The metric self-organization of matter-space-time implies a non-local correlation of its affine connections and the fulfillment of volumetric conservation of energy-momentum at any fixed moment of world time. Geodesic forces-accelerations in metric fields of Einstein’s gravity correspond to direct pushes of the Lomonosov gravitational liquid and the Umov transport of inertial densities. Mathematics of Russian Cosmism for the monistic all-unity of continuous mass-energy replaces Newtonian gravity ‘from there to here’ with the local etherial pressure ‘from here to there’ due to by the spatial asymmetry of material densities within a non-local whole. The inverse square law for the visible interactions between dense regions of etherial space-matter can be controlled locally by means of resonant interventions into the area of ​​test bodies.

Gravitational Wave (GW) astronomy provides an independent way to estimate cosmological parameters. The detection of GWs from a coalescing binary allows a direct measurement of its luminosity distance, so these sources are referred to as "standard sirens" in analogy to standard candles. In this talk, I investigate the impact of the Einstein Telescope, a third-generation detector which will detect tens of thousands of binary neutron stars. I focus on the non-flat CDM cosmology and some Dark Energy models. To evaluate the accuracy of cosmological parameters, I consider two types of mock datasets depending on whether or not a short Gamma-Ray Burst is detected and associated with the gravitational wave event using the THESEUS satellite. Depending on the mock dataset, different statistical estimators are applied: one assumes that the redshift is known, and another marginalizes over it, taking a specific prior distribution.

Halo Dark Matter (DM) Formation is a complex process, intertwining both nonlinear gravitational and cosmological phenomena.
One of the manifestations of this complexity is the shape of the resulting present-day DM halos : simulations and observations show that they are triaxial objects. Interestingly, those shapes carry cosmological information; We prove by two different methods that cosmology, and particularly the dark energy model, leaves a lasting trace on the present-day halos and their properties.

- First, we show that the overall shape (when carefully computed) of the DM halo exhibits a different behavior when the DE model is varied. We explain how that can be used to literally "read" the fully nonlinear power spectrum and estimate cosmological parameters (such as σ₈) within the halos' shape at z=0.

- Then, we implement machine learning methods to classify DM halos according to their corresponding cosmology: we associate to each simulated halo, « ellipsoidal » mass and shape profiles. Those are defined to efficiently keep track of the matter distribution anisotropies. Such attributes allow a properly trained learning device to find the dark energy model of the Universe within which these halos have grown. We also study the misleading methodological biases of Machine Learning approaches, aka "Clever Hans effects", and the way to fix them.

To that end, we worked with "Dark Energy Universe Simulations" DM halos: DM halos are grewed in three different dark energy models, whose parameters were chosen in agreement with both CMB and SN Ia data. Although the resulting cosmic matter distribution are thus extremely close from one cosmological model to another, a careful analysis using machine learning methods allowed to discriminate each DM halo according its cosmological model.

At large-scale distances where space-time is curved due to gravity, a nonzero minimal uncertainty in the momentum emerges. The presence of minimal uncertainty in momentum allows a modification to the quantum uncertainty principle, which is known as the Extended Uncertainty Principle (EUP). In this work, we handle the harmonic oscillator problem in the EUP scenario and obtain analytical exact solutions in classical and semiclassical domains. In the classical context, we establish the equations of motion of the oscillator and show that the EUP-corrected frequency is depending on the energy and deformation parameter. In the semiclassical domain, we derive the energy eigenvalue levels and demonstrate that the energy spectrum depends on $n^{2}$, as the feature of hard confinement. Finally, we investigate the impact of the EUP on the harmonic oscillator's thermodynamic properties by using the EUP-corrected partition functions in classical limit in the (A)dS backgrounds.

We investigate the background dynamics of a class of models with noncanonical scalar field and matter both in FLRW closed and open spacetime. The detailed dynamical system analysis is carried out in the bouncing scenario. Cosmological solutions satisfying the stability and bouncing conditions are obtained using the tools of a dynamical system.

We consider $R+R^2$ gravity model with a string-inspired function.
We analyze the model in slow-roll regime and estimate inflationary parameters using observational
data to restrict parameters including to the string-inspired function.

