The model including square of Ricci scalar in addition to Ricci scalar R which was proposed in 1980 leads to inflationary parameters coinciding with modern observations. With help of conformal transformation the R^2 model can be reduced to the model of General Relativity (GR) with potential of special form. The non-minimal coupled gravity model where the inflaton is the Standard Model Higgs boson leads to the same predictions for inflationary inflationary parameters. And at the same time with help of conformal transformation this model can be transform to the model of GR with the corresponding potential. The obtained models in GR belong to attractors models. More over in non-minimally coupled gravity the different types of interaction of scalar field with gravity can be considered, the different types of non-minimal coupling lead to different types of potential in coinciding model in GR. The cosmological attractors models generalize R^2 and Higgs-driven inflation models and lead to the same spectral index prediction with some freedoms in tensor-to-scalar ratio. We construct gravity models with Gauss-Bonnet term multiplied to a function of the scalar field (Einstein-Gauss-Bonnet gravity) leading to analytical expressions of inflationary parameters coinciding with inflationary parameters of cosmological attractor models. We reformulate the equations of the Einstein-Gauss-Bonnet gravity in the Friedmann universe in slow-roll regime in term of e-folding number. With help of this reformulation, we obtain gravity models with the Gauss-Bonnet term leading to analytical expressions of inflationary parameters coinciding with inflationary parameters of cosmological attractor models in the leading order approximation. Within the framework of the model we obtain an analytical expression for scalar power spectrum amplitude. We estimate relation of constant including to the Gauss-Bonnet term using experimental data for value of scalar power spectrum amplitude.

Searching for possible indicators of spatial topology of the Universe in the Cosmic Microwave Background data, one recognizes a quite promising interpretation which suggests that the shape of the space manifests itself in the form of anomalies in the large angular scale observations, such as the quadrupole and octopole alignment. Motivated by the presumptive existence of such a tempting connection, we study the chimney topology, TxTxR, which belongs to the class of toroidal topologies with a preferred direction. The infinite axis in this case may be attributed to the preferred axis of the aforementioned quadrupole and octopole alignment. We investigate the gravitational aspects of such a configuration. Namely, we reveal the form of the gravitational potential, sourced by point-like massive bodies. Starting from the perturbed Einstein equations, which ensure the proper demonstration of relativistic effects, one can derive the Helmholtz equation for the scalar perturbation (gravitational potential). Through distinct alternative methods, we present the physically meaningful nontrivial exact solutions of this equation. Our approach excludes any presumptions regarding the spatial distribution of gravitating sources. We show that the particular solution that appears in the form of summed Yukawa potentials is indeed very convenient for the use in numerical calculations, in the sense that it provides the desired accuracy with fewer terms in the series.

Since the concept of Dark Energy (i.e., effective Lambda-term in the GR equations) became a commonly-accepted paradigm in cosmology, numerous authors analyzed its effects on the dynamics of celestial bodies. However, such calculations were usually done only in the framework of static Schwarzschild-deSitter metric, which does not possess the adequate cosmological asymptotics at infinity and, as a result, only the conservative perturbations of the orbits were taken into account. So, the aim of the present work is to use more realistic Robertson-Walker asymptotics and, thereby, to analyze also the nonconservative (secular) perturbations of Keplerian orbits. As a mathematical tool, we employ the modified Kottler metric, which was derived in our earlier paper [Yu.V. Dumin. Phys. Rev. Lett., v.98, p.059001 (2007)]. As follows from our analysis of motion of a test body in the field of a gravitating mass, the resulting perturbations of the Keplerian orbits depend on a complex interplay between three crucial parameters of the problem - the initial radius of the orbit, Schwarzschild and deSitter radii, - which differ from each other by many orders of magnitude. Namely, if Lambda-term is sufficiently small (i.e., the deSitter radius is large), then orbital perturbation is almost completely compensated by the gravitational attraction. Next, when the magnitude of Lambda increases, the corresponding secular perturbation becomes significant and can reach the rate of the standard Hubble flow [Yu.V. Dumin. Grav. & Cosmol., v.26, p.307 (2020)]. This fact may have important consequences for the long-term dynamics of planets and stellar binaries. At last, if the Lambda-term increases further, the perturbation becomes so strong that the original orbit is completely destroyed and the test body escapes to infinity (i.e., a kind of the "sling effect" takes place). This might be relevant, e.g., to the formation of the so-called "hypervelocity stars".

