Abstract. To the experimental uncertainties on the present value H 0 of the LundmarkLemaître -Hubble constant, fundamental theoretical uncertainties of several kinds should also be added. In standard Cosmology, consistency problems are really serious. The cosmological constant is a source of well-known difficulties while the associated dark energy is assumed to be at the origin of the observed acceleration of the expansion of the Universe. But in alternative cosmologies, possible approaches without these problems exist. An example is the pattern based on the spinorial space-time (SST) we introduced in 1996-97 where the H t = 1 relation (t = cosmic time = age of the Universe) is automatically generated by a pre-existing cosmic geometry before standard matter and conventional forces, including gravitation and relativity, are introduced. We analyse present theoretical, experimental and observational uncertainties, focusing also on the possible sources of the acceleration of the expansion of the Universe as well as on the structure of the physical vacuum and its potential cosmological role. Particular attention is given to alternative approaches to both Particle Physics and Cosmology including possible preonic constituents of the physical vacuum and associated pre-Big Bang patterns. A significant example is provided by the cosmic SST geometry together with the possibility that the expanding cosmological vacuum releases energy in the form of standard matter and dark matter, thus modifying the dependence of the matter energy density with respect to the age and size of our Universe. The SST naturally generates a new leading contribution to the value of H. If the matter energy density decreases more slowly than in standard patterns, it can naturally be at the origin of the observed acceleration of the expansion of the Universe. The mathematical and dynamical structure of standard Physics at very short distances can also be modified by an underlying preonic structure. If preons are the constituents of the physical vacuum, as postulated two decades ago with the superbradyon (superluminal preon) hypothesis, the strongest implication would be the possibility that vacuum actually drives the expansion of the Universe. If an unstable (metastable) vacuum permanently expands, it can release energy in the form of conventional matter and of its associated kinetic energy. The SST can be the expression of such an expanding vacuum at cosmic level. We briefly discuss these and related issues, as well as relevant open questions including the problematics of the initial singularity and the cosmic vacuum dynamics in a pre-Big Bang era. The possibility to obtain experimental information on the preonic internal structure of vacuum is also considered.
This paper is dedicated to the memory of Henri Poincaré