Cosmology in the Next Millennium: Combining MAP and SDSS Data to Constrain Inflationary Models

Abstract

The basic cosmological parameters and the primordial power spectrum together completely specify predictions for the cosmic microwave background radiation anisotropy and large scale structure. Here we show how we can strongly constrain both $A_S^2(k)$ and the cosmological parameters by combining the data from the Microwave Anisotropy Probe (MAP) and the galaxy redshift survey from the Sloan Digital Sky Survey (SDSS). We allow $A_S^2(k)$ to be a free function, and thus probe features in the primordial power spectrum on all scales. The primordial power spectrum in 20 steps in $\log k$ to $k\le 0.5h$Mpc${}^{-1}$ can be determined to $\sim 16$ accuracy for $k\sim 0.01h$Mpc${}^{-1}$, and to $\sim 1$ accuracy for $k\sim 0.1h$Mpc${}^{-1}$. The uncertainty in the primordial power spectrum increases by a factor up to 3 on small scales if we solve simultaneously for the dimensionless Hubble constant $h$, the cosmological constant $\Lambda$, the baryon fraction ${\Omega }_b$, the reionization optical depth ${\tau }_{ri}$, and the effective bias between the matter density field and the redshift space galaxy density field $b_{eff}$. Alternately, if we restrict $A_S^2(k)$ to be a power law, we find that inclusion of the SDSS data breaks the degeneracy between the amplitude of the power spectrum and the optical depth inherent in the MAP data, significantly reduces the uncertainties in the determination of the matter density and the cosmological constant, and allows a determination of the galaxy bias parameter. Thus, combining the MAP and SDSS data allows the independent measurement of important cosmological parameters, and a measurement of the primordial power spectrum independent of inflationary models, giving us valuable information on physics in the early Universe, and providing clues to the correct inflationary model.

Substantial revisions to quantitative results as a result of more accurate calculation of derivatives; these new numerical results strengthen but do not change our qualitative results. Minor changes in wording. Several references added. Final version, to appear in ApJ January 1, 1999 issue, Vol. 510 #1

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Cited by in corpus (71)

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• The Clustering of Luminous Red Galaxies in the Sloan Digital Sky Survey Imaging Data
• The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data
• Cosmic Complementarity: Joint Parameter Estimation from CMB Experiments and Redshift Surveys
• Robust Dark Energy Constraints from Supernovae, Galaxy Clustering, and Three-Year Wilkinson Microwave Anisotropy Probe Observations
• The abundance of high-redshift objects as a probe of non-Gaussian initial conditions
• Reconstructing the primordial power spectrum
• Probing Planckian physics: resonant production of particles during inflation and features in the primordial power spectrum
• Features and New Physical Scales in Primordial Observables: Theory and Observation
• Clustering of Sloan Digital Sky Survey III Photometric Luminous Galaxies: The Measurement, Systematics and Cosmological Implications
• Probing the Reionization History of the Universe using the Cosmic Microwave Background Polarization
• Separating the Early Universe from the Late Universe: cosmological parameter estimation beyond the black box
• The Atacama Cosmology Telescope: a measurement of the primordial power spectrum
• Flux-averaging Analysis of Type Ia Supernova Data
• Model-Independent Reconstruction of the Primordial Power Spectrum from WMAP Data
• Measuring Time-Dependence of Dark Energy Density from Type Ia Supernova Data
• Constraints on the sound speed of dark energy
• Reconstructing the primordial power spectrum - a new algorithm
• On the APM power spectrum and the CMB anisotropy: Evidence for a phase transition during inflation?
• Cross-correlating the Sloan Digital Sky Survey with the Microwave Sky
• Where are the Luminous Red Galaxies (LRGs)? Using correlation measurements and lensing to relate LRGs to dark matter halos
• Reconstruction of the primordial power spectrum of curvature perturbations using multiple data sets
• Principal Power of the CMB
• Sloan Digital Sky Survey III Photometric Quasar Clustering: Probing the Initial Conditions of the Universe using the Largest Volume
• Reconstructing the Primordial Spectrum from WMAP Data by the Cosmic Inversion Method
• Maximum Likelihood Estimates of the Two- and Three-Dimensional Power Spectra of the APM Galaxy Survey
• Measuring the primordial power spectrum: Principal component analysis of the cosmic microwave background
• CMB Temperature and Polarization Anisotropy Fundamentals
• Can cosmology detect hierarchical neutrino masses?
• Remarks on the formulation of the cosmological constant/dark energy problems
• Dark Energy Constraints from Baryon Acoustic Oscillations
• Reconstructing the inflationary power spectrum from CMBR data
• Evolution of the X-ray luminosity and metallicity of starburst blown superbubbles
• Characterising the Primordial Cosmic Perturbations
• CONNECT: A neural network based framework for emulating cosmological observables and cosmological parameter inference
• How robust are inflation model and dark matter constraints from cosmological data?
• How to fool CMB parameter estimation
• Cosmic Inversion: Reconstructing primordial spectrum from CMB anisotropy
• Band-power reconstruction of the primordial fluctuation spectrum by the maximum likelihood reconstruction method
• Lensing Corrections to Features in the Angular Two-Point Correlation Function and Power Spectrum
• On the r-mode spectrum of relativistic stars in the low-frequency approximation
• Using galaxy-galaxy weak lensing measurements to correct the Finger-of-God
• Non-linear Galaxy Power Spectrum and Cosmological Parameters
• Constraining Isocurvature Fluctuations with the Planck Surveyor
• Reconstruction of the primordial fluctuation spectrum from the five-year WMAP data by the cosmic inversion method with band-power decorrelation analysis
• Model Independent Primordial Power Spectrum from Maxima, Boomerang, and DASI Data
• Primordial Power Spectrum Reconstruction
• Non-Gaussianity in Large Scale Structure and Minkowski Functionals
• Constraining Inflation
• Direct Wavelet Expansion of the Primordial Power Spectrum
• Inflationary Freedom and Cosmological Neutrino Constraints
• Wavelet Band Powers of the Primordial Power Spectrum from CMB Data
• Understanding the nature of luminous red galaxies (LRGs): Connecting LRGs to central and satellite subhalos
• Constraining Cut-off Physics in the Cosmic Microwave Background
• Exploring Large-scale Structure with Billions of Galaxies
• Euclid: The search for primordial features
• Cosmic Inversion II --An iterative method for reproducing the primordial spectrum from the CMB data--
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• ATLAS Probe: Breakthrough Science of Galaxy Evolution, Cosmology, Milky Way, and the Solar System
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• Light Sterile Neutrinos and Inflationary Freedom
• Primordial Power Spectrum features and $f_{NL}$ constraints
• Mutual Constraints Between Reionization Models and Parameter Extraction From Cosmic Microwave Background Data
• Searching for local features in primordial power spectrum using genetic algorithms
• Cosmological parameter determination from Planck and SDSS data in LambdaCHDM cosmologies
• Refining the nonlinear modelling of primordial oscillatory features
• From the Cosmological Microwave Background to Large-Scale Structure
• Exploring the origin of the fine structures in the CMB temperature angular power spectrum
• Next-generation test of cosmic inflation