A perspective on the CMB acoustic peak

T. A. Marriage

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arXiv · astro-ph/0203153

A perspective on the CMB acoustic peak

T. A. Marriage

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Abstract

CMB angular spectrum measurements suggest a flat universe. This paper clarifies the relation between geometry and the spherical harmonic index of the first acoustic peak ($\ell_{peak}$). Numerical and analytic calculations show that $\ell_{peak}$ is approximately a function of $Ω_K/Ω_M$ where $Ω_K$ and $Ω_M$ are the curvature ($Ω_K > 0$ implies an open geometry) and mass density today in units of critical density. Assuming $Ω_K/Ω_M \ll 1$, one obtains a simple formula for $\ell_{peak}$, the derivation of which gives another perspective on the widely-recognized $Ω_M$-$Ω_Λ$ degeneracy in flat models. This formula for near-flat cosmogonies together with current angular spectrum data yields familiar parameter constraints.

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T. A. Marriage. 2002-03-11. A perspective on the CMB acoustic peak. https://arxiv.org/abs/astro-ph/0203153

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