1. Why Planck does not measure the size of the sound horizon (in spite of what everyone says)
2. Why the CMB spectrum determines Omega_M h^2 and Omega_b h^2,
3. Why assuming flatness determines H_0, and
4. Why adding BAO determines curvature.
Discussion inspired in part by
http://fr.arxiv.org/abs/astro-ph/0006436
CMB Observables and Their Cosmological Implications
Wayne Hu, Masataka Fukugita, Matias Zaldarriaga, Max Tegmark
We show that recent measurements of the power spectrum of cosmic microwave background anisotropies by BOOMERanG and MAXIMA can be characterized by four observables, the position of the first acoustic peak l_1= 206 pm 6, the height of the first peak relative to COBE normalization H_1= 7.6 pm 1.4, the height of the second peak relative to the first H_2 = 0.38 pm 0.04, and the height of the third peak relative to the first H_3 = 0.43 pm 0.07. This phenomenological representation of the measurements complements more detailed likelihood analyses in multidimensional parameter space, clarifying the dependence on prior assumptions and the specific aspects of the data leading to the constraints. We illustrate their use in the flat LCDM family of models, where we find Omega_m h^{3.8} > 0.079 (or nearly equivalently, the age of the universe t_0 < 13-14 Gyr) from l_1 and a baryon density Omega_b h^2 > 0.019, a matter density Omega_m h^2 < 0.42 and tilt n>0.85 from the peak heights (95% CL). With the aid of several external constraints, notably nucleosynthesis, the age of the universe and the cluster abundance and baryon fraction, we construct the allowed region in the (Omega_m,h) plane; it points to high h (0.6< h < 0.9) and moderate Omega_m (0.25 < Omega_m < 0.6).
