Table of contents

The 14th conference in the series "Recent Developments in Gravity" was organized by the Theoretical Physics group of the Department of Physics, University of Ioannina, Greece. NEB-XIV (NEB-14) took place in Ioannina, Greece, from 8–11 June, 2010 at the Grand Serai Hotel.

The abstracts of all the talks, along with other details of the meeting, are to be found on the website of the conference http://neb14.physics.uoi.gr/index.htm.

The NEB series (initials from the Greek: Νεώτερες Εξελίξεις στην Βαρύτητα) is a series of meetings initiated in 1984 in Crete by the late Professor Vassilis Xanthopoulos and a group of Greek relativists. Since then this meeting has been held every other year at various cities in Greece, organized by different groups of Greek relativists and cosmologists. This was the third time it was organized at Ioannina (the other two times were in 1988 and 2000).

It was our pleasure to see that the international participation in these meetings has been rising constantly during the last few years and NEB-14 continued this tradition. The Conference was attended by a total of 106 participants, with 62 of them from Institutions outside of Greece. We had 20 plenary session invited speakers (15 of whom were of international origin), 42 parallel session talks and 2 posters.

The topics that are traditionally covered by the NEB conference series are:

• Cosmology (Dark Energy, Dark Matter, CMB etc)

• Gravitational Waves

• Alternative Theories of Gravity

• Relativistic Astrophysics

• Mathematical Relativity

• Quantum Gravity

During the present conference, the following variety of topics were addressed through the participants' talks and posters:

• mainstream and alternative models of dark energy and dark matter,

• construction and testing of new cosmological models,

• alternative (either 4-dimensional or higher-dimensional) theories of gravity and their predictions,

• the interplay of gravity with gauge theories,

• properties of astrophysical and miniature black holes and other massive astrophysical objects,

• cosmological perturbation spectra,

• modeling of astrophysical and cosmological observables via alternative theories,

• attempts to build a consistent quantum gravity theory.

We chose to place the emphasis in this meeting on subjects related to Observational and Theoretical Cosmology due to the rapid recent development of these research areas.

Our goal was to provide a stimulating environment for the presentation and discussion of the most recent cutting-edge research results in cosmology and classical and quantum gravity. We believe that this goal was achieved and we hope that the next meeting that will take place at Chania (Crete) in 2012 (NEB-15) will further raise the standards of this series.

Special thanks are due to the invited and keynote speakers for providing exciting talks and to all the participants for presenting interesting contributions and initiating fruitful discussions. We would also like to thank the Organizing Committee and the Scientific Committee for their valuable contributions to the organization of the meeting.

Finally we would like to thank our main sponsors – the University of Ioannina, the Academy of Athens, the National Bank of Greece and the 'Prokos' Bookstore – for providing financial support and making this meeting possible. Last but not least, we are grateful to the European Research and Training Network "UniverseNet" (MRTN-CT-2006035863-1) for providing the funds for the publication of the proceedings of our meeting.

The Editors Leandros Perivolaropoulos Panagiota Kanti

The Organizing Committee: L Perivolaropoulos (Ioannina) (Chair) P Kanti (Ioannina) (Co-Chair) C Kolasis (Ioannina) N Stergioulas (Thessaloniki) K Kokkotas (Thessaloniki, Tuebingen) D Papadopoulos (Thessaloniki) M Plionis (Athens) S Basilakos (Athens) E Vagenas (Athens) S Nesseris (Niels Bohr) N Pappas (Ioannina)

The Scientific Committee: A Ashtekar (Penn-State) N Batakis (Ioannina) D Christodoulou (ETH) G Contopoulos (Academy of Athens) C Frenk (University of Durham) V Frolov (Alberta)

The Plenary Invited Speakers: Prof. J A Font (University of Valencia) Prof. V Frolov (University of Alberta) Prof. R Gregory (University of Durham) Prof. O Lahav (UCL London) Prof. D Psaltis (University of Arizona ) Prof. S Sarkar (University of Oxford) Prof. J Sola (Barcelona University) Prof. R Woodard (University of Florida)

