PRISM: Sparse recovery of the primordial power spectrum

Paykari, P.; Lanusse, François; Starck, Jean-Luc; Sureau, F.; Bobin, J.

doi:10.1051/0004-6361/201322326

Cited by 20 publications

(16 citation statements)

References 83 publications

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“…2.1 from the C Data in all Planck spectra. † Also see [12], though we do not agree with some claims made in this paper regarding the MRL algorithm.…”

Section: Reconstruction Algorithmcontrasting

confidence: 96%

Primordial power spectrum from Planck

Hazra

Shafieloo

Souradeep

2014

J. Cosmol. Astropart. Phys.

101

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Abstract. Using modified Richardson-Lucy algorithm we reconstruct the primordial power spectrum (PPS) from Planck Cosmic Microwave Background (CMB) temperature anisotropy data. In our analysis we use different combinations of angular power spectra from Planck to reconstruct the shape of the primordial power spectrum and locate possible features. Performing an extensive error analysis we found the dip near ∼ 750 − 850 represents the most prominent feature in the data. Feature near ∼ 1800 − 2000 is detectable with high confidence only in 217 GHz spectrum and is apparently consequence of a small systematic as described in the revised Planck 2013 papers. Fixing the background cosmological parameters and the foreground nuisance parameters to their best fit baseline values, we report that the best fit power law primordial power spectrum is consistent with the reconstructed form of the PPS at 2σ C.L. of the estimated errors (apart from the local features mentioned above). As a consistency test, we found the reconstructed primordial power spectrum from Planck temperature data can also substantially improve the fit to WMAP-9 angular power spectrum data (with respect to power-law form of the PPS) allowing an overall amplitude shift of ∼ 2.5%. In this context low-and 100 GHz spectrum from Planck which have proper overlap in the multipole range with WMAP data found to be completely consistent with WMAP-9 (allowing amplitude shift). As another important result of our analysis we do report the evidence of gravitational lensing through the reconstruction analysis. Finally we present two smooth form of the PPS containing only the important features. These smooth forms of PPS can provide significant improvements in fitting the data (with respect to the power law PPS) and can be helpful to give hints for inflationary model building.

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“…2.1 from the C Data in all Planck spectra. † Also see [12], though we do not agree with some claims made in this paper regarding the MRL algorithm.…”

Section: Reconstruction Algorithmcontrasting

confidence: 96%

Primordial power spectrum from Planck

Hazra

Shafieloo

Souradeep

2014

J. Cosmol. Astropart. Phys.

101

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“…There is no fundamental limit to how densely P R (k) can be sampled though; the number of samples in k can even exceed the number of data points (e.g., the C s) if one is willing to forgo the possibility of an analysis based on exploring the likelihood/posterior and treat the issue as a deconvolution problem (i.e., an inversion of Equation 128) instead. Deconvolution techniques have been applied by several groups to CMB temperature data [492][493][494][495][496][497], CMB temperature+polarisation data [498][499][500] and combinations of CMB data with large scale structure data [501]. In order to get rid of spurious high-frequency spikes that are likely to occur for noisy data when the primordial spectrum is oversampled, these methods typically involve a smoothing procedure.…”

Section: Bottom-up: Reconstruction Of the Primordial Power Spectrummentioning

confidence: 99%

Features and new physical scales in primordial observables: Theory and observation

Chluba

Hamann

Patil

2015

Int. J. Mod. Phys. D

208

233

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June 22, 20152 All cosmological observations to date are consistent with adiabatic, Gaussian and nearly scale invariant initial conditions. These findings provide strong evidence for a particular symmetry breaking pattern in the very early universe (with a close to vanishing order parameter, ), widely accepted as conforming to the predictions of the simplest realizations of the inflationary paradigm. However, given that our observations are only privy to perturbations, in inferring something about the background that gave rise to them, it should be clear that many different underlying constructions project onto the same set of cosmological observables. Features in the primordial correlation functions, if present, would offer a unique and discriminating window onto the parent theory in which the mechanism that generated the initial conditions is embedded. In certain contexts, simple linear response theory allows us to infer new characteristic scales from the presence of features that can break the aforementioned degeneracies among different background models, and in some cases can even offer a limited spectroscopy of the heavier degrees of freedom that couple to the inflaton. In this review, we offer a pedagogical survey of the diverse, theoretically well grounded mechanisms which can imprint features into primordial correlation functions in addition to reviewing the techniques one can employ to probe observations. These observations include cosmic microwave background anisotropies and spectral distortions as well as the matter two and three point functions as inferred from large-scale structure and potentially, 21 cm surveys.

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“…Another example is the inversion of Planck data with Richardson-Lucy deconvolution [18]. An attractive method called PRISM which uses a 'sparsity' prior on features in the PPS in a wavelet basis to regularise the inverse problem was developed in [19] and has been subsequently applied to Planck data [20].…”

Section: Introductionmentioning

confidence: 99%

Search for features in the spectrum of primordial perturbations using Planck and other datasets

Hunt

Sarkar

2015

J. Cosmol. Astropart. Phys.

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We reconstruct the power spectrum of primordial curvature perturbations by applying a well-validated non-parametric technique employing Tikhonov regularisation to the first data release from the Planck satellite. To improve the reconstruction on small spatial scales we include data from the ground-based ACT and SPT experiments, the WiggleZ galaxy redshift survey, the CFHTLenS tomographic weak lensing survey, and spectral analysis of the Lyman-α forest. The reconstructed scalar spectrum (assuming the standard ΛCDM cosmology) is not scale-free but has an infrared cutoff at k 5 × 10 −4 Mpc −1 and several (2 − 3)σ features, of which two at wavenumber k/Mpc −1 ∼ 0.0018 and 0.057 had been seen already in WMAP data. A higher significance feature at k ∼ 0.12 Mpc −1 is indicated by Planck data, but may be sensitive to the systematic uncertainty around multipole ∼ 1800 in the 217x217 GHz cross-spectrum. In any case accounting for the 'look elsewhere' effect decreases its global significance to ∼ 2σ.

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PRISM: Sparse recovery of the primordial power spectrum

Cited by 20 publications

References 83 publications

Primordial power spectrum from Planck

Primordial power spectrum from Planck

Features and new physical scales in primordial observables: Theory and observation

Search for features in the spectrum of primordial perturbations using Planck and other datasets

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