SPACE, TIME AND FUNDAMENTAL INTERACTIONS

Time Reparametrization Invariance and Its Relation to the Dark Energy and Dark Matter Phenomena

Gueorguiev V. G.

The enigmatic nature of dark energy (DE) challenges our comprehension of the cosmos, appearing as the force responsible for the Universe’s accelerating expansion. This work considers the Einstein Cosmological Constant (\(\Lambda_E\)) as a manifestation of DE, interpreted through the framework of Reparametrization Invariant Scaling Symmetry (RISS). Within this paradigm, ?E emerges as a “kinetic energy"term, derived from relative temporal motion, setting it apart from the conventional kinetic energy based on spatial relative motion. Central to this exploration is the cosmic scale factor \(\lambda(t)\), a reparametrization construct capable of rendering \(\Lambda_E\) dynamically as relevant to the extended equations of Einstein’s General Relativity (EGR). Through meticulous derivations, the governing equations of \(\lambda(t)\) and its interplay with \(\Lambda_E\) are articulated. Imposing reparametrization symmetry on the equations of motion reveals a profound avenue for addressing the missing mass problem evident at galactic and extragalactic scales. Here, improper (non co-moving) temporal parametrizations introduce fictitious forces, whose presence is reconciled through the symmetry framework, ensuring a coherent treatment of the phenomena. This symmetry-based approach naturally yields the MOND-like relationship, Modified Newtonian Dynamics (MOND), \(g \sim \sqrt{a_0g_N}\) , where \(g\) denotes gravitational acceleration, \(a_0\) represents the fundamental MOND acceleration, and \(g_N\) is the Newtonian acceleration. The theoretical predictions for \(\Lambda_E\) and \(a_0\) demonstrate remarkable alignment with their observed magnitudes, lending credence to this interpretation. This synthesis of conceptual clarity and mathematical rigor underscores a potential unifying principle in our understanding of dark energy and dark matter gravitational phenomena and the broader cosmic tapestry.