A Joint Analysis for Cosmology and Photometric Redshift Calculation Using Cross Correlations

TL;DR

This paper introduces a method to calibrate photometric redshift bins using cross-correlation data within an MCMC framework, effectively constraining bin properties and reducing bias in cosmological parameter estimation.

Contribution

The novel approach integrates bin calibration into cosmological inference, demonstrating that cross-correlations can accurately determine redshift bin properties with minimal bias.

Findings

Redshift bin mean and width can be estimated with high precision.

Cross-correlations tightly constrain bin properties, reducing their impact on cosmological parameters.

Method achieves redshift accuracy suitable for future cosmological surveys.

Abstract

We present a method of calibrating the properties of photometric redshift bins as part of a larger Markov Chain Monte Carlo (MCMC) analysis for the inference of cosmological parameters. The redshift bins are characterised by their mean and variance, which are varied as free parameters and marginalised over when obtaining the cosmological parameters. We demonstrate that the likelihood function for cross-correlations in an angular power spectrum framework tightly constrains the properties of bins such that they may be well determined, reducing their influence on cosmological parameters and avoiding the bias from poorly estimated redshift distributions. We demonstrate that even with only three photometric and three spectroscopic bins, we can recover accurate estimates of the mean redshift of a bin to within $\Delta\mu \approx 3-4 \times10^{-3}$ and the width of the bin to $\Delta\sigma \approx 1\times10^{-3}$ for galaxies near $z = 1$. This indicates that we may be able to bring down the photometric redshift errors to a level which is in line with the requirements for the next generation of cosmological experiments.