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p. 1-12
Received: 3 October 2013; in revised form: 28 November 2013 / Accepted: 18 December 2013 / Published: 23 December 2013

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Abstract: Using the multiplicity of solutions for the projectable case of the covariant extension of Hořava-Lifshitz gravity, we show that an appropriate choice for the auxiliary field allows for an effective description of galaxy rotation curves. This description is based on static and spherically symmetric solutions of covariant Hořava-Lifshitz gravity and does not require Dark Matter.

p. 13-21
Received: 10 November 2013; Accepted: 27 December 2013 / Published: 3 January 2014

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Abstract: By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S ^{-1} of the cosmic scale factor S (t ), it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S ^{-1 } around the present epoch t_{0} , a non-vanishing shift per orbit (Δr) of the two-body relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H_{0} at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period P_{b} ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of (Δr) ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of (Δr) ≈ 2–4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S^{-1} (t) . More generally, it is valid for an arbitrary Hooke-like extra-acceleration whose “elastic” parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ_{1} of the first-order term of the power expansion of κ(t) can be preliminarily constrained in a model-independent way down to a κ_{1} ≲ 2 x 10^{-13} year^{-3 } level from latest Solar System’s planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≲ 10^{-8 } year^{-3} .

p. 22-61
Received: 6 November 2013; in revised form: 24 December 2013 / Accepted: 25 December 2013 / Published: 17 January 2014

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Abstract: A wide range of large scale observations hint towards possible modifications on the standard cosmological model which is based on a homogeneous and isotropic universe with a small cosmological constant and matter. These observations, also known as “cosmic anomalies” include unexpected Cosmic Microwave Background perturbations on large angular scales, large dipolar peculiar velocity flows of galaxies (“bulk flows”), the measurement of inhomogenous values of the fine structure constant on cosmological scales (“alpha dipole”) and other effects. The presence of the observational anomalies could either be a large statistical fluctuation in the context of ΛCDM or it could indicate a non-trivial departure from the cosmological principle on Hubble scales. Such a departure is very much constrained by cosmological observations for matter. For dark energy however there are no significant observational constraints for Hubble scale inhomogeneities. In this brief review I discuss some of the theoretical models that can naturally lead to inhomogeneous dark energy, their observational constraints and their potential to explain the large scale cosmic anomalies.

p. 62-71
Received: 12 December 2013; in revised form: 29 January 2014 / Accepted: 29 January 2014 / Published: 10 February 2014

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Abstract: In this study, we located and compared different types of horizons in the spherically symmetric Vaidya solution. The horizons we found were trapping horizons, which can be null, timelike, or spacelike, null surfaces with constant area change and also conformal Killing horizons. The conformal Killing horizons only exist for certain choices of the mass function. Under a conformal transformation, the conformal Killing horizons can be mapped into true Killing horizons. This allows conclusions drawn in the dynamical Vaidya spacetime to be related to known properties of static spacetimes. We found the conformal factor that performs this transformation and wrote the new metric in explicitly static coordinates. Using this construction we found that the tunneling argument for Hawking radiation does not umabiguously support Hawking radiation being associated with the trapping horizon. We also used this transformation to derive the form of the surface gravity for a class of physical observers in Vaidya spacetimes.

p. 72-80
Received: 17 December 2013; in revised form: 21 January 2014 / Accepted: 5 February 2014 / Published: 17 February 2014

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Abstract: Dark energy with negative pressure and positive energy density is believed to be responsible for the accelerated expansion of the universe. Quite a few theoretical models of dark energy are based on tachyonic fields interacting with itself and normal (bradyonic) matter. Here, we propose an experimental model of tachyonic dark energy based on hyperbolic metamaterials. Wave equation describing propagation of extraordinary light inside hyperbolic metamaterials exhibits 2 + 1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect bends this spacetime resulting in effective gravitational force between extraordinary photons. We demonstrate that this model has a self-interacting tachyonic sector having negative effective pressure and positive effective energy density. Moreover, a composite multilayer SiC-Si hyperbolic metamaterial exhibits closely separated tachyonic and bradyonic sectors in the long wavelength infrared range. This system may be used as a laboratory model of inflation and late time acceleration of the universe.

p. 81-88
Received: 29 December 2013; in revised form: 7 February 2014 / Accepted: 13 February 2014 / Published: 19 February 2014

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Abstract: The visible mass of the observable universe agrees with that needed for a flat cosmos, and the reason for this is not known. It is shown that this can be explained by modelling the Hubble volume as a black hole that emits Hawking radiation inwards, disallowing wavelengths that do not fit exactly into the Hubble diameter, since partial waves would allow an inference of what lies outside the horizon. This model of “horizon wave censorship” is equivalent to a Hubble-scale Casimir effect. This incomplete toy model is presented to stimulate discussion. It predicts a minimum mass and acceleration for the observable universe which are in agreement with the observed mass and acceleration, and predicts that the observable universe gains mass as it expands and was hotter in the past. It also predicts a suppression of variation on the largest cosmic scales that agrees with the low-l cosmic microwave background anomaly seen by the Planck satellite.

p. 89-159
Received: 9 January 2014; in revised form: 6 February 2014 / Accepted: 7 February 2014 / Published: 3 March 2014

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Abstract: In this review we summarize, expand, and set in context recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. We specifically consider the thermodynamics of higher-dimensional rotating asymptotically flat and AdS black holes and black rings in a canonical (fixed angular momentum) ensemble. We plot the associated thermodynamic potential—the Gibbs free energy—and study its behavior to uncover possible thermodynamic phase transitions in these black hole spacetimes. We show that the multiply-rotating Kerr-AdS black holes exhibit a rich set of interesting thermodynamic phenomena analogous to the “every day thermodynamics” of simple substances, such as reentrant phase transitions of multicomponent liquids, multiple first-order solid/liquid/gas phase transitions, and liquid/gas phase transitions of the van derWaals type. Furthermore, the reentrant phase transitions also occur for multiply-spinning asymptotically flat Myers–Perry black holes. These phenomena do not require a variable cosmological constant, though they are more naturally understood in the context of the extended phase space. The thermodynamic volume, a quantity conjugate to the thermodynamic pressure, is studied for AdS black rings and demonstrated to satisfy the reverse isoperimetric inequality; this provides a first example of calculation confirming the validity of isoperimetric inequality conjecture for a black hole with non-spherical horizon topology. The equation of state P = P(V,T) is studied for various black holes both numerically and analytically—in the ultraspinning and slow rotation regimes.

p. 160-188
Received: 27 November 2013; in revised form: 18 February 2014 / Accepted: 19 February 2014 / Published: 4 March 2014

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Abstract: We discuss the production of massive relic coherent gravitons in a particular class of ƒ(R) gravity, which arises from string theory, and their possible imprint in the Cosmic Microwave Background. In fact, in the very early Universe, these relic gravitons could have acted as slow gravity waves. They may have then acted to focus the geodesics of radiation and matter. Therefore, their imprint on the later evolution of the Universe could appear as filaments and a domain wall in the Universe today. In that case, the effect on the Cosmic Microwave Background should be analogous to the effect of water waves, which, in focusing light, create optical caustics, which are commonly seen on the bottom of swimming pools. We analyze this important issue by showing how relic massive gravity waves (GWs) perturb the trajectories of the Cosmic Microwave Background photons (gravitational lensing by relic GWs). The consequence of the type of physics discussed is outlined by illustrating an amplification of what might be called optical chaos.

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