Neutrino masses and beyond-$\mathrm{\Lambda }\mathrm{CDM}$ cosmology with LSST and future CMB experiments

Cosmological measurements over the next decade will enable us to shed light on the content and evolution of the Universe. Complementary measurements of the cosmic microwave background (CMB) and baryon acoustic oscillations are expected to allow an indirect determination of the sum of neutrino masses, within the framework of the flat $\mathrm{\Lambda }\mathrm{CDM}$ model. However, possible deviations from $\mathrm{\Lambda }\mathrm{CDM}$ such as a nonzero cosmological curvature or a dark energy equation of state with $w\ne -1$ would leave similar imprints on the expansion rate of the Universe and clustering of matter. We show how future CMB measurements can be combined with late-time measurements of galaxy clustering and cosmic shear from the Large Synoptic Survey Telescope to alleviate this degeneracy. Together, they are projected to reduce the uncertainty on the neutrino mass sum to 30 meV within this more general cosmological model. Achieving a $3\sigma$ measurement of the minimal 60 meV mass sum (or $4\sigma$ assuming $w=-1$) will require a fivefold improved measurement of the optical depth to reionization, obtainable through a large-scale CMB polarization measurement.

Figure 1

Degradation in the error on the sum of neutrino masses with extensions to the canonical $\mathrm{\Lambda }\mathrm{CDM}$ model, as in Allison et al. [7]. Inset shows degeneracy with total CDM energy density when $w_0$, $w_a$, and ${\mathrm{\Omega }}_k$ are opened up as free parameters. The forecast uncertainty $\sigma (\mathrm{\Sigma }{m}_{\nu })$ increases from 28 to 72 meV in this case.

Figure 2

(Left) The relative change in the power spectrum for the case of cosmic shear (top) and galaxy clustering (bottom) when the total neutrino mass and $w_0$ are varied, corresponding to Bin 5 of our setup ($z\in [1.12,1.46]$). Also shown for comparison is the LSST noise spectrum considered in this redshift range. (Right) The autopower spectra for the fiducial cosmological parameters, shown for all the shear (red) and clustering (blue) redshift bins considered, including scale cuts. Darker colors correspond to higher redshift bins. For reference, the grey line corresponds to a scale of $k=0.1{\mathrm{Mpc}}^{-1}$.

Figure 3

(Left) Forecast error on $\mathrm{\Sigma }{m}_{\nu }$ achievable with CMB-S4 (grey lines), LSST shear (blue lines), LSST clustering (red lines), LSST clustering and shear (green lines), and all together (orange lines), combined with Planck primary CMB data as described in Sec. 3a, in the presence of an uncertain dark energy equation of state. (Center), (Right) Forecast error on $w_0$ and $w_a$ with different combinations of probes, revealing the degeneracies with $\mathrm{\Sigma }{m}_{\nu }$ in each case. The corresponding forecast values are given in Table 2.

Figure 4

Achievable constraints on $\mathrm{\Sigma }{m}_{\nu }$ (blue line), $w_0$ (burgundy line), $w_a$ (green line), and ${\mathrm{\Omega }}_k$ (yellow line) as a function of the CMB noise level in intensity $N_T$. Forecasts are shown as a ratio to the constraints achievable for a $1\mu \mathrm{K}\text{−}\mathrm{arcmin}$ experiment. Although $w_0$, $w_a$, and ${\mathrm{\Omega }}_k$ do not degrade significantly with $N_T$, the uncertainty on the sum of neutrino masses could improve by $\sim 40\%$ from a Stage-3 experiment ($\sim 10\mu \mathrm{K}\text{−}\mathrm{arcmin}$) to S4. Also shown (dotted blue line) are the achievable constraints on $\mathrm{\Sigma }{m}_{\nu }$ when $w_0$, $w_a$, and ${\mathrm{\Omega }}_k$ are fixed to their fiducial $\mathrm{\Lambda }\mathrm{CDM}$ values. The relative degradation with increasing CMB noise level is much more modest in this case.

Figure 5

Effect of selected systematics on the forecasted neutrino mass sum, dark energy parameters, and curvature errors. Each point corresponds to the result of assuming absolute control about each of the systematics, while marginalizing over the rest.

Figure 6

Forecast errors on the multiplicative bias parameters for the different shear bins with LSST and CMB-S4. The dotted line shows the LSST requirement of 0.5% [71, 72, 73].