Keynote speakers: Prof. I Bakas (University of Patras) Prof. K Dimopoulos (University of Lancaster) Prof. D Giannios (Princeton University) Prof. N Mavromatos (Kings College, London) Prof. D Polarski (University Montpellier II) Prof. M Sakellariadou (Kings College, London) Prof. T Sotiriou (University of Cambridge) Prof. N Tetradis (University of Athens) Prof. C Tsagas (University of Thessaloniki)

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The generalized McVittie space-times, which are the natural extensions of a class of metrics introduced by McVittie in 1933 to model the space-time outside a spherical object embedded in an expanding universe, have recently been proposed by Faraoni and Jacques as candidate space-times for cosmological black holes. In this paper I analyze the singularities and horizon structure of the generalized McVittie space-times, and show that any expanding space-time of this type that satisfies the null energy condition and develops apparent horizons must asymptote to a standard McVittie solution. Furthermore, if the scale factor is asymptotically exponential then the space-time is future-incomplete and can be joined smoothly to an eternally-inflating Kottler (Schwarzschild-de Sitter) solution. I argue that no generalized McVittie space-time, apart from the Schwarzschild solution, can adequately represent a black hole, because all singular points are surrounded by anti-trapped regions rather than trapped regions.

We suggest a method that could be used to discriminate a Kerr black hole from any other supermassive axisymmetric astrophysical object by analyzing the gravitational-wave signal from an extreme mass ratio inspiral (EMRI). The method is based on the quite distinct qualitative features that characterize a slightly nonintegrable system. According to the Poincaré-Birkhoff theorem, whenever a resonance of frequencies arise in an axisymmetric perturbed Kerr metric, instead of the anticipated KAM curves of the integrable Kerr case, a Birkhoff chain of islands appears on a surface of sections. The orbits of this chain of islands have a fixed ratio of frequencies. The idea is to exploit this feature to check if the inspiraling low-mass object spends a finite interval of time to cross this resonance, while its orbit evolves adiabatically due to the radiation of gravitational waves.

We present constraints on the axion-photon coupling scale M for light axion-like particles by combining recent Supernova Type Ia data with the latest measurements of the Hubble expansion at redshifts between 0 and 2. Allowing for a coupling between axions and photons leads to a modification of the inferred luminosity distances for supernovae due to the conversion of photons to axions in the presence of intergalactic magnetic fields. We constrain such couplings by considering deviations from the luminosity-angular diameter distance relation d_L = d_A(1+z)². We find that for intergalactic magnetic fields of order 1 nG, current supernova and Hubble expansion data rule out a region in the coupling scale M between 10¹⁰ and 10¹¹ GeV.

I provide a broad framework to embed gradient flow equations in non–relativistic field theory models that exhibit anisotropic scaling. The prime example is the heat equation arising from a Lifshitz scalar field theory; other examples include the Allen–Cahn equation that models the evolution of phase boundaries. Then, I review recent results reported in arXiv:1002.0062 describing instantons of Hořava-Lifshitz gravity as eternal solutions of certain geometric flow equations on 3–manifolds. These instanton solutions are in general chiral when the anisotropic scaling exponent is z = 3. Some general connections with the Onsager–Machlup theory of non-equilibrium processes are also briefly discussed in this context. Thus, theories of Lifshitz type in d + 1 dimensions can be used as off-shell toy models for dynamical vacuum selection of relativistic field theories in d dimensions.

On the basis of the Carter-Israel conjecture, today we believe that some compact and massive objects in the Galaxy and in the Universe are Kerr black holes. However, this idea cannot yet be confirmed by observations. We can currently obtain reliable estimates of the masses of these objects, but we do not know if the space-time around them is described by the Kerr metric and if they have an event horizon. A fundamental limit for a Kerr black hole is the Kerr bound |a_∗| ≤ 1. Here I discuss some astrophysical implications associated with the violation of this bound, which can thus be used to test the Carter-Israel conjecture.

