Reconstruction of the Primordial Power Spectrum by Direct Inversion

Details Reconstruction of the Primordial Power Spectrum by Direct Inversion Reconstruction of the Primordial Power Spectrum by Direct Inversion

2009-09-28

arxiv.org/abs/0909.5092v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

23 pages, 9 figures

Scientific paper

We introduce a new method for reconstructing the primordial power spectrum, $P(k)$, directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation transfer function. The degeneracy of the multipole $\ell$ to wavenumber $k$ linear mapping is thus reduced. This enables the inversion to be carried out at each point along a Monte Carlo Markov Chain (MCMC) exploration of the combined $P(k)$ and cosmological parameter space. We present best--fit $P(k)$ obtained with this method along with other cosmological parameters.

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