Constraint on the Effective Number of Neutrino Species from the WMAP and SDSS LRG Power Spectra

TL;DR

The paper constrains the effective number of neutrino species $N_\nu$ by combining the WMAP3 CMB power spectrum with the SDSS LRG galaxy power spectrum, demonstrating that LSS data breaks the $N_\nu$–$\omega_m$ degeneracy present in CMB alone. Using a flat $\Lambda$CDM model with $N_\nu$ as a free parameter and a non-linear bias model for the LRGs, they find $0.9 < N_\nu < 8.2$ at 95% C.L., with a central value $N_\nu=3.1^{+5.1}_{-2.2}$, indicating consistency with the standard three-neutrino scenario but leaving room for nonstandard physics. The analysis also translates the lower bound on $N_\nu$ into a lower limit on the reheating temperature $T_R > 2$ MeV in MeV-scale reheating scenarios, providing a CMB+LSS probe of early-universe conditions that is complementary to BBN. Anticipated Planck measurements could further tighten these bounds and sharpen tests of relativistic degrees of freedom in the early cosmos.

Abstract

We derive constraint on the effective number of neutrino species N_nu from the cosmic microwave background power spectrum of the WMAP and galaxy clustering power spectrum of the SDSS luminous red galaxies (LRGs). Using these two latest data sets of CMB and galaxy clustering alone, we obtain the limit 0.9 < N_nu < 8.2 (95% C.L.) for the power-law LambdaCDM flat universe, with no external prior. The lower limit corresponds to the lower bound on the reheating temperature of the universe T_R > 2 MeV.

Figures (3)

• Figure 1: $\Delta \chi^2$ as functions of $N_\nu$. The red solid line uses the WMAP 3-year data alone and the green dashed line uses WMAP 3-year and SDSS LRG power spectrum.
• Figure 2: The best fit values of some of the cosmological parameters as functions of $N_\nu$. The red solid lines are for the WMAP 3-year data alone and the green dashed lines are for WMAP 3-year and SDSS LRG power spectrum combined.
• Figure 3: Taken from the calculation in Ref. Ichikawa:2005vw. (a) The relation between the effective neutrino number $N_\nu$ and the reheating temperature $T_R$. (b) The solid line shows the $^4$He abundance $Y_p$ as a function of the reheating temperature $T_R$. The dashed line is calculated with Fermi distributed neutrinos with $N_\nu$ of the panel (a) (namely, only the change in the expansion rate due to the incomplete thermalization is taken into account). The baryon-to-photon ratio is fixed at $\eta = 5 \times 10^{-10}$.