# Towards determining the neutrino mass hierarchy: weak lensing and galaxy clustering forecasts with baryons and intrinsic alignments

## TL;DR

This paper evaluates how baryonic physics and intrinsic alignments affect the ability of future surveys to measure neutrino masses and distinguish their hierarchy, finding that combined data can reduce uncertainties but hierarchy distinction remains challenging.

## Contribution

It provides the first combined weak lensing and galaxy clustering Fisher analysis including baryons, intrinsic alignments, and neutrinos for hierarchy determination.

## Key findings

- Baryons significantly degrade neutrino mass forecasts, doubling uncertainties.
- Combining galaxy clustering and CMB priors reduces forecast uncertainties to about 9-16%.
- Forecasts suggest hierarchy distinction remains difficult with current methods.

## Abstract

The capacity of Stage IV lensing surveys to measure the neutrino mass sum and differentiate between the normal and inverted mass hierarchies depends on the impact of nuisance parameters describing small-scale baryonic astrophysics and intrinsic alignments. For a Euclid-like survey, we perform the first combined weak lensing and galaxy clustering Fisher analysis with baryons, intrinsic alignments, and massive neutrinos for both hierarchies. We use a matter power spectrum generated from a halo model that captures the impact of baryonic feedback and adiabatic contraction. For weak lensing, we find that baryons cause severe degradation to forecasts of the neutrino mass sum, $\Sigma$, approximately doubling $\sigma_{\Sigma}$. We show that including galaxy clustering constraints from Euclid and BOSS, and cosmic microwave background (CMB) Planck priors, can reduce this degradation to $\sigma_{\Sigma}$ to 9% and 16% for the normal and inverted hierarchies respectively. The combined forecasts, $\sigma_{\Sigma_{\rm{NH}}}=0.034\, \rm{eV}$ and $\sigma_{\Sigma_{\rm{IH}}}=0.034\, \rm{eV}$, preclude a meaningful distinction of the hierarchies but could be improved upon with future CMB priors on $n_s$ and information from neutrinoless double beta decay to achieve a 2$\sigma$ distinction. The effect of intrinsic alignments on forecasts is shown to be minimal, with $\sigma_{\Sigma}$ even experiencing mild improvements due to information from the intrinsic alignment signal. We find that while adiabatic contraction and intrinsic alignments will require careful calibration to prevent significant biasing of $\Sigma$, there is less risk presented by feedback from energetic events like AGN and supernovae.