We present a N=2 supergravity model that interpolates between all the single dilaton truncations of the gauged SO(8), N=8 maximal supergravity. We provide explicit non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits, exploiting the non-trivial transformation of the Fayet-Iliopoulos parameters under electromagnetic duality to connect the electric and the magnetic configurations. Among the obtained class of solutions, we were able to recover the known results in the case of the STU model, while all the other charged solutions are new. We also provide the asymptotic charges, thermodynamics and boundary conditions of these black hole solutions and show that the correspondent configurations introduce a triple trace deformation in the dual theory.
We then consider a new supersymmetric truncation of the maximal supergravity and find non-extremal and supersymmetric black holes in this new sector. These black holes can be uplifted to higher dimensions and can be interpreted as new M2-brane and D2-brane with a regular supersymmetric limit.
We expect that the introduced infinitely many black hole configurations can turn out to be a playground to test ideas of holography, microscopic state counting and condensed matter, as well as a small step towards the characterization of all the supersymmetric solutions of M-theory.

We propose a simple geometrical mechanism for the flattening of galactic rotation curves at large distances, the local compression of field lines around their planes induced by elongated dark mater halos, and elaborate on its possible role in Nature. Fitting a number of rotation curves from the SPARC database with deformed versions of two popular models of dark matter halos, namely the Navarro-Frenk-White (NFW) and the Burkert profiles, we collect some evidence that prolate dark mater distributions improve by five or more percent the agreement with data for a wide fraction of the galaxies that we have examined. Moreover, the rotation curves of some galaxies seem to suggest the presence of string type objects at their centers which might be black hole jets comprised of baryonic or dark matter, tidal streams, or cosmic strings. If taken at face value, all these results would favor cold dark matter models (CDM) with respect to scenarios based on self-interacting dark matter (SiDM), modified gravity, or modified Newtonian dynamics (MOND).

In addition, we propose a new method for the study of rotation curves, namely performing the same analysis for different types of DM profiles (NFW, Burkert, Einasto, etc.) to see whether or not certain key features persist. We believe this approach could be useful for making model-independent conclusions about the properties of dark halos.

Scalar field models are known for their dynamical nature i.e, dynamical equation of state parameter to explain the late time cosmic acceleration of the universe unlike cosmological constant which is known for its constant equation of state. Quintessence cosmological model or canonical scalar field with a potential is one such simplest class of model which is introduced to account for late time acceleration of the universe. Till now, there are numerous scalar field models proposed like canonical, non-canonical, galileon scalar field models etc. which can be broadly classified into two classes, namely, thawing and tracking. In the present work, we mathematically investigate different kinds of scalar field potentials under quintessence cosmological model using tracking parameter to examine whether these potentials are showing thawing or tracking behaviour. Tracking parameter is considered because during cosmic evolution the dynamics of tracking depends susceptibily on the variation of this particular parameter. We analyze each potential using this parameter and accordingly get their behaviour. It is found that among the four potentials used, three are showing tracking properties and only one is showing thawing property as per the tracking parameter . The tracking and thawing properties / behavior are discussed in result and discussion section of the paper.

Dark Energy, a form of repulsive gravity, is causing an accelerated expansion of the Universe. Recent astrophysical measurements have confirmed this accelerated expansion where the LCDM model provides a quantitative description of this expansion rate. As is well known there are a number of free parameters of unknown origin in the LCDM model, in particular, the cosmological constant L (or Dark Energy (DE)) forms one of these free parameters. In this contribution we describe a recent model which attributes DE to the Born self-energy contained within the electric field which surrounds a finite-sized electron within the WHIM (Warm-Hot Intergalactic Medium). Upon using readily available literature values for the intergalactic (IG) baryon density, IG hydrogen ionization fraction, the best estimate for the electron radius, as well as, Hubble parameter data many properties attributed to DE can be quantitatively explained. In particular, our model quantitively explains

(i) the magnitude of DE today,

(ii) the DE to ordinary matter mass ratio today,

(iii) has an equation of state of w = -1, as expected for DE, and

(iv) exhibits a deceleration-acceleration transition at a redshift of z ~ 0.8 in agreement with Hubble parameter observations.

