may therefore simply be an indication that our braneworld is about to change its Lorentzian signature to an Euclidean one, while remaining fully regular. An explicit example of this behaviour satisfying the weak and strong energy conditions is presented.Comment: LaTeX, 4 pages. Uses the eas.cls class. To appear in the proceedings of the Spanish Relativity Meeting ERE'0

Cosmological milestones and energy conditions

Until recently, the physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the "big bang", and possibly a "big crunch". However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with "big rips" and "sudden singularities" added to the mix, as well as renewed interest in non-singular cosmological events such as "bounces" and "turnarounds". In this talk, we present an extensive catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, using generalized power series, purely kinematical definitions of these cosmological events are provided in terms of the behaviour of the scale factor a(t). The notion of a "scale-factor singularity" is defined, and its relation to curvature singularities (polynomial and differential) is explored. Second, dynamical information is extracted by using the Friedmann equations (without assuming even the existence of any equation of state) to place constraints on whether or not the classical energy conditions are satisfied at the cosmological milestones. Since the classification is extremely general, and modulo certain technical assumptions complete, the corresponding results are to a high degree model-independent.Comment: 8 pages, 1 table, conference proceedings for NEB XII conference in Nafplio, Greec

ww-singularities in cosmological models

Recently a new type of cosmological singularity has been postulated for infinite barotropic index $w$ in the equation of state $p=w \rho$ of the cosmological fluid, but vanishing pressure and density at the singular event. Apparently the barotropic index $w$ would be the only physical quantity to blow up at the singularity. In this talk we would like to discuss the strength of such singularities and compare them with other types. We show that they are weak singularities.Comment: 4 pp, jpconf.cls, to appear in Proceedings of Spanish Relativity Meeting 2010 (ERE 2010) held in Granada, Spai

The Hubble series: Convergence properties and redshift variables

In cosmography, cosmokinetics, and cosmology it is quite common to encounter physical quantities expanded as a Taylor series in the cosmological redshift z. Perhaps the most well-known exemplar of this phenomenon is the Hubble relation between distance and redshift. However, we now have considerable high-z data available, for instance we have supernova data at least back to redshift z=1.75. This opens up the theoretical question as to whether or not the Hubble series (or more generally any series expansion based on the z-redshift) actually converges for large redshift? Based on a combination of mathematical and physical reasoning, we argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z>1, corresponding to a universe less than half its current size. Furthermore, we shall argue on theoretical grounds for the utility of an improved parameterization y=z/(1+z). In terms of the y-redshift we again argue that the radius of convergence of any series expansion in y is less than or equal to 1, so that y-based expansions are likely to be good all the way back to the big bang y=1, but that y-based expansions must break down for y<-1, now corresponding to a universe more than twice its current size.Comment: 15 pages, 2 figures, accepted for publication in Classical and Quantum Gravit

Classical and semi-classical energy conditions

The standard energy conditions of classical general relativity are (mostly) linear in the stress-energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically non-linear in the stress-energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this article we will first review the standard energy conditions and their various limitations. (Including the connection to the Hawking--Ellis type I, II, III, and IV classification of stress-energy tensors). We shall then turn to the averaged, nonlinear, and semi-classical energy conditions, and see how much can be done once semi-classical quantum effects are included.Comment: V1: 25 pages. Draft chapter, on which the related chapter of the book "Wormholes, Warp Drives and Energy Conditions" (to be published by Springer), will be based. V2: typos fixed. V3: small typo fixe

Detecting the cosmic acceleration with current data

The deceleration parameter q as the diagnostic of the cosmological accelerating expansion is investigated. By expanding the luminosity distance to the fourth order of redshift and the so-called y-redshift in two redshift bins and fitting the SNIa data (Union2), the marginalized likelihood distribution of the current deceleration parameter shows that the cosmic acceleration is still increasing, but there might be a tendency that the cosmic acceleration will slow down in the near future. We also fit the Hubble evolution data together with SNIa data by expanding the Hubble parameter to the third order, showing that the present decelerating expansion is excluded within $2\sigma$ error. Further exploration on this problem is also approached in a non-parametrization method by directly reconstructing the deceleration parameter from the distance modulus of SNIa, which depends neither on the validity of general relativity nor on the content of the universe or any assumption regarding cosmological parameters. More accurate observation datasets and more effective methods are still in need to make a clear answer on whether the cosmic acceleration will keep increasing or not.Comment: 20 pages, 5 figures, 3 table

How strong is the evidence for accelerated expansion?

We test the present expansion of the universe using supernova type Ia data without making any assumptions about the matter and energy content of the universe or about the parameterization of the deceleration parameter. We assume the cosmological principle to apply in a strict sense. The result strongly depends on the data set, the light-curve fitting method and the calibration of the absolute magnitude used for the test, indicating strong systematic errors. Nevertheless, in a spatially flat universe there is at least a 5 sigma evidence for acceleration which drops to 1.8 sigma in an open universe.Comment: 16 pages, 3 figure

Anisotropic dark energy stars

A model of compact object coupled to inhomogeneous anisotropic dark energy is studied. It is assumed a variable dark energy that suffers a phase transition at a critical density. The anisotropic Lambda-Tolman-Oppenheimer-Volkoff equations are integrated to know the structure of these objects. The anisotropy is concentrated on a thin shell where the phase transition takes place, while the rest of the star remains isotropic. The family of solutions obtained depends on the coupling parameter between the dark energy and the fermion matter. The solutions share several features in common with the gravastar model. There is a critical coupling parameter that gives non-singular black hole solutions. The mass-radius relations are studied as well as the internal structure of the compact objects. The hydrodynamic stability of the models is analyzed using a standard test from the mass-radius relation. For each permissible value of the coupling parameter there is a maximum mass, so the existence of black holes is unavoidable within this model.Comment: 12 pages, 6 figures, final manuscript, Accepted for publication in Astrophysics & Space Scienc

Could the cosmic acceleration be transient? A cosmographic evaluation

A possible slowing down of the cosmic expansion is investigated through a cosmographic approach. By expanding the luminosity distance to fourth order and fitting the SN Ia data from the most recent compilations (Union, Constitution and Union 2), the marginal likelihood distributions for the deceleration parameter today suggest a recent reduction of the cosmic acceleration and indicate that there is a considerable probability for $q_0>0$. Also in contrast to the prediction of the $\Lambda$CDM model, the cosmographic $q(z)$ reconstruction permits a cosmic expansion history where the cosmic acceleration could already have peaked and be presently slowing down, which would imply that the recent accelerated expansion of the Universe is a transient phenomenon. It is also shown that to describe a transient acceleration the luminosity distance needs to be expanded at least to fourth order. The present cosmographic results depend neither on the validity of general relativity nor on the matter-energy contents of the Universe.Comment: 11 pages, 4 figures. Accepted for publication in Classical and Quantum Gravit