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4.3. Harmonics of CBR Anisotropies

so I will only briefly mention it for completeness. The positions of the acoustic peaks are particularly sensitive to Omega and lambda, and even low accuracy data available at present lead to a meaningful constraint on a combination of Omega and lambda.

The first acoustic peak appears at l = pi (the distance to the last-scattering surface)/(the sound horizon) (Hu & Sugiyama 1995). Its position l1 is approximated as

Equation 15 (15)

for the parameter range that concerns us. This means that the position of the acoustic peak is about l appeq 220 if Omega + lambda = 1, but it shifts to a high l as Omega-1/2 if lambda = 0. On the other hand, there is little power to determine Omega separately from lambda, unless full information of Cl is used. The harmonics Cl measured at small angles revealed the acoustic peak (Scott et al. 1996), and its position favours a universe not far from flat (Hancock et al. 1998). More exhaustive analyses of Lineweaver (1998) and Efstathiou et al. (1999) show a limit Omega + lambda/2 > 0.52 (1sigma). (The contours of the confidence level fall approximately on the curve given by (15) with l1 = constant.) This means that a zero Lambda universe is already marginal, when combined with Omega from other arguments. If a flat universe is chosen from CBR, a non-zero Lambda will be compelling.