Path Integral Marginalization for Cosmology: Scale Dependent Galaxy Bias & Intrinsic Alignments

TL;DR

This paper introduces a path-integral likelihood method to marginalize over unknown systematic functions in cosmology, improving parameter estimation in galaxy bias and intrinsic alignments.

Contribution

The authors develop a novel formalism extending likelihood analysis to include continuous functions, enabling better handling of systematic uncertainties in cosmological data.

Findings

Scale-dependent galaxy bias degrades cosmological parameter constraints unless bias variance is known to 10%.

Removing intrinsic alignments with a flat prior reduces dark energy Figure-of-Merit by 20%.

Knowledge of scale and redshift dependence to better than 10% can double the dark energy Figure-of-Merit.

Abstract

We present a path-integral likelihood formalism that extends parameterized likelihood analyses to include continuous functions. The method finds the maximum likelihood point in function-space, and marginalizes over all possible functions, under the assumption of a Gaussian-distributed function-space. We apply our method to the problem of removing unknown systematic functions in two topical problems for dark energy research : scale-dependent galaxy bias in redshift surveys; and galaxy intrinsic alignments in cosmic shear surveys. We find that scale-dependent galaxy bias will degrade information on cosmological parameters unless the fractional variance in the bias function is known to 10%. Measuring and removing intrinsic alignments from cosmic shear surveys with a flat-prior can reduce the dark energy Figure-of-Merit by 20%, however provided that the scale and redshift-dependence is known to better than 10% with a Gaussian-prior, the dark energy Figure-of-Merit can be enhanced by a factor of two with no extra assumptions.