In this work, we apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field, which has been previously in
vestigated in the literature. For a coupling function $Q = -(alpha dot{rho}_m + beta dot{rho}_{phi} )$, we have found that it can be rewritten in the form $Q = 3H (alpha rho_m + beta dot{phi}^2)/(1-alpha +beta)$, so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the following scenarios $alpha=0$, $alpha = beta$ and $alpha = -beta$, separately and in order to describe the cosmological evolution for each solution we have calculated various observables. We find that there are not any new stable late-time solutions apart from those found of standard quintessence, nevertheless, the stability conditions are severely altered. A notable result found with respect to previous works is that in our case, with the exception of the matter dominated solution, the remaining critical points behave as scaling although the stiff matter solution and the dark energy dominated state can be recovered in the limit $beta rightarrow 0$ and $beta rightarrow 1$, respectively. Moreover, it is shown that for $alpha = beta $ and $alpha = - beta$ (in general for $alpha eq 0$), a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature.
We construct from first principles a general relativistic approach to study Schwarzschild black hole (BH) rotation curves and estimate the mass-to-distance ratio of the active galactic nucleus of NGC 4258 in terms of astrophysical observable quantiti
es. The presented method allows one to clearly distinguish and quantify the general and special relativistic contributions to the total redshift expression. The total relativistic redshift/blueshift comprises three components: the gravitational redshift due to the spacetime curvature generated by the mass of the BH in its vicinity, the kinematic shift, originated by the photons local Doppler effect, and the redshift due to a special relativistic boost that describes the motion of a galaxy from a distant observer. We apply our method to the largest data set of highly redshifted water megamaser measurements on the accretion disk of the NGC 4258 active galaxy and use this general relativistic method to estimate its BH mass-to-distance ratio: M/D = (0.5326 +/- 0.00022) x 10^7 solar masses/Mpc.
Within the framework of Unimodular Gravity, we consider non-gravitational interactions between dark matter and dark energy. Particularly, we describe such interactions in the dark sector by considering diffusion models that couple the cold dark matte
r fluid with the dark energy component, where the latter has the form of a variable cosmological constant. For the first time, we solve the cosmological evolution of these models from the radiation dominated era to the present day. We show how the diffusion processes take place by analyzing the cosmological evolution of the energy density parameters $Omega_{cdm}$ and $Omega_{Lambda}$, as well as that of the Hubble parameter. Finally, we perform the statistical analysis, imposing constraints on the diffusion parameters, by using data from Planck 2018, SH0ES, Pantheon, and H0LICOW collaborations. We found that cosmological diffusion models in the framework of Unimodular Gravity can ease the current tension in the value of $H_0$. We also show that the very far future cosmological evolution for all diffusion models is eternally accelerating without future singularities.
We obtain the mass parameter for a class of static and spherically symmetric regular black holes (BHs) (namely Bardeen, Hayward and Ay{o}n-Beato-Garc{i}a BHs) which are solutions of Einsteins field equations coupled to nonlinear electrodynamics (NED)
in terms of redshifts and blueshifts of photons emitted by geodesic particles (for instance, stars) orbiting around these BHs. The motion of photons is not governed by null geodesics for these type of spacetime geometries which reflects the direct effects of the electrodynamic nonlinearities in the photon motion; hence, an effective geometry needs to be constructed to study null trajectories [Phys. Rev. D61, 045001 (2000)]. To achieve the above, we first study the constants of motion from the analysis of the motion of both geodesic particles moving in stable circular orbits and photons ejected from them and reaching a distant observer (or detector) in the equatorial plane for the above mentioned regular BHs. The relationship between red/blueshifts of photons and the regular BH observables is presented. We also numerically find the bounds on the photon shifts for these regular BH cases.
