The Cosmological Constant from the Extended Theory of Gravitation in Clifford Spaces Carlos Castro October, 2014 Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta; perelmanc@hotmail.com Abstract The exploration of the novel physical consequences of the Extended Theory of Gravity in C -spaces (Clifford spaces) is continued. One of the most salient physical feature of the extended gravitational theory in C -spaces is that one can generate an effective stress energy tensor mimicking the effects of “dark” matter/energy. In particular, it is found that the presence of the cosmological constant, along with a plausible mechanism to explain its extremely small value and/or its cancellation, can be understood entirely from a purely Clifford algebraic and geometric perspective. For this reason we believe that this theory may have important consequences in Cosmology and further research in Gravitation and Particle Physics. Keywords : Clifford algebras; Extended Relativity in Clifford Spaces; Cosmological Constant, Cosmology. 1 Introduction : C-space Relativity In the past years, the Extended Relativity Theory in C -spaces (Clifford spaces) and Clifford-Phase spaces were developed [1], [2]. The Extended Relativity theory in Clifford- spaces (C-spaces) is a natural extension of the ordinary Relativity theory whose general- ized coordinates are Clifford polyvector-valued quantities which incorporate the lines, ar- eas, volumes, and hyper-volumes degrees of freedom associated with the collective dynam- ics of particles, strings, membranes, p-branes (closed p-branes) moving in a D-dimensional target spacetime background. C-space Relativity permits to study the dynamics of all (closed) p-branes, for different values of p, on a unified footing. 1