A plane-symmetric Bianchi-I model is explored in f (R, T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor. The model with strange quark matter (SQM) is studied in f (R, T) theory. Exact solutions are obtained for a particular form of f (R, T) = R + 2λT, under the assumption of the expansion scalar proportional to the shear scalar, and a special law of variation of the Hubble parameter. The model presents a cosmological scenario of transition from early deceleration to late-time acceleration. It is very interesting to note that even in the absence of f (R, T) gravity, SQM accelerates the universe. This model illustrates that SQM can be considered as an alternative to dark energy.

It is well known that the universe is undergoing accelerated expansion during recent times, and that it underwent decelerated expansion at early times. The deceleration parameter, which is essentially the second derivative of the scale factor, can be used to describe these eras, with a negative parameter for acceleration, and a positive parameter for deceleration. Apart from the standard ΛCDM model in general relativity, there are many cosmological models in various other theories of gravity. In order to describe these models, especially the deviation from general relativity, the jerk parameter was introduced, which is basically the third derivative of the scale factor. In the ΛCDM model in general relativity, the jerk parameter j is constant and j = 1. The constant jerk parameter, j = 1, leads to two different scale factor solutions, one power-law and the other exponential. The power law solution corresponds to a model in which our universe expands with deceleration, while the exponential solution corresponds to the model in which it expands by accelerating. In this study, the cosmological consequences of such a selection of the jerk parameter on non-minimally coupled f(R, T) theory of gravity (where R is the Ricci scalar and T is the trace of the energy-momentum tensor) and the dynamic properties of these models are investigated on a flat Friedmann-Lemaitre-Robertson-Walker background.

We consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the $R^2$ gravity model with an additional scalar field and the corresponding two-field chiral cosmological model with the cosmological constant and nonstandard kinetic part of the action, the general solutions have been obtained. We analyze the correspondence of the cosmic time solutions obtained and different possible evolutions of the Hubble parameters in the Einstein and Jordan frames. The talk is based on the paper V.R. Ivanov, S.Yu. Vernov, Eur. Phys. J. C 81 (2021) 985 [https://doi.org/10.1140/epjc/s10052-021-09792-4] and recent investigations.

Supermassive black holes accreting matter at very high, perhaps even super-Eddington rates appear in the sky as a special class of luminous active galactic nuclei. These sources -- hereafter extreme quasars for brevity -- can be identified in relatively large numbers from major optical surveys over a broad range of redshifts thanks to selection criteria defined on the basis the so-called Eigenvector 1/quasar main sequence parameter space. The systematic trends of the main sequence are believed to reflect a change in accretion modes: at high accretion rates, an optically thick, geometrically thick, advection dominated accretion disk is expected to develop. Even if the physical processes occurring in advection-dominated accretion flows are still not fully understood, a robust inference from the models -- supported by a wealth of observational data -- is that extreme quasars should radiate at an extreme, well defined Eddington ratio with small scatter i.e., at a maximum radiative efficiency for a given black hole mass. This result makes it possible to derive redshift-independent "virial luminosity" estimates from measurements of emission line widths. The method relies on the estimate of the virial mass via a photoionization approach and is conceptually equivalent to the luminosity estimates based from line width in early and late type galaxies, and a sizeable sample of extreme quasars has the potential to yield an independent measure of the main cosmological parameters.

A major issue related to the cosmological application of extreme quasars is the identification of proper emission lines whose broadening is due to a virial velocity field over a wide range of redshift and luminosity. In addition, there are several caveats and missing pieces of informations before a rigorous standardization may become possible. Most relevant issues are the anisotropy of continuum emission and the geometry of the line emitting regions. Related concerns are the powerful high ionization winds, and the chemical composition of the line emitting gas. These issues are compounded with circumnuclear and host galaxy star formation that may also reach extreme levels, and with the presence of circumnuclear dust. While extinction due to dust does not seem to affect the rest frame UV and optical spectra of most sources, a fraction of them may still be partly embedded in a cocoon of gas and dust, and reddened to various extents. Nonetheless, large samples of extreme quasars can be built overcoming at least some statistical effects. We discuss several aspects related to a better understanding of their structure and of the complex interplay between accretion flow and line emitting region, as well as their formation and evolution from primordial epochs to the present-day Universe. We report on preliminary attempts to exploit extreme quasars as cosmological distance indicators, and we briefly discuss the perspective of the method and its extension over a broad range of redshift. Extreme quasars have the potential to provide a new class of distance indicators covering cosmic epochs from almost present day up to less than 1 Gyr from the Big Bang, much beyond the limits of other optical cosmological indicators such as supernovae.