Power law cosmology model comparison with CMB scale information
  Despite the ability of the cosmological concordance model ($\Lambda$CDM) to
describe the cosmological observations exceedingly well, power law expansion of
the Universe scale radius, $R(t)\propto t^n$, has been proposed as an
alternative framework. We examine here these models, analyzing their ability to
fit cosmological data using robust model comparison criteria. Type Ia
supernovae (SNIa), baryonic acoustic oscillations (BAO) and acoustic scale
information from the cosmic microwave background (CMB) have been used. We find
that SNIa data either alone or combined with BAO can be well reproduced by both
$\Lambda$CDM and power law expansion models with $n\sim 1.5$, while the
constant expansion rate model $(n=1)$ is clearly disfavored. Allowing for some
redshift evolution in the SNIa luminosity essentially removes any clear
preference for a specific model. The CMB data are well known to provide the
most stringent constraints on standard cosmological models, in particular,
through the position of the first peak of the temperature angular power
spectrum, corresponding to the sound horizon at recombination, a scale
physically related to the BAO scale. Models with $n\geq 1$ lead to a divergence
of the sound horizon and do not naturally provide the relevant scales for the
BAO and the CMB. We retain an empirical footing to overcome this issue: we let
the data choose the preferred values for these scales, while we recompute the
ionization history in power law models, to obtain the distance to the CMB. In
doing so, we find that the scale coming from the BAO data is not consistent
with the observed position of the first peak of the CMB temperature angular
power spectrum for any power law cosmology. Therefore, we conclude that when
the three standard probes are combined, the $\Lambda$CDM model is very strongly
favored over any of these alternative models, which are then essentially ruled
out.
