Modified Regge calculus as an explanation of dark energy

Using the Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor a(t) in the Einstein-de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: (1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and (2) we assume that luminosity distance DL is related to graphical proper distance Dp by the equation DL = (1+z)√Dp·Dp, where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and ΛCDM are compared using the data from the Union2 Compilation, i.e. distance moduli and redshifts for type Ia supernovae. We find that a best fit line through logDL versus logz gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit ΛCDM gives SSE = 1.79 using Ho = 69.2 kms-1 Mpc, ΩM = 0.29 and ΩΛ = 0.71. The best fit EdS gives SSE = 2.68 using Ho 60.9 km s-1 Mpc. The best-fit MORC gives SSE = 1.77 and Ho = 73.9 km s-1 Mpc using R = A-1 = 8.38 Gcy and m = 1.71 x 1052 kg, where R is the current graphical proper distance between nodes, A-1 is the scaling factor from our non-trivial inner product, and m is the nodal mass. Thus, the MORC improves the EdS as well as ΛCDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e. there is no dark energy and the universe is always decelerating. (paper)