We perform a detailed forecast on how well a Euclid -like survey will be able to constrain dark energy and neutrino parameters from a combination of its cosmic shear power spectrum , galaxy power spectrum , and cluster mass function measurements .
We find that the combination of these three probes vastly improves the survey ’ s potential to measure the time evolution of dark energy .
In terms of a dark energy figure-of-merit defined as ( \sigma ( w _ { \mathrm { p } } ) \sigma ( w _ { a } ) ) ^ { -1 } , we find a value of 690 for Euclid -like data combined with Planck -like measurements of the cosmic microwave background ( CMB ) anisotropies in a 10-dimensional cosmological parameter space , assuming a \Lambda CDM fiducial cosmology .
For the more commonly used 7-parameter model , we find a figure-of-merit of 1900 for the same data combination .
We consider also the survey ’ s potential to measure dark energy perturbations in models wherein the dark energy is parameterised as a fluid with a nonstandard non-adiabatic sound speed , and find that in an optimistic scenario in which w _ { 0 } deviates by as much as is currently observationally allowed from -1 , models with \hat { c } _ { \mathrm { s } } ^ { 2 } = 10 ^ { -6 } and \hat { c } _ { \mathrm { s } } ^ { 2 } = 1 can be distinguished at more than 2 \sigma significance .
We emphasise that constraints on the dark energy sound speed from cluster measurements are strongly dependent on the modelling of the cluster mass function ; significantly weaker sensitivities ensue if we modify our model to include fewer features of nonlinear dark energy clustering .
Finally , we find that the sum of neutrino masses can be measured with a 1 \sigma precision of 0.015 eV , even in complex cosmological models in which the dark energy equation of state varies with time .
The 1 \sigma sensitivity to the effective number of relativistic species N _ { eff } ^ { ml } is approximately 0.03 , meaning that the small deviation of 0.046 from 3 in the standard value of N _ { eff } ^ { ml } due to non-instantaneous decoupling and finite temperature effects can be probed with 1 \sigma precision for the first time .