We solve analytically and numerically the generalized Einstein equations in scalar-tensor cosmologies to obtain the evolution of dark energy and matter linear perturbations. We compare our results with the corresponding results for minimally coupled quintessence perturbations. We find that Scalar-Tensor dark energy density perturbations are amplified by a factor of about 10⁴ compared to minimally coupled quintessence perturbations on scales less than about 1000h⁻¹Mpc (sub-Hubble scales). On these scales dark energy perturbations constitute a fraction of about 10% compared to matter density perturbations. Scalar-Tensor dark energy density perturbations are anti-correlated with matter linear perturbations on sub-Hubble scales. This anti-correlation of matter with negative pressure perturbations induces a mild amplification of matter perturbations by about 10% on sub-Hubble scales. The evolution of scalar field perturbations on sub-Hubble scales is scale independent and therefore corresponds to a vanishing effective speed of sound (c_sΦ = 0). We briefly discuss the observational implications of our results which may include predictions for galaxy and cluster halo profiles which are modified compared to ΛCDM. The observed properties of these profiles are known to be in some tension with the predictions of ΛCDM.

Astrometric data from the future GAIA and OBSS missions will allow a more precise calculation of the local galactic circular speed, and better measurements of galactic movements relative to the CMB will be obtained by post-WMAP missions (ie Planck). Contemporary development of high specific impulse electric propulsion systems (ie VASIMIR) will enable the development of space probes able to properly compensate the galactic circular speed as well as the resulting attraction to the centre of our galaxy. The probes would appear immobile to an ideal observer fixed at the centre of the galaxy, in contrast of every other galactic object, which would appear moving according to their local galactic circular speed and their proper motions. Arranging at least three of these galactically static probes in an extended formation and measuring reciprocal distances of the probes over time with large angle laser ranges could allow a direct measurement of the metric expansion of the universe. Free-drifting laser-ranged targets released by the spacecrafts could also be used to measure and compensate solar system's induced local perturbations. For further reducing local effects and increase the accuracy of the results, the distance between the probes should be maximized and the location of the probes should be as far as possible from the Sun and any massive object (ie Jupiter, Saturn). Gravitational waves could also induce random errors but data from GW observatories like the planned LISA could be used to correct them.

We present a new estimator defined in real space to extract the weak lensing convergence from temperature maps of the Cosmic microwave background radiation. This estimator is build upon the minimum variance estimator defined in harmonic space. Despite being by construction suboptimal, its implementation proves less sensitive to the experimental noise and to the bias of the mode coupling derived from the finite size of the map.

We discuss the existence of inflationary solutions in a class of renormalization group improved polynomial f(R) theories, which have been studied recently in the context of the asymptotic safety scenario for quantum gravity. These theories seem to possess a nontrivial ultraviolet fixed point, where the dimensionful couplings scale according to their canonical dimensionality. Assuming that the cutoff is proportional to the Hubble parameter, we obtain modified Friedmann equations which admit both power law and exponential solutions. We establish that for sufficiently high order polynomial the solutions are reliable, in the sense that considering still higher order polynomials is very unlikely to change the solution.

The particle production process is reviewed, through which cosmic inflation can produce a scale invariant superhorizon spectrum of perturbations of suitable fields starting from their quantum fluctuations. Afterwards, in the context of the inflationary paradigm, a number of mechanisms (e.g. curvaton, inhomogeneous reheating etc.) through which such perturbations can source the curvature perturbation in the Universe and explain the formation of structures such as galaxies are briefly described. Finally, the possibility that cosmic vector fields also contribute to the curvature perturbation (e.g. through the vector curvaton mechanism) is considered and its distinct observational signatures are discussed, such as correlated statistical anisotropy in the spectrum and bispectrum of the curvature perturbation.

We present results from simulations of magneto-rotational stellar core collapse along with Alfvén oscillations in magnetars. These simulations are performed with the CoCoA/CoCoNuT code, which is able to handle ideal MHD flows in dynamical spacetimes in general relativity. Our core collapse simulations highlight the importance of genuine magnetic effects, like the magneto-rotational instability, for the dynamics of the flow. For the modelling of magnetars we use the anelastic approximation to general relativistic MHD, which allows for an effective suppression of fluid modes and an accurate description of Alfvén waves. We further compute Alfvén oscillation frequencies along individual magnetic field lines with a semi-analytic approach. Our work confirms previous results based on perturbative approaches regarding the existence of two families of quasi-periodic oscillations (QPOs), with harmonics at integer multiples of the fundamental frequency. Additional material is presented in the accompanying contribution by Gabler et al (2010b) in these proceedings.

This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set ('tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.

