We present a new analysis on how to distinguish between isotropic and anisotropic cosmological models based on tracking the angular displacements of a large number of distant quasars over an extended period of time, and then performing a multipole-ve
ctor decomposition of the resulting displacement maps. We find that while the GAIA mission operating at its nominal specifications does not have sufficient angular resolution to resolve anisotropic universes from isotropic ones using this method within a reasonable timespan of ten years, a next-generation GAIA-like survey with a resolution ten times better should be equal to the task. Distinguishing between different anisotropic models is however more demanding. Keeping the observational timespan to ten years, we find that the angular resolution of the survey will need to be of order 0.1 micro-arcsecond in order for certain rotating anisotropic models to produce a detectable signature that is also unique to models of this class. However, should such a detection become possible, it would immediately allow us to rule out large local void models.
We perform a detailed forecast on how well a {sc 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. W
e find that the combination of these three probes vastly improves the surveys 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 {sc Euclid}-like data combined with {sc 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 surveys 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 emph{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 $2sigma$ 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, (abridged)
