Physical effects involved in the measurements of neutrino masses with future cosmological data

Abstract

Future Cosmic Microwave Background experiments together with upcoming galaxy and 21-cm surveys will provide extremely accurate measurements of different cosmological observables located at different epochs of the cosmic history. The new data will be able to constrain the neutrino mass sum with the best precision ever. In order to exploit the complementarity of the different redshift probes, a deep understanding of the physical effects driving the impact of massive neutrinos on CMB and large scale structures is required. The goal of this work is to describe these effects, assuming a summed neutrino mass close to its minimum allowed value. We find that parameter degeneracies can be removed by appropriate combinations, leading to robust and model independent constraints. A joint forecast of the sensitivity of Euclid and DESI surveys together with a CORE-like CMB experiment leads to a $1σ$ uncertainty of $14$~meV on the summed neutrino mass. However this particular combination gives rise to a peculiar degeneracy between $M_ν$ and the optical depth at reionization. Independent constraints from 21-cm surveys can break this degeneracy and decrease the $1σ$ uncertainty down to $12$~meV.

Figures (8)

• Figure 1: Relative change in the CMB spectra induced by increasing the summed neutrino mass from $M_\nu=60$ meV to $M_\nu=150$ meV. The plots show the residuals of the lensed $TT$ (top), lensed $EE$ (middle) and lensing potential (bottom) power spectrum, as a function of multipoles $\ell$ with a linear (left) or logarithmic (right) scale. The light/pink and darker/green shaded rectangles refer, respectively, to the binned noise spectrum of a cosmic-variance-limited or CORE-like experiment, with linear bins of width $\Delta \ell=25$. The physical baryon density $\omega_b$ and the scalar spectral index $n_s$ are kept fixed. In the first case (green solid line) the value of the Hubble constant is fixed at the reference value, while in all the other cases (labeled as fixed $\theta_s$) $h$ decreases in order to keep $\theta_s$ consistent with the reference model. Moreover, in the third case (dotted blue line), we tried to compensate for the changes in the lensing spectrum by increasing $A_s$, and in the fourth case (dotted-dashed black) we aim at the same result by increasing $\omega_\mathrm{cdm}$.
• Figure 3: Relative error on $r_s/D_V$. Gray error bars refer to the current BAO measurements: from left to right 6dFGRS Beutler:2011hx, SDSS MGS Ross:2014qpa, LOW-Z, C-MASS Anderson:2013zyy. Black error bars mark the expected sensitivity of the future DESI experiment Allison:2015qcaFont-Ribera:2013rwa. Green solid line and red dashed lines are the same as in figure \ref{['fig:difftt']}, i.e. higher $M_\nu$ with fixed $h$ (green solid line) and higher $M_\nu$ with fixed $\theta_s$ and varying $h$ (red dashed line). However, here the black dot dashed line is obtained by increasing $M_\nu$ and varying $h$ and $\omega_{\rm cdm}$ as in equations (\ref{['eq:corr_BAO']}).
• Figure 4: Marginalized one- and two- $\sigma$ contours in the plane $\left( \omega_{\rm cdm}, M_\nu \right)$ (left panel) and $\left(H_0, M_\nu \right)$ (right panel), for CMB-CORE or BAO-DESI mock data. The black dashed lines show the directions of degeneracy given in equations (\ref{['eq:corr_CMB']}), and the blue ones in equations (\ref{['eq:corr_BAO']}).
• Figure 5: Marginalized one- and two- $\sigma$ contours in the plane $\left( \theta_s(z_{\rm dec}), M_\nu \right)$ (left) and $\left(r(z_\mathrm{drag})/D_V(z=1), M_\nu \right)$ (right), for CMB-CORE or BAO-DESI mock data. In the CORE contours, samples are coloured according to the value of $H_0$.
• Figure 6: Relative error on the galaxy lensing $C_\ell^{ll}$ in the first redshift bin ($0<z<0.42$, left panel) and in the tenth redshift bin ($1.7<z<2.5$, right panel). Here the redshift range is $0<z<2.5$ and is divided in ten equi-populated redshift bins. The light pink rectangles refers to the observational error. The light green shaded area shows the relative error associated to our model for the theoretical uncertainty on $P_m(k,z)$. Green solid and red dashed lines are the same as in figure \ref{['fig:difftt']}, i.e. higher $M_\nu$ with fixed $h$ (green solid line) and higher $M_\nu$ with fixed $\theta_s$ and varying $h$ (red dashed line). The blue dotted line, besides the higher $M_\nu$, implies a smaller value of $h$ ($\Delta h \sim - 3 \Delta \omega_\nu$), an increase of $n_s$ by 0.4% and of $A_s$ by 2%.