W. M. Stuckey, T. J. McDevitt, M. Silberstein
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.
View original:
http://arxiv.org/abs/1110.3973
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