Measuring the Hubble function with standard candle clustering

TL;DR

This paper introduces a novel method called Clustering of Standard Candles (CSC) that estimates the Hubble function $H(z)$ from supernovae data by analyzing their clustering and velocities, independent of cosmological assumptions.

Contribution

The paper presents a new model-independent technique to measure $H(z)/H_{0}$ using supernova clustering and velocities, extending cosmological measurements beyond traditional distance-based methods.

Findings

Potential to constrain $H(z)/H_{0}$ to 5-13% with LSST

Method is model-independent and does not rely on background cosmology

Forecasts show applicability up to redshift $z=0.6$

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 $z=0.6$.