Robust Neutrino Constraints by Combining Low Redshift Observations with
  the CMB
  We illustrate how recently improved low-redshift cosmological measurements
can tighten constraints on neutrino properties. In particular we examine the
impact of the assumed cosmological model on the constraints. We first consider
the new HST H0 = 74.2 +/- 3.6 measurement by Riess et al. (2009) and the
sigma8*(Omegam/0.25)^0.41 = 0.832 +/- 0.033 constraint from Rozo et al. (2009)
derived from the SDSS maxBCG Cluster Catalog. In a Lambda CDM model and when
combined with WMAP5 constraints, these low-redshift measurements constrain sum
mnu<0.4 eV at the 95% confidence level. This bound does not relax when allowing
for the running of the spectral index or for primordial tensor perturbations.
When adding also Supernovae and BAO constraints, we obtain a 95% upper limit of
sum mnu<0.3 eV. We test the sensitivity of the neutrino mass constraint to the
assumed expansion history by both allowing a dark energy equation of state
parameter w to vary, and by studying a model with coupling between dark energy
and dark matter, which allows for variation in w, Omegak, and dark coupling
strength xi. When combining CMB, H0, and the SDSS LRG halo power spectrum from
Reid et al. 2009, we find that in this very general model, sum mnu < 0.51 eV
with 95% confidence. If we allow the number of relativistic species Nrel to
vary in a Lambda CDM model with sum mnu = 0, we find Nrel =
3.76^{+0.63}_{-0.68} (^{+1.38}_{-1.21}) for the 68% and 95% confidence
intervals. We also report prior-independent constraints, which are in excellent
agreement with the Bayesian constraints.
