A Clifford-Gravity Based Cosmology, Dark Matter and Dark Energy Carlos Castro Center for Theoretical Studies of Physical Systems Clark Atlanta, GA. 30314 May 2014 Abstract A Clifford-Gravity based model is exploited to build a generalized ac- tion (beyond the current ones used in the literature) and arrive at relevant numerical results which are consistent with the presently-observed de Sit- ter accelerating expansion of the universe driven by a very small vacuum energy density ρ obs ∼ 10 -120 (MP ) 4 (MP is the Planck mass) and provide promising dark energy/matter candidates in terms of the 16 scalars cor- responding to the degrees of freedom associated with a Cl(3, 1)-algebra valued scalar field Φ in four dimensions. Keywords: Clifford Algebras, Gravity, Yang-Mills, Grand Unification, Infla- tion, Cosmology, Strings. 1 Introduction Clifford, Division, Exceptional and Jordan algebras are deeply related and es- sential tools in many aspects in Physics [1], [2], [3] . A Clifford Cl(5,C ) Unified Gauge Field Theory formulation of Conformal Gravity and U (4) × U (4) × U (4) Yang-Mills in 4D was recently reviewed in [4] along with its implications for the Pati-Salam group SU (4) × SU (2) L × SU (2) R , and T rinif ication GUT models of 3 fermion generations based on the group SU (3) C × SU (3) L × SU (3) R . In the past years, the Extended Relativity Theory in C -spaces (Clifford spaces) and Clifford-Phase spaces were developed [5], [6]. The Extended Rela- tivity theory in Clifford-spaces (C-spaces) is a natural extension of the ordinary Relativity theory whose generalized coordinates are Clifford polyvector-valued quantities which incorporate the lines, areas, volumes, and hyper-volumes de- grees of freedom associated with the collective dynamics of particles, strings, membranes, p-branes (closed p-branes) moving in a D-dimensional target space- time background. 1