Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error

TL;DR

This work develops a forward-modeling, MCMC-based forecast for neutrino masses and cosmological parameters using a Euclid-like spectroscopic survey. It combines a complete one-loop perturbation theory description of the galaxy power spectrum with a tree-level bispectrum, including non-linear bias, redshift-space distortions, IR BAO resummation, Alcock-Paczynski effects, and UV counterterms, while accounting for theoretical uncertainties via a correlated two-loop envelope. The results show that Euclid-like data alone can measure the total neutrino mass with ~28 meV precision, which improves to ~13 meV when combined with Planck, and could reach ~11 meV under optimistic bispectrum assumptions; the joint data also yield percent- or per-mille-level constraints on other parameters, including a highly precise Hubble constant. The study emphasizes the importance of a full-shape, multi-statistic approach and a robust theoretical-error covariance to avoid overestimating information from mildly non-linear scales, providing a roadmap for real-data analyses with Euclid and similar surveys.

Abstract

We present a Markov-Chain Monte-Carlo (MCMC) forecast for the precision of neutrino mass and cosmological parameter measurements with a Euclid-like galaxy clustering survey. We use a complete perturbation theory model for the galaxy one-loop power spectrum and tree-level bispectrum, which includes bias, redshift space distortions, IR resummation for baryon acoustic oscillations and UV counterterms. The latter encapsulate various effects of short-scale dynamics which cannot be modeled within perturbation theory. Our MCMC procedure consistently computes the non-linear power spectra and bispectra as we scan over different cosmologies. The second ingredient of our approach is the theoretical error covariance which captures uncertainties due to higher-order non-linear corrections omitted in our model. Having specified characteristics of a Euclid-like spectroscopic survey, we generate and fit mock galaxy power spectrum and bispectrum likelihoods. Our results suggest that even under very agnostic assumptions about non-linearities and short-scale physics a future Euclid-like survey will be able to measure the sum of neutrino masses with a standard deviation of 28 meV. When combined with the Planck cosmic microwave background likelihood, this uncertainty decreases to 13 meV. Over-optimistically reducing the theoretical error on the bispectrum down to the two-loop level marginally tightens this bound to 11 meV. Moreover, we show that the future large-scale structure (LSS) spectroscopic data will greatly improve constraints on the other cosmological parameters, e.g. reaching a percent (per mille) error on the Hubble constant with LSS alone (LSS + Planck).

Figures (7)

• Figure 1: Monopole, quadrupole and hexadecapole of the one-loop galaxy power spectrum and the tree-level monopole bispectrum for the equilateral configuration at $z=1$: theoretical curves for $m_\nu = 0.1$ eV (blue line), $m_\nu = 0$ eV (black line), along with the mock data. The errorbars on short scales blow up because of the theoretical uncertainty added to the covariance. Note that the monopole power spectrum and bisepectrum increase at high momenta due to the strong shot noise contribution.
• Figure 2: $1\sigma$ and $2\sigma$ contours in plane $m_\nu-A$ for the real space (left panel) and redshift space (right panel) analyses. $m_\nu$ is quoted in units of $\,\text{eV}$. See also Tab. \ref{['tab:constraints']} for the marginalized constraints.
• Figure 3: $1\sigma$ contours for bias parameters and RSD counterterm coefficients obtained for different combinations of the power spectrum and bispectrum likelihoods. Black crosses reflect the fiducial values listed in Table \ref{['tab:bias']}. The counterterm values $c_i$ are quoted in units [Mpc$/h]^2$, the shot noise $P_{\text{shot}}$ in units [Mpc$/h]^3$.
• Figure 4: 2d posterior contours and non-normalized 1d marginalized distributions for the total neutrino mass $m_\nu$ in units $[\,\text{eV}]$ and other parameters of the base $\Lambda$CDM, see also Tab. \ref{['tab:constraints']} for the corresponding $1\sigma$ confidence limits. The filled and half-filled contours represent $68\%$ and $95\%$ confidence limits. The blue dashed lines correspond the Planck 2018 baseline results reproduced with the mock Planck likelihood.
• Figure 5: The 2d posterior contours and non-normalized 1d 2d posterior contours and non-normalized 1d marginalized distributions for the total neutrino mass $m_\nu$ in units $[\,\text{eV}]$ and other parameters of the base $\Lambda$CDM, see also Tab. \ref{['tab:constraints']} for the corresponding $1\sigma$ confidence limits. The filled and half-filled contours represent $68\%$ and $95\%$ confidence limits.