Cosmic Inversion: Reconstructing primordial spectrum from CMB anisotropy

Details Cosmic Inversion: Reconstructing primordial spectrum from CMB anisotropy Cosmic Inversion: Reconstructing primordial spectrum from CMB anisotropy

2001-11-29

arxiv.org/abs/astro-ph/0111549v1

Phys.Rev.D65:083007,2002

Astronomy and Astrophysics

Astrophysics

10 pages, 7 figures

Scientific paper

10.1103/PhysRevD.65.083007

We investigate the possibility of reconstructing the initial spectrum of density fluctuations from the cosmic microwave background (CMB) anisotropy. As a first step toward this program, we consider a spatially flat, CDM dominated universe. In this case, it is shown that, with a good accuracy, the initial spectrum satisfies a first order differential equation with the source determined by the CMB angular correlation function. The equation is found to contain singularities arising from zeros of the acoustic oscillations in the transfer functions. Nevertheless, we find these singularities are not fatal, and the equation can be solved nicely. We test our method by considering simple analytic forms for the transfer functions. We find the initial spectrum is reproduced within 5% accuracy even for a spectrum that has a sharp spike.

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