Many authors get taken up with the idea that a power law for the scale factor versus time

a(t) = (t/tgives a good fit to the supernova data in a flat Universe. If_{o})^{n}

Dand it gives the goodness of fits shown in the graph below:_{L}(z) = (c/H_{o})(1+z)[(1+z)^{1-1/n}-1]/(1-1/n)

This plot shows the Δχ

qwhile for power law models_{o}= Ω_{m}/2-Ω_{v}= 1.5*Ω_{m}- 1

qNote that the Einstein-de Sitter model is in both families (n = 2/3, Ω_{o}= (1-n)/n

A later supernova dataset (JLA with 740 SNe) gives much the same picture as shown in the figure below:

Again the red dot shows a non-accelerating power law model with n = 1, which fails to fit the SNe data and should be rejected. Accelerating power law models with n close to 1.4 do fit the latest supernova dataset.

A problem with the accelerating power law models is that
they completely destroy the agreement between the CMB angular power
spectrum and the observations. The time of last scattering is much too
late, so the acoustic scale is too long. For example, if *n =
5/4*, then *z = 1089* occurs at 50 Myr instead of 0.4 Myr so
the acoustic scale is off by a factor of 125.
This is illustrated below with a plot of the dark energy fraction
Ω_{DE} *vs.* the equation of state w for
flat wCDM models.

Finally, the current model independent
estimates for the age of the Universe and the Hubble
constant actually give *H _{o} t_{o}*
close to 1
while the power law model wants

Tutorial:
Part 1 |
Part 2 |
Part 3 |
Part 4

FAQ |
Age |
Distances |
Bibliography |
Relativity

© 2009-2015 Edward L. Wright. Last modified 26 Mar 2015