It is shown, from the two independent approaches of McCrea-Milne and of Zeldovich, that one can fully recover the set equations corresponding to the relativistic equations of the expanding universe of Friedmann-Lemaitre-Robertson-Walker geometry. Alt
hough similar, the Newtonian and relativistic set of equations have a principal difference in the content and hence define two flows, local and global ones, thus naturally exposing the Hubble tension at the presence of the cosmological constant Lambda. From this, we obtain absolute constraints on the lower and upper values for the local Hubble parameter, sqrt{Lambda c^2/3} simeq 56.2$ and sqrt{Lambda c^2} simeq 97.3 (km/sec Mpc^{-1}), respectively. The link to the so-called maximum force--tension issue in cosmological models is revealed.
The currently released datasets of the observational surveys reveal the redshift dependence of the physical features of cosmic voids. We study the void induced hyperbolicity, that is the deviation of the photon beams propagating the voids, taking int
o account the redshift dependence of the void size indicated by the observational surveys. The cumulative image distortion parameter is obtained for the case of a sequence of variable size voids and given underdensity parameters. The derived formulae applied along with those of redshift distortion ones, enable one to trace the number and the physical parameters of the line-of-sight voids from the analysis of the distortion in the galactic surveys.}
The cosmological constant if considered as a fundamental constant, provides an information treatment for gravitation problems, both cosmological and of black holes. The efficiency of that approach is shown via gedanken experiments for the information
behavior of the horizons for Schwarzschild-de Sitter and Kerr-de Sitter metrics. A notion of entropy regarding any observer and in all possible non-extreme black hole solutions is suggested, linked also to Bekenstein bound. The suggested information approach forbids the existence of naked singularities.
The Hubble tension is shown to be solvable, without any free parameter, conceptually and quantitatively, within the approach of modified weak-field General Relativity involving the cosmological constant $Lambda$. That approach enables one to describe
in a unified picture both the dynamics of dark matter containing galaxies and the accelerated expansion of the Universe, thus defining a {it local} Hubble constant of a local flow and the {it global} one. The data on the dark matter content of peculiar galaxy samples are shown to be compatible to that unified picture. Future more refined surveys of galaxy distribution, hierarchical dynamics and flows within the vicinity of the Local group and the Virgo supercluster can be decisive in revealing the possible common nature of the dark sector.
We study the black holes shadow for Schwarzschild - de Sitter and Kerr - de Sitter metrics with the contribution of the cosmological constant Lambda. Based on the reported parameters of the M87* black hole shadow we obtain constraints for the $Lambda
$ and show the agreement with the cosmological data. It is shown that, the coupling of the Lambda-term with the spin parameter reveals peculiarities for the photon spheres and hence for the shadows. Within the parametrized post-Newtonian formalism the constraint for the corresponding Lambda-determined parameter is obtained.
We consider the observational aspects of the value of dark energy density from quantum vacuum fluctuations based initially on the Gurzadyan-Xue model. We reduce the Djorgovski-Gurzadyan integral equation to a differential equation for the co-moving h
orizon and then, by means of the obtained explicit form for the luminosity distance, we construct the Hubble diagram for two classes of observational samples. For supernova and gamma-ray burst data we show that this approach provides viable predictions for distances up to $z simeq 9$, quantitatively at least as good as those provided by the lambda cold dark matter ($Lambda$CDM) model. The Hubble parameter dependence $H(z)$ of the two models also reveals mutual crossing at $z=0.4018$, the interpretation of which is less evident.
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $Lambda$. It is shown that according to the current accuracy of satellite measurements the obtaine
d error limits for $Lambda$ is self-consistent with cosmological observations. The corrections of $Lambda$ term are derived for the strong field Lense-Thirring precession i.e. the frame dragging effect and for the nutation. As a result, in the context of recently proposed $Lambda$-gravity we obtain constraints for $Lambda$ in both relativistic and weak-field limits. Namely, for the latter we analyze several Keplerian systems at different scales. We find that the obtained constraints for the modified gravity corrections are several orders of magnitude tighter than those available for such effects as gravitational redshift, gravitational time delay and geodetic precession in Solar System.
The sparsity parameter for clusters of galaxies is obtained in the context of $Lambda$-gravity. It is shown that, the theoretical estimated values are within the reported error limits of the measured data. Thus, in the future the sparsity parameter c
an serve as an informative new test to detect the discrepancy between General Relativity and $Lambda$-gravity.
The evolution of galaxy clusters can be affected by the repulsion described by the cosmological constant. This conclusion is reached within the modified weak-field General Relativity approach where the cosmological constant Lambda enables to describe
the common nature of the dark matter and the dark energy. Geometrical methods of theory of dynamical systems and the Ricci curvature criterion are used to reveal the difference in the instability properties of galaxy clusters which determine their evolutionary paths. Namely, it is shown that the clusters determined by the gravity with Lambda-repulsion tend to become even more unstable than those powered only by Newtonian gravity, the effect to be felt at cosmological time scales.
The contribution of the thermal dust component in galactic halo rotation is explored based on the microwave data of Planck satellite. The temperature asymmetry of Doppler nature revealed for several edge-on galaxies at several microwave frequencies i
s analyzed regarding the contribution of the thermal dust emission. We derive the dust contribution to the galactic halo rotation using the data in three bands, 353GHz, 545GHz and 857GHz for two nearby galaxies M81 and M82. The relevance of the revealed properties on the halo rotation is then discussed in the context of the modified gravity theories proposed to describe the dark matter configurations.
