Data compression of measurements of peculiar velocities of Supernovae Ia

Abstract

We study the compression of information present in the correlated perturbations to the luminosity distance in the low-redshift ($z<0.1$) supernovae Ia due to peculiar velocities of these supernovae. We demonstrate that the naïve compression into angular velocity power spectrum does not work efficiently, due to thickness of the spherical shell over which the supernovae are measured. Instead, we show that measurements can be compressed into measurements of $f^{2}P(k)$, where $f$ is the logarithmic rate of growth of linear perturbations and $P(k)$ is their power spectrum. We develop an optimal quadratic estimator and show that it recovers all information for $\Lambda CDM$ models for surveys of $N\sim 10,000$ or more supernovae. We explicitly demonstrate robustness with respect to the assumed fiducial model and the number of power spectrum bins. Using mock catalogues of SNe Ia we estimate that future low redshift surveys will be able to probe ${\sigma }_8$ to 6% accuracy with $10,000$ SNe Ia.

arXiv commentAccepted to PRD; Added reference

References in corpus (21)

• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2
• Estimating the Power Spectrum of the Cosmic Microwave Background
• Confirmation of general relativity on large scales from weak lensing and galaxy velocities
• The Carnegie Supernova Project: The Low-Redshift Survey
• Correlated Fluctuations in Luminosity Distance and the (Surprising) Importance of Peculiar Motion in Supernova Surveys
• Fluctuations of the luminosity distance
• A Local Hubble Bubble from SNe Ia?
• Is there Evidence for a Hubble bubble? The Nature of Type Ia Supernova Colors and Dust in External Galaxies
• Dipole of the luminosity distance: a direct measure of H(z)
• Cosmological Constraints from Type Ia Supernovae Peculiar Velocity Measurements
• Determining the Motion of the Local Group Using SN Ia Light Curve Shapes
• The Velocity Field from Type Ia Supernovae Matches the Gravity Field from Galaxy Surveys
• The Peculiar Velocities of Local Type Ia Supernovae and their Impact on Cosmology
• The Velocity Field of the Local Universe from Measurements of Type Ia Supernovae
• A Comparison of Local SNIa with the IRAS PSCz Gravity Field
• Power Spectrum Shape from Peculiar Velocity Data
• Precision measurements of large scale structure with future type Ia supernova surveys

Cited by in corpus (2)

• Target Selection for the DESI Peculiar Velocity Survey
• Measuring the velocity field from type Ia supernovae in an LSST-like sky survey