Measuring the Hubble function with standard candle clustering

Abstract

Supernova Ia magnitude surveys measure the dimensionless luminosity distance $H_{0}D_{L}$. However, from the distances alone one cannot obtain quantities like $H(z)$ or the dark energy equation of state, unless further cosmological assumptions are imposed. Here we show that by measuring the power spectrum of density contrast and of peculiar velocities of supernovae one can estimate also $H(z)/H_{0}$ regardless of background or linearly perturbed cosmology and of galaxy-matter bias. This method, dubbed Clustering of Standard Candles (CSC) also yields the redshift distortion parameter $\beta(k,z)$ and the biased matter power spectrum in a model-independent way. We forecast that an optimistic (pessimistic) LSST may be able to constrain $H(z)/H_{0}$ to 5-13% (9-40%) in redshift bins of $\Delta z=0.1$ up to at least $z=0.6$.