Multiple Time Dimensions: An Alternative to “Dark Energy”

Abstract

[eng] The astronomical observations based on the Cosmic Distance Ladder prescribe an Acceleration in the Expansion of the Universe, unless either mass-luminosity theory is not correct, or it is considered that the time in which the speed of light is measured does not remain constant and behaves dynamically as the spatial dimensions: expanding. Thus, the relationship between both types of coordinates positive&negative, which is a hypothesis of free choice, would define the dynamics of the Universe. Updating in a single hypothesis several alternative cosmological well known models: with additional dimensions (Kaluza), of temporary nature (Milne), in rotational dynamics (Gödel), which in the limit away from the Singularity, requires variable parameters (Dirac), all of them separately discarded by the astronomical observations. Together and properly combined, build an alternative to the Hyperinflation and Dark Energy hypothesis, which with the appropriate choice of the coordinate relationship, is consistent with the Supernova Type Ia observations and Gamma Ray Burst, GRB. The cosmological GR equations in 5D would be undetermined, so to choose the functions that relate them, extra hypothesis will be required, such as: consistency with General Relativity, Hyperbolicity, Causality, the Cosmological Principle, Conservation of Mass-Energy, increase in Entropy and consistency with astrophysical observations. The multi-temporal formalism requires that the speed of light depends on the relationship between temporal coordinates that shapes the geometry and thus the Distance Ladder is affected by the transformation between proper and coordinated time. With multi-temporality, Λ would be embedded in the evolution according to the GR equations and not as "addendum". A symmetry chosen between the temporal coordinates that comply with the previous "constraints", builds a temporary "hologram" that can describe within the differential geometry equations the dynamics in the Universe Expansion (including Initial Hyperinflation and Current Acceleration). The formulation of the simplest hypothesis is the requirement of a conserved quantity, and the rotational conjecture is a choice that persists degraded to obvious and direct example, because it prescribes the observed dynamics. There could be others. If the temporal dimensions rotate, (analogy in the abstract sense, which describes a symmetry between temporal coordinates), on the spatial dimensions conserving the "temporal momentum" - which would only happen in the referred limit- (analogy in the abstract sense, which describes the conservation constraint): the Universe would be isotropic and homogeneous -in space, but not in time, always in the referred limit-; causal -in expansion do not close the CTC for the masses, but for the photons, in the referred limit-; the GR would be valid away from the singularities -the speed of light, c constant with respect to the proper time, and the gravitational constant, Λ, would be variable with respect to the time coordinate, but they would not be the reference for all the observers in every moment -. This is not only consistent with the observations of Accelerated Expansion, galactic rotation, virial speed in the clusters or the inhomogeneities of the CMB, but also predicts several observations to be made in very distant galaxies (Z > 2), such as: "over redshift", overabundance of metals, much larger stellar masses, more "Keplerian" curves, the low density of black dwarfs or GLMLT stars, the distribution of quasars and super-massive early black holes. This will not be a demonstration of the existence of extra-temporal dimensions, and less of the rotation of the temporal plane, but an example that astronomical measurements do not univocally demonstrate a phenomenological interpretation of Dark Energy, integrating it into an evolution that does not have to be accelerated, but apparently accelerated by projecting on a temporary temporal manifold the proper time. It would not be conclusive to affirm that the Universe expanded by an inflaton field or a Vacuum Energy. It is possible, only possible, that at the Beginning the Expansion was slow and is currently contracting gravitationally and that the Cosmic Distance Ladder to the coordinate time, is different if it is taken with respect to proper time. For this, it is only necessary that time has more than one dimension and thought GR equations may include then, Lambda, in its 5D formalism.