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This article attempts to explain the underlying physics of several recent experiments and astrophysical observations that have been mystifying the physics community for quite some time. So far, none of the advanced theories beyond the standard models of particle physics and cosmology have shown sufficient potential to resolve these mysteries. The reason for this failure may lie in the fact that these theories are based on the concept of  extra space dimensions  that appears to be in conflict with numerous experiments, in particular with recent Large Hadron Collider data. Therefore, the novel idea of extra number systems is introduced, replacing the idea of extra space dimensions. This approach is complemented by a set of fundamental physical principles that provide the constraints and guidelines for a modified physical formulation in agreement with known experimental reality. However, such a theory requires novel physical concepts in conjunction with novel symmetry groups. These groups give rise to additional types of matter, termed hypercomplex masses (which are responsible for the extreme hypercomplex gravitational fields, see below, and are also denoted as  matter flavour ), including, for instance, particles of negative mass, identified with dark matter. Furthermore, four-dimensional Minkowski spacetime, assumed to be a quasi  de Sitter  spaced   S   1  ,  3$dS^{1,3}$    dual spacetime ,D  d   S   1  ,  3$DdS^{1,3}$   , with imaginary time coordinate; that is, time is a  complex quantity . The three spatial coordinates are shared by the two spacetimes. Dark matter is assumed to reside inD  d   S   1  ,  3$DdS^{1,3}$    and therefore is principally invisible. On the other hand, its gravitational interaction with ordinary matter ( m  ≥ 0) in spacetimed   S   1  ,  3$dS^{1,3}$    is directly perceptible. The novel group structure predicts the existence of a fourth particle family of negative masses; that is, besides the dark matter particle  χ  of massm  χ   ≈   −  80.77$m_{\chi}\approx-80.77$    GeV/c 2 , there is the dark neutrino  ν χ   of massm   ν  χ    ≈   −  3.23$m_{\nu_{\chi}}\approx-3.23$    eV/c 2 . Moreover, the hypercomplex group structure of gravity (S  U   (  2  )    ×  S   U   (  2  )$SU(2)\times SU(2)$   ) postulates three gravitational bosons for cosmological fields [resulting from Einstein’s theory of general relativity (GR)], the gravitonν   G  N$\nu_{G_{N}}$    with spin 2, the novel gravitophotonν   g  p$\nu_{gp}$    with spin 1 (existence of weak gravitomagnetic fields of GR), and the quintessence particle  ν q   with spin 0, which, when present, mediates an interaction between ordinary matter ( m  ≥ 0) and the ubiquitous scalar field of dark energy. In addition, the existence of extreme gravity fields (hypercomplex gravity) is postulated, based on the second group  SU (2), and an interaction between electromagnetism and hypercomplex gravity is predicted, mediated by three additional hypercomplex-gravity bosons. Some long-standing problems of cosmology will be addressed; namely, the Big Bang scenario and the origin of dark energy and the nature of dark matter and their relation to the modified Newtonian dynamics hypothesis will be discussed.

Gravity Beyond Einstein? Part II: Fundamental Physical Principles, Number Systems, Novel Groups, Dark Energy, and Dark Matter, MOND