(v) Finally, the model provides a viable candidate for Dark Matter; the CDM in the LCDM model.

Further detail concerning this DE model can be found in Astrophys. Space Sci 365, 64 (2020).

Killing vector fields can be used as gauge vector potentials since the associated electromagnetic field tensor automatically satisfies the source-free Maxwell's equations in vacuum spacetimes. This fact enabled Wald to find the form of the electromagnetic tensor corresponding to Kerr black hole immersed in a uniform test magnetic field.

We present the generalisation of this result which is valid for static black holes surrounded by nonlinear electromagnetic fields. The first obstacle we encountered when dealing with the nonlinear electrodynamics was that the above-described ansatz no longer works. Secondly, finding the exact solution in a closed form proved to be a rather challenging task because it would require solving a highly nonlinear differential equation.

The alternative approach is via perturbative expansion around the original Wald's solution. We obtain the equation which determines the lowest order correction to the gauge vector field 1-form and magnetic scalar potential. With the main focus on Born-Infeld and Euler-Heisenberg theories on the Schwarzschild background, we calculate the aforementioned correction. Also, we show that this perturbative correction doesn't change electric and magnetic Komar charges or the asymptotic behaviour of the field. Finally, stating physical arguments, we justify the usage of perturbative approach.

References:

[1] R. Wald: "Black hole in a uniform magnetic field", Phys. Rev. D 10 (1974) 1680--1685

[2] A. Bokulić and I. Smolić: "Schwarzschild spacetime immersed in test nonlinear electromagnetic €fields", Class. Qu‹antum Grav. 37 (2020) 055004

The background-independent quantum gravity is the necessary framework to construct generally relativistic quantum field theory. By assuming the ADM decomposition of spacetime, it is possible to define the metric-independent Fock space for this formulation. This space, known as spin network, is invariant under the SU(2) symmetry and the spatial diffeomorphisms transformations. It is the Fock space for the model called loop quantum gravity in which the canonical operators are the quantized holonomies of the Ashtekar connection and the fluxes of densitized dreibein. I will present an improved construction of the lattice gravity and its gauge-fixed cosmological reduction based on the same lattice variables.

The approach is based on the geometric expansion of holonomies into power series up to the quadratic order terms in the regularization parameter. As a result, a more accurate procedure is obtained in which the symmetry of holonomies assigned to links is directly reflected in the related distribution of connections. The application of the procedure to the Hamiltonian constraint regularization provides its lattice analog, the domain of which has a natural structure of elementary cells sum. In consequence, the related scalar constraint operator, which spectrum is independent of intertwiners, can be defined.

The cosmological phase space reduction of lattice gravity requires rigorous application of gauge-fixing conditions that reduce the SU(2) symmetry and the spatial diffeomorphisms invariance. The internal symmetry is fixed to the Abelian case and the diffeomorphisms invariance is simultaneously reduced to spatial translations. The obtained Hamiltonian constraint is finite (without any cut-off introduction) and exact (without the holonomy expansion around short links). Furthermore, it has the expected form of the sum over elementary cuboidal cells. Finally, the simple structure of its homogeneities and anisotropies should allow to describe the quantum cosmological evolution of the Universe in terms of transition amplitudes, instead of using perturbative approximations.

Astrophysical accretion processes near the black hole candidates, such as active galactic nuclei (AGN), X-ray binary (XRB), and other astrophysical sources, are associated with high-energetic emission of radiation of relativistic particles and outflows (winds and/or jets). It is widely believed that the magnetic field plays a very important role to explain such high energetic processes in the vicinity of those astrophysical sources. In the present research note, we propose that the black hole is embedded in an asymptotically uniform magnetic field. We investigate the dynamical motion of charged particles in the vicinity of a weakly magnetized black hole. We show that in the presence of the magnetic field, the radius of the innermost stable circular orbits (ISCO) for a charged particle is located close to the black hole's horizon. The fundamental frequencies, such as Keplerian and epicyclic frequencies of the charged particle are split into two parts due to the magnetic field, as an analog of the Zeeman effect. The orbital velocity of the charged particle measured by a local observer has been computed in the presence of the external magnetic field. We also present an analytical expression for the four-acceleration of the charged particle orbiting around black holes. Finally, we determine the intensity of the radiating charged accelerating relativistic particle orbiting around the magnetized black hole.