DESI and other dark energy experiments in the era of neutrino mass measurements

TL;DR

The paper provides a unified Fisher-matrix forecast framework for future cosmological measurements, highlighting the impact of treating the sum of neutrino masses as a free parameter and evaluating how multi-probe surveys (DESI, BOSS/eBOSS, Euclid, WFIRST, LSST, Planck, DES) enhance constraints on dark energy, curvature, and gravity. It demonstrates that broadband information and cross-probe combinations crucially improve parameter precision, with neutrino mass uncertainty notably degrading dark energy FoMs unless growth and amplitude measurements (from lensing and redshift-space distortions) are included. The results indicate that Stage IV redshift surveys can reach Σmν sensitivities near 0.01–0.02 eV and can help distinguish the neutrino mass hierarchy only in favorable cases, while curvature can be constrained to ΔΩ_k ≲ 0.001 and dark energy parameters to the 1–2% level in many combinations. The study also reveals that Planck polarization significantly strengthens constraints, that Lyα forest data provide unique high-redshift leverage (notably on α_s), and that there is substantial complementarity across photometric and spectroscopic probes, though survey overlap yields modest gains for core parameters. Overall, the paper offers a rigorous, baseline forecast suite to benchmark future cosmological analyses and to guide the design and interpretation of next-generation dark energy experiments.

Abstract

We present Fisher matrix projections for future cosmological parameter measurements, including neutrino masses, dark energy, curvature, modified gravity, the inflationary perturbation spectrum, non-Gaussianity, and dark radiation. We focus on DESI and generally redshift surveys (BOSS, HETDEX, eBOSS, Euclid, and WFIRST), but also include CMB (Planck) and weak gravitational lensing (DES and LSST) constraints. The goal is to present a consistent set of projections, for concrete experiments, which are otherwise scattered throughout many papers and proposals. We include neutrino mass as a free parameter in most projections, as it will inevitably be relevant -- DESI and other experiments can measure the sum of neutrino masses to ~0.02 eV or better, while the minimum possible sum is ~0.06 eV. We note that the BAO-only use of galaxy clustering is substantially degraded as a dark energy probe in the presence of neutrino mass uncertainty -- using broadband galaxy power is critical, especially pushing it to as small a scale as possible, and big gains are achieved by combining lensing survey constraints with redshift survey constraints. We do not try to be especially innovative, e.g., in careful treatments of potential systematic errors -- these projections are intended as a straightforward baseline for comparison to more detailed analyses.

Figures (4)

• Figure 1: Signal-to-noise ratio per Å used for DESI quasar spectra (detector noise, not absorption noise), for different $g$ magnitudes, accounting for mean Ly$\alpha$ forest absorption. (We only use the blue DESI spectrograph -- we could squeeze out a little more BAO information at $z\gtrsim 3.7$ by including the red spectrograph.)
• Figure 2: $\bar{n} P(k=0.14 \ h\text{Mpc}^{-1}, \mu=0.6)$ comparison. DESI does not include the Ly$\alpha$ forest contribution, which would bring it to effective $\bar{n}P\sim 0.3$ at $z\sim 2.5$ (over a much wider area than HETDEX and WFIRST).
• Figure 3: Fractional error on the dilation factor as a function of redshift, per unit $\ln a$, i.e., this is some sense a distance error density (plotting points aggregated over different bin widths, as is sometimes done, is essentially like plotting densities in different units on the same scale -- of course, to add up information one still needs to integrate the inverse square of the curve). In other words, the effect of a width $\Delta z$ is removed in this plot.
• Figure 4: Inverted (blue) vs. normal (red) hierarchies, given the current mass-squared difference measurements from 2012PhRvD..86a0001B. Each line shows the mass of one of the neutrinos, plotted as a function of the sum of masses in each case (in the inverted case the two most massive neutrinos have almost indistinguishable mass on this plot). The green and gray bands indicate the 1 and 2 sigma error for an experiment with $\sigma_{m_\nu}=0.017$eV, assuming no prior on $\sum m_\nu$, for a fiducial model with $\sum m_\nu=0.057$eV.