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تسجيل مستخدم جديدPRISM: Sparse Recovery of the Primordial Power Spectrum
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The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation mechanisms. Here, we introduce a new method to estimate this spectrum from the empirical power spectrum of cosmic microwave background (CMB) maps. A sparsity-based linear inversion method, coined textbf{PRISM}, is presented. This technique leverages a sparsity prior on features in the primordial power spectrum in a wavelet basis to regularise the inverse problem. This non-parametric approach does not assume a strong prior on the shape of the primordial power spectrum, yet is able to correctly reconstruct its global shape as well as localised features. These advantages make this method robust for detecting deviations from the currently favoured scale-invariant spectrum. We investigate the strength of this method on a set of WMAP 9-year simulated data for three types of primordial power spectra: a nearly scale-invariant spectrum, a spectrum with a small running of the spectral index, and a spectrum with a localised feature. This technique proves to easily detect deviations from a pure scale-invariant power spectrum and is suitable for distinguishing between simple models of the inflation. We process the WMAP 9-year data and find no significant departure from a nearly scale-invariant power spectrum with the spectral index $n_s = 0.972$. A high resolution primordial power spectrum can be reconstructed with this technique, where any strong local deviations or small global deviations from a pure scale-invariant spectrum can easily be detected.
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The primordial power spectrum is an indirect probe of inflation or other structure-formation mechanisms. We introduce a new method, named textbf{PRISM}, to estimate this spectrum from the empirical cosmic microwave background (CMB) power spectrum. Th
is is a sparsity-based inversion method, which leverages a sparsity prior on features in the primordial spectrum in a wavelet dictionary to regularise the inverse problem. This non-parametric approach is able to reconstruct the global shape as well as localised features of spectrum accurately and proves to be robust for detecting deviations from the currently favoured scale-invariant spectrum. We investigate the strength of this method on a set of WMAP nine-year simulated data for three types of primordial spectra and then process the WMAP nine-year data as well as the Planck PR1 data. We find no significant departures from a near scale-invariant spectrum.
The primordial power spectrum describes the initial perturbations that seeded the large-scale structure we observe today. It provides an indirect probe of inflation or other structure-formation mechanisms. In this letter, we recover the primordial po
wer spectrum from the Planck PR1 dataset, using our recently published algorithm PRISM. PRISM is a sparsity-based inversion method, that aims at recovering features in the primordial power spectrum from the empirical power spectrum of the cosmic microwave background (CMB). This ill-posed inverse problem is regularised using a sparsity prior on features in the primordial power spectrum in a wavelet dictionary. Although this non-parametric method does not assume a strong prior on the shape of the primordial power spectrum, it is able to recover both its general shape and localised features. As a results, this approach presents a reliable way of detecting deviations from the currently favoured scale-invariant spectrum. We applied PRISM to 100 simulated Planck data to investigate its performance on Planck-like data. We also tested the algorithms ability to recover a small localised feature at $k sim 0.125$ Mpc$^{-1}$, which caused a large dip at $ell sim 1800$ in the angular power spectrum. We then applied PRISM to the Planck PR1 power spectrum to recover the primordial power spectrum. We find no significant departures from the fiducial Planck PR1 near scale-invariant primordial power spectrum with $A_s=2.215times10^{-9}$ and $n_s = 0.9624$.
The shape of the primordial matter power spectrum Plin(k) encodes critical information on cosmological parameters. At large scales, the observable galaxy power spectrum Pobs(k) is expected to follow the shape of Plin(k), but on smaller scales the eff
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A small deviation from scale invariance in the form of oscillations in the primordial correlation spectra has been predicted by various cosmological models. In this paper we review a recently developed method to search for these features in the data
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CMB observations provide a precise measurement of the primordial power spectrum on large scales, corresponding to wavenumbers $10^{-3}$ Mpc$^{-1}$ < k < 0.1 Mpc$^{-1}$, [1-8]. Luminous red galaxies and galaxy clusters probe the matter power spectrum
on overlapping scales (0.02 Mpc$^{-1}$ < k < 0.7 Mpc$^{-1}$ [9-18]), while the Lyman-alpha forest reaches slightly smaller scales (0.3 Mpc$^{-1} < k < 3$ Mpc$^{-1}$; [19]). These observations indicate that the primordial power spectrum is nearly scale-invariant with amplitude close to $2 times 10^{-9}$, [5, 20-25]. They also strongly support Inflation and motivate us to obtain constraints reaching to smaller scales on the primordial curvature power spectrum and by implication on Inflation. One could obtain limits to much higher values of $k < 10^5$ Mpc$^{-1}$ and with less sensitivity even higher to $k < 10^{19}- 10^{23}$ Mpc$^{-1}$ using limits from CMB spectral distortions(SD)and on ultracompact minihalo objects(UCMHs)and Primordial Black Holes(PBHs). In this paper, we revisit and collect all the known constraints on both PBHs and UCMHs. We show that unless one uses SD, PBHs give us very relaxed bounds on the primordial curvature perturbations. UCMHs are very informative over a reasonable $k$ range($3 < k < 10^6$ Mpc$^{-1}$)and lead to significant upper-bounds on the curvature spectrum. We review the conditions under which the tighter constraints on the UCMHs could imply extremely strong bounds on the fraction of Dark Matter that could be PBHs. Failure to satisfy these conditions would lead to over production of the UCMHs, which is inconsistent with the observations. Therefore, we can almost rule out PBH within their overlap scales with the UCMHs. We consider the UCMH bounds from experiments such as $gamma$-rays, Neutrinos, Reionization, pulsar-timing and SD. We show that they lead to comparable results independent of the form of DM.
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