Reconstructing the Primordial Spectrum with CMB Temperature and Polarization

Abstract

We develop a new method to reconstruct the power spectrum of primordial curvature perturbations, $P(k)$, by using both the temperature and polarization spectra of the cosmic microwave background (CMB). We test this method using several mock primordial spectra having non-trivial features including the one with an oscillatory component, and find that the spectrum can be reconstructed with a few percent accuracy by an iterative procedure in an ideal situation in which there is no observational error in the CMB data. In particular, although the previous ``cosmic inversion'' method, which used only the temperature fluctuations, suffered from large numerical errors around some specific values of $k$ that correspond to nodes in a transfer function, these errors are found to disappear almost completely in the new method.

18 pages, 17 figures, submitted to PRD

References in corpus (45)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• 4-Year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• An All-Sky Analysis of Polarization in the Microwave Background
• Statistics of Cosmic Microwave Background Polarization
• Wilkinson Microwave Anisotropy Probe (WMAP) First Year Observations: TE Polarization
• The Trans-Planckian Problem of Inflationary Cosmology
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
• Detection of Polarization in the Cosmic Microwave Background using DASI
• Anisotropies in the Cosmic Microwave Background: An Analytic Approach
• CMB Anisotropies: Total Angular Momentum Method
• Suppressing the lower Multipoles in the CMB Anisotropies
• The Robustness of Inflation to Changes in Super-Planck-Scale Physics
• CBR Anisotropy and the Running of the Scalar Spectral Index
• Reconstructing the primordial power spectrum
• Cosmic Microwave Background Polarization
• On the Dependence of the Spectra of Fluctuations in Inflationary Cosmology on Trans-Planckian Physics
• Suppressing CMB Quadrupole with a Bounce from Contracting Phase to Inflation
• The Imprint of Gravitational Waves on the Cosmic Microwave Background
• Does the small CMB quadrupole moment suggest new physics?
• Superimposed Oscillations in the WMAP Data?
• Primordial power spectrum from WMAP
• Non-commutative inflation and the CMB
• Double Inflation and the Low CMB Quadrupole
• Polarization of the Microwave Background due to Primordial Gravitational Waves
• Model-Independent Reconstruction of the Primordial Power Spectrum from WMAP Data
• CMB Power Spectrum from Noncommutative Spacetime
• Reconstructing the primordial power spectrum - a new algorithm
• Inflation with a running spectral index in supergravity
• Noncommutative Inflation and the CMB Multipoles
• Addendum to "Superimposed Oscillations in the WMAP Data?"
• Running of the Scalar Spectral Index from Inflationary Models
• What Can WMAP Tell Us About The Very Early Universe? New Physics as an Explanation of Suppressed Large Scale Power and Running Spectral Index
• Reconstructing the Primordial Spectrum from WMAP Data by the Cosmic Inversion Method
• Chaotic hybrid new inflation in supergravity with a running spectral index
• Stochastic Inflation and the Lower Multipoles in the CMB Anisotropies
• An Infrared Cutoff Revealed by the Two Years of COBE-DMR Observations of Cosmic Temperature Fluctuations
• Inflation model with lower multipoles of the CMB suppressed
• An inflation model with large variations in spectral index
• Cosmic Inversion: Reconstructing primordial spectrum from CMB anisotropy
• Smooth hybrid inflation in supergravity with a running spectral index and early star formation
• Direct Wavelet Expansion of the Primordial Power Spectrum
• Cosmic Inversion II --An iterative method for reproducing the primordial spectrum from the CMB data--
• Grand Unified Inflation Confronts WMAP

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• Features and New Physical Scales in Primordial Observables: Theory and Observation
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• Multiple inflation and the WMAP 'glitches' II. Data analysis and cosmological parameter extraction
• Possible Explanation to Low CMB Quadrupole
• Oscillations in the inflaton potential?
• Helical Magnetic Fields from Inflation
• Reconstruction of the Primordial Power Spectrum using Temperature and Polarisation Data from Multiple Experiments
• Non-Gaussianity from violation of slow-roll in multiple inflation
• Reconstruction of the primordial power spectrum of curvature perturbations using multiple data sets
• Testing for double inflation with WMAP
• Reconciling the local void with the CMB
• Non-parametric reconstruction of the primordial power spectrum at horizon scales from WMAP data
• Reconstruction of the Primordial Power Spectrum by Direct Inversion
• Precision of Inflaton Potential Reconstruction from CMB Using the General Slow-Roll Approximation
• Band-power reconstruction of the primordial fluctuation spectrum by the maximum likelihood reconstruction method
• Cosmic Discordance: Detection of a modulation in the primordial fluctuation spectrum
• Reconstruction of the primordial fluctuation spectrum from the five-year WMAP data by the cosmic inversion method with band-power decorrelation analysis
• Primordial Power Spectrum Reconstruction
• Probing Inflation and Dark Energy with Current Cosmological Observations
• Single field inflation with modulated potential in light of the Planck and BICEP2
• Primordial Power Spectrum features and $f_{NL}$ constraints
• PRISM: Sparse Recovery of the Primordial Power Spectrum
• A Note on Noncommutative Brane Inflation
• Noncommutative KKLMMT Model
• Scale dependence of the primordial spectrum from combining the three-year WMAP, Galaxy Clustering, Supernovae, and Lyman-alpha forests
• Reconstructing the EFT of Inflation from Cosmological Data
• Slow-roll reconstruction for running spectral index