We study the effects of dark energy (DE) anisotropic stress on features of the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian (PPF) formalism to emulate an effective DE, and model its anisotropic stress properties through a
two-parameter equation that governs its overall amplitude ($g_0$) and transition scale ($c_g$). For the background cosmology, we consider different equations of state to model DE including a constant $w_0$ parameter, and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first constrain these parameters by using the Pantheon, BAO, $H_0$ and CMB Planck data. Then, we analyze the role played by these parameters in the linear PS. In order for the anisotropic stress not to provoke deviations larger than $10%$ and $5%$ with respect to the $Lambda$CDM PS at $k sim 0.01 ,h/text{Mpc}$, the parameters have to be in the range $-0.30< g_0 < 0.32$, $0 leq c_g^2 < 0.01$ and $-0.15 < g_0 < 0.16$, $0 leq c_g^2 < 0.01$, respectively. Additionally, we compute the leading nonlinear corrections to the PS using standard perturbation theory in real and redshift space, showing that the differences with respect to the $Lambda$CDM are enhanced, especially for the quadrupole and hexadecapole RSD multipoles.
In this paper we show that an equivalence between Horndeski and beyond Horndeski theories and general relativity with an effective imperfect fluid can be formally established. The formal equivalence is discussed for several particular cases of intere
st. Working in the cosmological framework, it is shown that, while the effective stress-energy tensor of viable Horndeski theories is formally equivalent to that of an imperfect fluid with anisotropic stresses and vanishing heat flux vector, the effective stress-energy tensor of beyond Horndeski theories is equivalent to the one of a perfect fluid instead.
We study the innermost stable circular orbit (ISCO) of a spinning test particle moving in the vicinity of an axially symmetric rotating braneworld black hole (BH). We start with the description of the event horizon, static limit surface and ergospher
e region of such BH and bring out the effect of tidal charge parameter on ergosphere. It is found that the ISCO of rotating braneworld BH is very sensitive to braneworld BH parameter C (also known as tidal charge parameter) in addition to its rotation parameter. We further discovered that the orbital radius of the spinning test particles changes non monotonously with the braneworld BH tidal charge parameter. It is found that for rotating braneworld BH the allowed range of the particle spin grows as the tidal charge parameter C decreases, in contrast with the Kerr Newman BH. We also found the similar behavior of the particles spin for the braneworld Reissner Nordstrom (C < 0) BH in contrast with its counterpart having (C > 0).
We derive closed formulas for the mass and spin parameters of a Kerr black hole in terms of a minimal quantity of observational data: the red-/blue-shifts of photons emitted by massive particles (stars) moving on geodesics around the black hole and t
heir respective orbital radius. It turns out that given a set of two (three) stars revolving around the black hole, these formulas involve just eight (twelve) observational data. For the case of a single star orbiting the black hole we need a minimal set of four observational measurements to analytically determine both parameters.
In this paper we investigate the so called phantom barrier crossing issue in a cosmological model based in the scalar-tensor theory with non-minimal derivative coupling to the Einsteins tensor. Special attention will be paid to the physical bounds on
the squared sound speed. The numeric results are geometrically illustrated by means of a qualitative procedure of analysis that is based on the mapping of the orbits in the phase plane onto the surfaces that represent physical quantities in the extended phase space, that is: the phase plane complemented with an additional dimension relative to the given physical parameter. We find that the cosmological model based in the non-minimal derivative coupling theory -- this includes both the quintessence and the pure derivative coupling cases -- has serious causality problems related with superluminal propagation of the scalar and tensor perturbations. Even more disturbing is the finding that, despite that the underlying theory is free of the Ostrogradsky instability, the corresponding cosmological model is plagued by the Laplacian (classical) instability related with negative squared sound speed. This instability leads to an uncontrollable growth of the energy density of the perturbations that is inversely proportional to their wavelength. We show that independent of the self-interaction potential, for the positive coupling the tensor perturbations propagate superluminally, while for the negative coupling a Laplacian instability arises. This latter instability invalidates the possibility for the model to describe the primordial inflation.
The mass parameters of compact objects such as Boson Stars, Schwarzschild, Reissner Nordstrom and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred, zblue) of photons emitted by particles moving along circular geodesic
s around these objects and the radius of their orbits. We found bounds for the values of (zred, zblue) that may be observed. For the case of Kerr black hole, recent observational estimates of SrgA* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.
