The COBE normalization for standard cold dark matter

The COBE detection of CMB anisotropies provides the best way of fixing the amplitude of fluctuations on the largest scales. This normalization is usually given for an n=1 spectrum, including only the anisotropy caused by the Sachs- Wolfe effect. This is certainly not a good approximation for a model containing any reasonable amount of baryonic matter. In fact, even tilted S-W spectra are not a good fit to models like CDM. Here we normalize standard CDM (sCDM) to the 2-year COBE data, and quote the best amplitude in terms of the conventionally used measures of power. We also give normalizations for some specific variants of this standard model, and we indicate how the normalization depends on the assumed values of n, OmegaB and H₀. For sCDM we find =19. 91. 5uK, corresponding to sigma₈=1. 340. 10, with the normalization at large scales being B= (8. 161. 04) 10⁵ (Mpc/h) ⁴, and other numbers given in the Table. The measured rms temperature fluctuation smoothed on 10deg is a little low relative to this normalization. This is mainly due to the low quadrupole in the data: when the quadrupole is removed, the measured value of sigma (10) is quite consistent with the best-fitting. The use of should be preferred over sigma (10), when its value can be determined for a particular theory, since it makes full use of the data.