Probing dark energy: Methods and strategies

Abstract

The presence of dark energy in the Universe is inferred directly from the accelerated expansion of the Universe, and indirectly, from measurements of cosmic microwave background (CMB) anisotropy. Dark energy contributes about 2/3 of the critical density, is very smoothly distributed, and has large negative pressure. Its nature is very much unknown. Most of its discernible consequences follow from its effect on evolution of the expansion rate of the Universe, which in turn affects the growth of density perturbations and the age of the Universe, and can be probed by the classical kinematic cosmological tests. Absent a compelling theoretical model (or even a class of models), we describe the dark energy by an effective equation-of-state w = pX /ρX which is allowed to vary with time. We describe and compare different approaches for determining w(t), including magnitude-redshift (Hubble) diagram, number counts of galaxies and clusters, and CMB anisotropy, focusing particular attention on the use of a sample of several thousand type Ia supernova with redshifts z < ∼ 1.7, as might be gathered by the proposed SNAP satellite. Among other things, we derive optimal strategies for constraining cosmological parameters using type Ia supernovae. While in the near term CMB anisotropy will provide the first measurements of w, supernovae and number counts appear to have the most potential to probe dark energy.

Can luminosity distance measurements probe the equation of state of dark energy?

“…really optimise the redshift distribution within the redshift range in order to minimise this largest eigenvalue, keeping constant the total number of supernovae. This does not yield the same result as minimising the determinant of C as done in [9] where the optimal determinant is obtained at the cost of an even higher largest eigenvalue. However, as for the minimum determinant, the optimum is reached for a redshift distribution consisting in 3 delta functions, that are given in Table 2 with respect to a flat distribution is not large enough to consider seriously such an extreme option, which has very severe drawbacks.…”

“…Some conclude that it is hopeless given expected uncertainties of large statistics SNe Ia measurements [1], others provide reasonably accurate estimations of w X (z), either based on Monte-Carlo experiments [2], or even on available SNe Ia data [4]. Before attempting to clarify what causes these fundamental differences, we will warn the reader about a potential misconception that may arise from Equation 8: both its numerator and denominator are insensitive to H 0 because r scales as H −1 0 .…”

“…However, one should notice that the problem is very different if Ω M is frozen, in which case the errors on w 0 and w 1 go down by more than one order of magnitude. In [2,4], Ω M is fixed, unlike in [1] where Ω M is estimated and marginalized over. This explains partly why these papers reach different conclusions.…”

Cosmological physics with black holes (and possibly white dwarfs)

“…Dark energy becomes dynamically significant, affecting the expansion rate and geometry of the universe, and modifying D L , at z ∼ < 1 (see, e.g. Huterer & Turner, 2001, for a review). Indeed, as emphasized by Hu & Haiman (2003), once cosmic microwave background anisotropies are measured by Planck, D L will be known accurately at z ∼ 1000, and a lowredshift (z ∼ 0) measurement will provide the best complement to constrain dark energy parameters.…”

Oxidised cosmic acceleration

“…The new no-go theorems have important consequences for experiments which seek to measure the effective w with precision, such as SNIa searches, weak lensing surveys, CMB measurements, and large-scale structure observations [56,57,58,59,60,61]. From a purely four-dimensional viewpoint, there is no way to distinguish between a cosmological constant Λ and other models purely by measurements of w. For example, by using a "slow-rolling" scalar field and flattening its potential, one can engineer a model in which w approaches w = −1 arbitrarily closely, and so cannot be distinguished from Λ by any experiment with finite resolution in w. This statement rests on the assumption that one can make the potential as flat as one pleases.…”