On the perturbation of the luminosity distance by peculiar motions

Abstract

We consider some aspects of the perturbation to the luminosity distance $d(z)$ that are of relevance for SN1a cosmology and for future peculiar velocity surveys at non-negligible redshifts. 1) Previous work has shown that the correction to the lowest order perturbation $\delta d/d=-\delta v/cz$ has the peculiar characteristic that it appears to depend on the absolute state of motion of sources, rather than on their motion relative to that of the observer. The resolution of this apparent violation of the equivalence principle is that it is necessary to allow for evolution of the velocities with time, and also, when considering perturbations on the scale of the observer-source separation, to include the gravitational redshift effect. We provide an expression for $\delta d/d$ that provides a physically consistent way to measure peculiar velocities and determine their impact for SN1a cosmology. 2) We then calculate the perturbation to the redshift as a function of source flux density, which has been proposed as an alternative probe of large-scale motions. We show how the inclusion of surface brightness modulation modifies the relation between $\delta z(m)$ and the peculiar velocity, and that, while the noise properties of this method might appear promising, the velocity signal is swamped by the effect of galaxy clustering for most scales of interest. 3) We show how, in linear theory, peculiar velocity measurements are biased downwards by the effect of smaller scale motions or by measurement errors (such as in photometric redshifts). Our results nicely explain the effects seen in simulations by Koda et al.\ 2013. We critically examine the prospects for extending peculiar velocity studies to larger scales with near-term future surveys.

14 pages, 0 figures, revised version for MNRAS

References in corpus (6)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Dipoles in the Sky
• Anti-lensing: the bright side of voids
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
• Luminosity and surface brightness distribution of K-band galaxies from the UKIDSS Large Area Survey
• A direct probe of cosmological power spectra of the peculiar velocity field and the gravitational lensing magnification from photometric redshift surveys

Cited by in corpus (13)

• General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum
• Second-order gauge-invariant formalism for the cosmological observables: Complete verification of their gauge-invariance
• Exploring the Redshift-Space Peculiar Velocity Field and its Power Spectrum
• N-body simulations of gravitational redshifts and other relativistic distortions of galaxy clustering
• Relativistic Effects on Galaxy Redshift Samples due to Target Selection
• Maximum Cosmological Information from Type-Ia Supernova Observations
• Boosting gravitational waves: a review of kinematic effects on amplitude, polarization, frequency and energy density
• The art of building a smooth cosmic distance ladder in a perturbed universe
• Measuring our peculiar velocity from spectroscopic redshift surveys
• A probabilistic framework for cosmological inference of peculiar velocities
• Emergence of smooth distance and apparent magnitude in a lumpy Universe
• Living in a Non-Flat Universe: Theoretical Formalism
• Cosmic Dipoles from Large-Scale Structure Surveys