Modified Regge calculus as an explanation of dark energy

TL;DR

This paper introduces a modified Regge calculus model that explains supernova data without dark energy, suggesting the universe's acceleration is not necessary and it remains decelerating.

Contribution

The paper proposes two modifications to Regge calculus and demonstrates that this approach fits supernova data as well as the standard cosmological models without requiring dark energy.

Findings

MORC fits supernova data with SSE comparable to $\\Lambda$CDM.

MORC suggests universe is always decelerating, negating dark energy.

Modified Regge calculus improves fit over Einstein-de Sitter model.

Abstract

Using 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 luminosity distance $D_L$ is related to graphical proper distance $D_p$ by the equation $D_L = (1+z)\sqrt{\overrightarrow{D_p}\cdot \overrightarrow{D_p}}$, where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and $\Lambda$CDM 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 $\displaystyle \log{(\frac{D_L}{Gpc})}$ versus $\log{z}$ gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit $\Lambda$CDM gives SSE = 1.79 using $H_o$ = 69.2 km/s/Mpc, $\Omega_{M}$ = 0.29 and $\Omega_{\Lambda}$ = 0.71. The best fit EdS gives SSE = 2.68 using $H_o$ = 60.9 km/s/Mpc. The best fit MORC gives SSE = 1.77 and $H_o$ = 73.9 km/s/Mpc using $R = A^{-1}$ = 8.38 Gcy and $m = 1.71\times 10^{52}$ kg, where $R$ is the current graphical proper distance between nodes, $A^{-1}$ is the scaling factor from our non-trival inner product, and $m$ is the nodal mass. Thus, MORC improves EdS as well as $\Lambda$CDM 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.