Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates

This paper presents a novel approach to the cosmological constant problem by the use of the Clifford algebras of space $C{l}_{3,0}$ and anti-space $C{l}_{0,3}$ with a particular focus on the paravector representation, emphasizing the fact that both algebras have a center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration $3H_{0}c$. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space $C{l}_{3,0}$ corresponds to the anti-de Sitter (AdS) flat ($k=0$) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra $C{l}_{0,3}$ leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.