New Upper Limit on the Total Neutrino Mass from the 2 Degree Field Galaxy Redshift Survey

We constrain $f_{\nu }\equiv {\Omega }_{\nu }/{\Omega }_{\mathrm{m}}$, the fractional contribution of neutrinos to the total mass density in the Universe, by comparing the power spectrum of fluctuations derived from the 2 Degree Field Galaxy Redshift Survey with power spectra for models with four components: baryons, cold dark matter, massive neutrinos, and a cosmological constant. Adding constraints from independent cosmological probes we find $f_{\nu }<0.13$ (at 95% confidence) for a prior of $0.1<{\Omega }_{\mathrm{m}}<0.5$, and assuming the scalar spectral index $n=1$. This translates to an upper limit on the total neutrino mass $m_{\nu ,\mathrm{t}\mathrm{o}\mathrm{t}}<1.8\mathrm{e}\mathrm{V}$ for “concordance” values of ${\Omega }_{\mathrm{m}}$ and the Hubble constant.

Figure 1

Power spectra for ${\Omega }_{\nu }=0$ (solid line), ${\Omega }_{\nu }=0.01$ (dashed line), and ${\Omega }_{\nu }=0.05$ (dot-dashed line) with amplitudes fitted to the 2dFGRS power spectrum data (vertical bars) in redshift space. We have fixed ${\Omega }_{\mathrm{m}}=0.3$, ${\Omega }_{\Lambda }=0.7$, $h=0.7$, and ${\Omega }_{\mathrm{b}}{h}^2=0.02$. The vertical dashed lines limit the range in $k$ used in the fits.

Figure 2

Confidence contours at 68% (solid line), 95% (dashed line), and 99% (dotted line) in the plane of $f_{\nu }\equiv {\Omega }_{\nu }/{\Omega }_{\mathrm{m}}$ and $\Gamma \equiv {\Omega }_{\mathrm{m}}h$, with marginalization over $h$ and ${\Omega }_{\mathrm{b}}{h}^2$ using Gaussian priors, and over $A$ using a uniform prior in $0.5<A<10$. The left panel shows the case of no prior on ${\Omega }_{\mathrm{m}}$, and the right panel the case of a uniform “top hat” prior on ${\Omega }_{\mathrm{m}}$ in $0.1<{\Omega }_{\mathrm{m}}<0.5$.

Figure 3

Probability distributions, normalized so that the area under each curve is equal to 1, for $f_{\nu }$ with marginalization over the other parameters, as explained in the text, for $N_{\nu }=3$ massive neutrinos and $n=0.9$ (dotted line), $1.0$ (solid line), and $1.1$ (dashed line).