Measuring the Hubble function with standard candle clustering

Understand

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.