Abstract:
A novel model of dark matter (DM), elastically compressible, can contribute to the acceleration of our Universe expansion. While each galaxy compresses its own DM within its gravitation field, the DM bordering neighboring galaxies, far from their centers, is pulled apart. It is shown that, although the DM pressure tends to zero at such locations, the DM compressibility tends to infinity. This allows the DM to expand between galaxies without gravitation hindrance. The model is consistent with the coupled distributions of baryonic and dark matters, with black hole formation at the centers of large galaxies, with galactic flat rotation curves, with a Tully-Fisher relation, and with Milgrom’s MOND relation. Results are discussed.

The
nineteenth century’s quest for the missing matter (Vulcan) ended with the
publication of Einstein’s General Theory of Relativity. We contend that the
current quest for the missing matter is parallel in its perseverance and in its
ultimate futility. After setting the search for dark matter in its historic perspective,
we critique extant dark matter models and offer alternative explanations—derived
from a Lorentz-invariant Lagrangian—that will, at the very least, sow seeds of
doubt about the existence of dark matter.

Abstract:
It is proposed that the principle of equivalence—which recognizes momentary equivalence between gravitational and inertial force—is cosmologicalized in an expanding spherical distribution of matter, whereby spacetime itself acts as the accelerating frame of reference of the inertial mass of an object on the surface of the sphere, and the inertial force thus generated is momentarily equivalent at a certain radial distance to the gravitational force experienced by the gravitational mass of the object. The spacetime accelerating frame of reference is parametrized by the cosmological constant Λ. The relation between inertial mass of an object and the cosmological constant can be generalized as a correlation between the matter density in the universe and the cosmological constant. Since matter density dilutes in an expanding universe, it is predicted that the Λ-term should be time varying.

Abstract:
It is known that all candidates in dark matter (DM) particles (neutrinos, axions, supersymmetric particles etc.) can not explain the basic properties of DM. The same can be said on the proposed candidates in dark energy (DE) (for example, quintessence). In the paper it is shown that some problems connected with DM and DE can be solved in the framework of the byuon theory. Basic axioms and some conclusions of this theory are discussed. The existence of fundamental unobserved elements in nature, byuons is declared. Physical space in our Universe is the quantum medium of special objects 4b, formed in four-contact interactions of byuons (m4b c2 ≈ 33eV). These objects determine the average density of substance (DM) in the Universe ~10-29 g cm-3. The byuon theory predicts a new interaction of natural objects with physical vacuum. This new force can cause the observed acceleration of our Universe. The estimations show that it is higher than the gravitational force at distances of order to 1026-1028 cm. Some other consequences of the byuon theory are considered.

Abstract:
The investigations into the structure of the gravitation field formed by stars, galaxies and their clusters have allowed an alternative explanation for the effect of red shift in stellar spectra; they also have “stopped” the expansion of the Universe and disregarded “dark” energy (DE). The characteristic features of the structure of gravitational field for large galaxies give a clear indication of the mysterious “dark” matter (DM) which enables eliminating it in the Universe. And, finally, the theory of granular space may prove the existence of the Universe as a unique one.

Abstract:
The purpose of this paper is to seek a connection between noncommutative geometry, an offshoot of string theory, and certain aspects of dark matter and dark energy. The former case is based on a simple mathematical argument showing that the main manifestation of dark matter in connection with flat galactic rotation curves is also a consequence of noncommutative geometry. The latter case requires an examination of the local effect of noncommutative geometry and the subsequent extension to the global phenomenon of an accelerating Universe.

Abstract:
It is currently a generally accepted opinion in astrophysics that the phenomenon of dark matter and dark energy can be explained only by existence of microcosm contents unknown to us. This assumption seems to be quite reasonable, since the Monoverse hypothesis following from the postulate about non-exceedance of the speed of light in the special theory of relativity, leaves no place for dark matter and dark energy in macrocosm. However, the assumption is erroneous, as dark matter and dark energy are actually invisible parallel universes in six-dimensional space, as shown in the article. Therefore, they can be detected only during research of macrocosm. Research of the phenomenon of dark matter and dark energy is presented in the article. Moreover, it is performed using previously unknown experiments that have allowed proof of general scientific principle of physical reality of concrete imaginary numbers. In the special theory of relativity, this principle has refuted the postulate of light speed non-exceedance. It has also allowed adjustment of relativistic formulas. It follows from the adjusted relativistic formulas that we live in a hidden Multiverse. The article explains the nature of mutual invisibility of parallel universes of the hidden Multiverse and proves verifiability of the hypothesis of the hidden Multiverse. The hypothesis has explained the nature of dark matter and dark energy as well as given an idea where antimatter is and why it does not annihilate with matter. It has also explained where tachyons are and why they do not violate the principle of causality. According to the hypothesis, the hidden Multiverse is connected to other Multiverses through portals, forming dark space. Multiverses of dark space together with the hidden Multiverse form a Hyperverse.

Abstract:
The frequency spectrum of the cosmical Zero Point Energy (ZPE) and its total density are so far unknown in their details. In the present complementary investigation, a revised theory forms the basis for studies of this concept in two respects. It first applies to the observable universe considered as an entity, as well as to included subregions such as the galaxies with supermassive black holes. Second, experiments are proposed on the maximum Casimir force arising between two metal plates of different materials and with a vanishing air gap in their spacing. This serves the purpose of making an indirect determination of the ZPE energy density in the laboratory, i.e. at the Earth’s orbit. The ZPE energy density is interpreted as dark matter density and its pressure gradient as dark energy force density.

Abstract:
In the present paper an attempt is made to develop a fractional integral and differential, deterministic and projective method based on the assumption of the essential discontinuity observed in real systems (note that more than 99% of the volume occupied by an atom in real space has no matter). The differential treatment assumes continuous behaviour (in the form of averaging over the recent past of the system) to predict the future time evolution, such that the real history of the system is "forgotten". So it is easy to understand how problems such as unpredictability (chaos) arise for many dynamical systems, as well as the great difficulty to connecting Quantum Mechanics (a probabilistic differential theory) with General Relativity (a deterministic differential theory). I focus here on showing how the present theory can throw light on crucial astrophysical problems like dark matter and dark energy.