We extend a general-relativistic ideal magneto-hydrodynamical code to include the effects of elasticity. Using this numerical tool we analyse the magneto-elastic oscillations of highly magnetised neutron stars (magnetars). In simulations without magnetic field we are able to recover the purely crustal shear oscillations within an accuracy of about a few per cent. For dipole magnetic fields between 5 × 10¹³ and 10¹⁵ G the Alfvén oscillations become modified substantially by the presence of the crust. Those quasi-periodic oscillations (QPOs) split into three families: Lower QPOs near the equator, Edge QPOs related to the last open field line and Upper QPOs at larger distance from the equator.

We summarize the main results of a broad analysis on electrostatic, spherically symmetric (ESS) solutions of a class of non-linear electrodynamics models minimally coupled to gravitation. Such models are defined as arbitrary functions of the two quadratic field invariants, constrained by several physical admissibility requirements, and split into different families according to the behaviour of these lagrangian density functions in vacuum and on the boundary of their domains of definition. Depending on these behaviours the flat-space energy of the ESS field can be finite or divergent. For each model we qualitatively study the structure of its associated gravitational configurations, which can be asymptotically Schwarzschild-like or with an anomalous non Schwarzschild-like behaviour at r → ∞ (but being asymptotically flat and well behaved anyhow). The extension of these results to the non-abelian case is also briefly considered.

Strong magnetic fields can efficiently extract rotational energy from compact objects launching the relativistic jets observed in active galactic nuclei (AGN), microquasars and gamma-ray bursts (GRBs). Magnetohydrodynamical (MHD) acceleration of jets in the ideal MHD limit is not an ultra-efficient process. This makes internal collisions an unlikely mechanism for the jet emission. I argue that non-ideal MHD effects may both boost the acceleration efficiency and power the jet emission. I show that much of the GRB and blazar phenomenology can be understood as result of magnetic dissipation and that the early afterglow phases from GRBs appear to support the picture of MHD driving.

I review recent work ([1, 2]) on holographic superconductivity with Einstein-Gauss-Bonnet gravity, and show how the critical temperature of the superconductor depends on both gravitational backreaction and the Gauss-Bonnet parameter, using both analytic and numerical arguments. I also review computations of the conductivity, finding the energy gap, and demonstrating that there is no universal gap ratio, ω_g/T_c, for these superconductors.

We consider Friedmann-Lemaître-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, in the era when the energy density of the scalar potential dominates over the energy density of ordinary matter. To study the regime suggested by the local weak field tests (i.e. close to the so-called limit of general relativity) we propose a nonlinear approximation scheme, solve for the phase trajectories, and provide a complete classification of possible solutions. We argue that the topology of phase trajectories in the nonlinear approximation is representative of those of the full system, and thus can tell for which scalar-tensor models general relativity functions as an attractor. To the classes of models which asymptotically approach general relativity we give the solutions also in cosmological time and conclude with some observational implications.

Motivated by recent results, indicating that the dark matter (DM) constituents can be collisional, we assume that the DM itself possesses also some sort of thermodynamical properties. In this case, the Universe matter-content can be treated as a gravitating fluid of positive pressure, and, therefore, together with all the other physical characteristics, the energy of this fluid's internal motions should be taken into account as a source of the universal gravitational field. In principle, this form of energy can compensate, also, the extra (dark) energy, needed to compromise spatial flatness, while, the post-recombination Universe remains ever-decelerating. What is more interesting, is that, at the same time (i.e., in the context of the collisional-DM approach), the theoretical curve, representing the distance modulus as a function of the cosmological redshift, fits the Hubble diagram of an extended sample of SN Ia events quite accurately. However, as we demonstrate, this is not the case for someone who, although living in a Universe filled with collisional DM, insists in adopting the traditional, collisionless-DM approach. From the point of view of such an observer, the distant light-emitting sources seem to lie farther (i.e., they appear to be dimmer) than expected, while, the Universe appears to be either accelerating or decelerating, depending on the value of the cosmological redshift.

