Indication for Primordial Anisotropies in the Neutrino Background from the Wilkinson Microwave Anisotropy Probe and the Sloan Digital Sky Survey

We demonstrate that combining cosmic microwave background anisotropy measurements from the 1st year Wilkinson Microwave Anisotropy Probe observations with clustering data from the Sloan galaxy redshift survey yields an indication for primordial anisotropies in the cosmological neutrino background.

Figure 1

The effect of NB anisotropies on the CMB temperature angular power spectrum. The standard model with parameters which provide the maximum likelihood best fit to WMAP is plotted (see 4) against the same model but with no NB anisotropies. The 1st year WMAP data is also plotted for comparison.

Figure 2

Joint 2-dimensional posterior probability contour plots in the $c_{\mathrm{vis}}^2-n_s$ (top) and $c_{\mathrm{vis}}^2-A_s$ (bottom) planes, showing the 68% and 95% contours from the $\mathrm{WMAP}+\mathrm{\text{other CMB}}$ data alone (cyan/light gray) and adding Sloan matter power spectrum information (black). Degeneracies between these parameters are evident and no lower limit on $c_{\mathrm{vis}}^2$ can be placed with CMB data alone.

Figure 3

Illustration of the role of galaxy clustering data in constraining $c_{\mathrm{vis}}^2$. With CMB data only (scatter plot), lower values of $c_{\mathrm{vis}}^2$ can be compensated by a redder spectral index and a lower amplitude of the fluctuations. Inclusion of the Sloan data disfavors models with low $n_s$, thereby cutting away most samples with low $c_{\mathrm{vis}}^2$. The solid black contour is the joint $2\sigma$ posterior from CMB and Sloan.

Figure 4

Relaxing the assumption on the background neutrino density by including the number of neutrino families $N_{\nu }$ as a free parameter: joint 2-dimensional posterior probability contour plots in the $c_{\mathrm{vis}}^2-N_{\nu }$ plane, enclosing 68% and 95% probability from the $\mathrm{WMAP}+\mathrm{\text{other CMB}}$ data alone (cyan/light gray), adding Sloan matter power spectrum information (black, solid) and further imposing a conservative BBN constraint on $N_{\nu }$ (black, dashed). The indication that $c_{\mathrm{vis}}^2>0$ is largely independent on prior knowledge of $N_{\nu }$, since the joint $\mathrm{WMAP}+\mathrm{SDSS}$ data can constrain $c_{\mathrm{vis}}^2$ and $N_{\nu }$ simultaneously. The prediction of the standard model is shown by the cross.