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

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.