Bekenstein's Tensor-Vector-Scalar (TeVeS) theory has had considerable success as a relativistic theory of Modified Newtonian Dynamics. In the strong-field regime it makes many predictions that differ from General Relativity implying this regime provides an excellent testing ground for the theory using both current and future observations of neutron stars and black holes in both the electromagnetic and gravitational wave spectrum. I look at the current status of black hole and neutron star solutions in both the original TeVeS theory and its generalisation, including some key observational properties that differ from General Relativity.

The coupling between dark energy and the pseudoscalar of electromagnetism, if there is any, would induce a rotation of the polarization plane of the cosmic microwave background (CMB). This results in a non-vanishing B-mode and parity-violating TB and EB correlations. Taking into account this effect, we calculate the full set of power spectra of cosmic microwave background (CMB) temperature and polarization anisotropies. We also give the constraint on the coupling strength from WMAP seven year data.

We report work towards a relativistic formulation for modeling strongly magnetized neutron stars, rotating or in a close circular orbit around another neutron star or black hole, under the approximations of helical symmetry and ideal MHD. The quasi-stationary evolution is governed by the frst law of thermodynamics for helically symmetric systems, which is generalized to include magnetic felds. The formulation involves an iterative scheme for solving the Einstein-Maxwell and relativistic MHD-Euler equations numerically. The resulting configurations for binary systems could be used as self-consistent initial data for studying their inspiral and merger.

In this review, I discuss briefly stringent tests of Lorentz-violating quantum space-time foam models inspired from String/Brane theories, provided by studies of high energy Photons from intense celestial sources, such as Active Galactic Nuclei or Gamma Ray Bursts. The theoretical models predict modifications to the radiation dispersion relations, which are quadratically suppressed by the string mass scale, and time delays in the arrival times of photons (assumed to be emitted more or less simultaneously from the source), which are proportional to the photon energy, so that the more energetic photons arrive later. Although the astrophysics at the source of these energetic photons is still not understood, and such non simultaneous arrivals, that have been observed recently, might well be due to non simultaneous emission as a result of conventional physics effects, nevertheless, rather surprisingly, the observed time delays can also fit excellently the stringy space-time foam scenarios, provided the space-time defect foam is inhomogeneous. The key features of the model, that allow it to evade a plethora of astrophysical constraints on Lorentz violation, in sharp contrast to other field-theoretic Lorentz-violating models of quantum gravity, are: (i) transparency of the foam to electrons and in general charged matter, (ii) absence of birefringence effects and (iii) a breakdown of the local effective lagrangian formalism.

The Bondi-Metzner-Sachs group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of General Relativity. However, in quantum gravity, complexified or euclidean versions of General Relativity are frequently considered. McCarthy has shown that there are forty-two generalizations of B for these versions of the theory and a variety of further ones, either real in any signature, or complex. A firm foundation for quantum gravity can be laid by following through the analogue of Wigner's programme for special relativity with B replacing the Poincare group P. Here the main results which have been obtained so far in this research programme are reported and the more important open problems are stated.

We study the late time evolution of Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source and a scalar field arising in the conformal frame of f(R) theories nonminimally coupled to matter. We prove using the approach of dynamical systems, that equilibria corresponding to non-negative local minima for V are asymptotically stable. We show that if γ, the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the latter eventually dominates. The results are valid for a large class of nonnegative potentials without any particular assumptions about the behavior of the potential at infinity.

The Genetic Algorithm is a heuristic that can be used to produce model independent solutions to an optimization problem, thus making it ideal for use in cosmology and more specifically in the analysis of type Ia supernovae data. In this work we use the Genetic Algorithms (GA) in order to derive a null test on the spatially flat cosmological constant model ΛCDM. This is done in two steps: first, we apply the GA to the Constitution SNIa data in order to acquire a model independent reconstruction of the expansion history of the Universe H(z) and second, we use the reconstructed H(z) in conjunction with the Om statistic, which is constant only for the ΛCDM model, to derive our constraints. We find that while ΛCDM is consistent with the data at the 2σ level, some deviations from ΛCDM model at low redshifts can be accommodated.

The corrections to the gravitational potential due to a Sol extra dimensional compact manifold are studied. We compare the range of the corrections to the range of the 3-torus corrections. It is found that for small values of the radius of the extra dimensions the Sol manifold corrections are large compared to the 3-torus corrections. Also, Sol manifolds corrections can be larger, comparable or smaller compared to the 3-torus case, for larger compactification radii.

In an almost de Sitter space-time, the stochastic semiclassical Einstein-Langevin equations with cosmological constant non-zero Λ have been written in the TT-gauge in a perturbative way (e.g. as zero-order and first order equations). Applying order reduction to zero and first order equations we found approximate solutions to those equations. To understand how large are the physical perturbations on different time scales, a two point correlation function of the intrinsic and induced fluctuations have been computed explicitly and their spectrum as well.

We study the emission in the bulk of tensor-type gravitons by a simply rotating (4 + n)-dimensional black hole. The decoupling of the radial and angular part of the graviton field equation makes it possible to solve them analytically (in the limit of low-energy emitted particles and low-angular momentum of the black hole) and find the corresponding absorption probability. We also move to solve these equations numerically. The comparison between analytic and numerical results shows a very good agreement in low and intermediate energy regimes. Finally, the energy and angular momentum emission rates were calculated in order to explore their dependence on the number of additional spacelike dimensions of the spacetime background and the angular momentum of the black hole. Interesting conclusions about the significance of tensor-type gravitons as energy carriers in the context of Hawking radiation were reached.

A large number of observations suggest that our universe entered at low redshifts a stage with accelerated expansion rate. Many models, Dark Energy (DE) models, able to explain this departure from conventional cosmology have been proposed. These models are conceptually very different, either introducing some new component with sufficiently negative pressure, or modifying the gravitational interaction on cosmic scales. Some of these DE models are reviewed here. Future high precision observations probing both the background and the perturbations will single out viable models.

The black hole in the center of the Milky Way has been observed and modeled intensely during the last decades. It is also the prime target of a number of new experiments that aim to zoom into the vicinity of its horizon and reveal the inner working of its spacetime. In this review we discuss our current understanding of the gravitational field of Sgr A* and the prospects of testing the Kerr nature of its spacetime via imaging, astrometric, and timing observations.

Noncommutative spectral geometry succeeds in explaining the physics of the Standard Model of electroweak and strong interactions in all its details as determined by experimental data. Moreover, by construction the theory lives at very high energy scales, offering a natural framework to address early universe cosmological issues. After introducing the main elements of noncommutative spectral geometry, I will summarise some of its cosmological consequences and discuss constraints on the gravitational sector of the theory.

We discuss a possible framework for the construction of a quantum gravity theory where the principles of QFT and general relativity can coexist harmonically. Moreover, in order to fix the correct gauge group of the theory we study the most general one, the affine group and its natural reduction to the orthogonal group. The price we pay for simplifying the geometry is the presence of matter fields associated with the nonmetric degrees of freedom of the original setup. The result is independent of the starting theory.

The idea that the cosmological term Λ should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, ρ_Λ = Λ/(8π G), namely one that has remained immutable since the origin of time. A smoothly evolving vacuum energy density ρ_Λ = ρ_Λ(ξ(t)) that inherits its time-dependence from cosmological functions ξ = ξ(t), such as the Hubble rate H(t) or the scale factor a(t), is not only a qualitatively more plausible and intuitive idea, but is also suggested by fundamental physics, in particular by quantum field theory (QFT) in curved space-time. To implement this notion, is not strictly necessary to resort to ad hoc scalar fields, as usually done in the literature (e.g. in quintessence formulations and the like). A "running" Λ term can be expected on very similar grounds as one expects (and observes) the running of couplings and masses with a physical energy scale in QFT. Furthermore, the experimental evidence that the equation of state (EOS) of the dark energy (DE) could be evolving with time/redshift (including the possibility that it might currently behave phantom-like) suggests that a time-variable Λ = Λ(t) term (possibly accompanied by a variable Newton's gravitational coupling too, G = G(t)) could account in a natural way for all these features. Remarkably enough, a class of these models (the "new cosmon") could even be the clue for solving the old cosmological constant problem, including the coincidence problem.

This is intended to be a brief introduction and overview of Hořava-Lifshitz gravity. The motivation and all of the various versions of the theory (to date) are presented. The dynamics of the theory are discussed in some detail, with a focus on low energy viability and consistency, as these have been the issues that attracted most of the attention in the literature so far. Other properties of the theory and developments within its framework are also covered, such as: its relation to Einstein-aether theory, cosmology, and future perspectives.

The "Conformal Dynamical Equivalence" (CDE) approach is briefly reviewed, and some of its applications, at various astrophysical levels (Sun, Solar System, Stars, Galaxies, Clusters of Galaxies, Universe as a whole), are presented. According to the CDE approach, in both the Newtonian and general-relativistic theories of gravity, the isentropic hydrodynamic flows in the interior of a bounded gravitating perfect-fluid source are dynamically equivalent to geodesic motions in a virtual, fully defined fluid source. Equivalently, the equations of hydrodynamic motion in the former source are functionally similar to those of the geodesic motions in the latter, physically, fully defined source. The CDE approach is followed for the dynamical description of the motions in the fluid source. After an observational introduction, taking into account all the internal physical characteristics of the corresponding perfect-fluid source, and based on the property of the isentropic hydrodynamic flows (quite reasonable for an isolated physical system), we examine a number of issues, namely, (i) the classical Newtonian explanation of the celebrated Pioneer-Anomaly effect in the Solar System, (ii) the possibility of both the attractive gravity and the repulsive gravity in a non-quantum Newtonian framework, (iii) the evaluation of the masses - theoretical, dynamical, and missing - and of the linear dimensions of non-magnetized and magnetized large-scale cosmological structures, (iv) the explanation of the flat-rotation curves of disc galaxies, (v) possible formation mechanisms of winds and jets, and (vi) a brief presentation of a conventional approach - toy model to the dynamics of the Universe, characterized by the dominant collisional dark matter (with its subdominant luminous baryonic "contamination"), correctly interpreting the cosmological observational data without the need of the notions dark energy, cosmological constant, and universal accelerating expansion.

We review the theory of stationary, axisymmetric spacetimes with black holes surrounded by a massive torus and present a numerical scheme for finding self-consistent solutions in a compactified grid that reaches to spatial infinity. Such numerical solutions have been utilized in studying nonaxisymmetric dynamical instabilities occurring in the torus.

Describing curved space-time as a four-dimensional manifold strained by the presence of matter or of texture defects, an additional term in the Lagrangian of space-time has to be introduced besides the Ricci scalar, accounting for the strain. The additional term produces dark matter-like effects around any given body. These effects show up both in the angular speed of freely orbiting objects and in the gravitational lensing of light. These results are obtained and discussed while treating a spherically symmetric stationary space-time configuration.

We review work published in [1, 2] on the thermodynamics of gauge theories on FLRW backgrounds through the AdS/CFT correspondence. Contrary to analogous studies of the so-called Bjorken flow, the backgrounds we consider are homogeneous and isotropic. This permits the exact determination of the gravitational dual, which is identified with the AdS-Schwarzschild geometry, expressed in coordinates that set the boundary metric in the FLRW form. We review the calculation of the stress-energy tensor of the dual CFT on the FLRW background, as well as the temperature and entropy of the CFT, which are related to the temperature and entropy of the black hole. We also derive the equation of cosmological evolution through the use of appropriate boundary conditions.

We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schrödinger type equation. We find the analytical solution of this system by applying the Hirota direct method which produces the dissipative soliton solutions to formulate the dynamical evolution of the nonlinear structure formation.

Observers drifting relative to the smooth Hubble flow have expansion rates different from that of the Universe itself. As a result, observers with small peculiar velocities in linearly perturbed Friedmann universes can experience accelerated expansion, while the universe is actually decelerating. The effect is local, but the affected scales can be large enough to give the (false) impression that the whole universe has recently entered an accelerating phase. Recent surveys reporting large-scale peculiar velocities substantially larger than previously anticipated add a certain degree of observational support to the aforementioned theoretical result.

The problem of time in quantum gravity arises due to the diffeomorphisms invariance of the theory and appears via the Hamiltonian constraint, in the canonical quantizations. There is a need for a description where one can ask some timeless questions that still encode some sense of temporality. The decoherent histories approach to quantum theory, already at the kinematical level admits an internal time. Several alternative proposals for resolving the problem of time via the decoherent histories, exist, and in this contribution we focus on one particular and examine how it manifests itself at some simple cosmological models.