A theoretician's analysis of the supernova data and the limitations in determining the nature of dark energy

Abstract

Current cosmological observations show a strong signature of the existence of a dark energy component with negative pressure. The most obvious candidate for this dark energy is the cosmological constant (with the equation of state wX=p/ρ=−1), which, however, raises several theoretical difficulties. This has led to models for a dark energy component that evolves with time. We discuss certain questions related to the determination of the nature of the dark energy component from observations of high‐redshift supernovae. The main results of our analysis are as follows. (i) Even if the precise value of wX is known from observations, it is not possible to determine the nature of the unknown dark energy source using only kinematical and geometrical measurements. We have given explicit examples to show that different types of sources can give rise to a given wX. (ii) Although the full data set of supernova observations (which are currently available) strongly rule out models without dark energy, the high‐Ψ(z > 0.25) and low‐ (z < 0.25) redshift data sets, individually, admit decelerating models with zero dark energy. Any possible evolution in the absolute magnitude of the supernovae, if detected, might allow the decelerating models to be consistent with the data. (iii) We have introduced two parameters, which can be obtained entirely from theory, to study the sensitivity of the luminosity distance on wX. Using these two parameters, we have argued that although one can determine the present value of wX accurately from the data, one cannot constrain the evolution of wX.

Probing the cosmic distance-duality relation with the Sunyaev-Zel’dovich effect, X-ray observations and supernovae Ia

“…Potentially, it will become more useful once higher redshift cluster data are made available. The above parametrizations are clearly inspired by similar expressions for the ω(z)-equation of state parameter in timevarying dark energy models (see, for instance, Padmanabhan & Choudury 2003;Linder 2003;Cunha et al 2007;Silva et al 2007). In the limit of very low redshifts (z 1), we have η = 1 and D L = D A as should be expected, and, more important for our subsequent analysis, the value η 0 = 0 must be favored by the Etherington principle.…”

Cosmic distance duality relation and the shape of galaxy clusters

“…The above parametrizations are clearly inspired by similar expressions for the ω(z)-equation of state parameter of dark energy models (Padmanabhan & Choudury 2003;Linder 2003;Cunha et al 2007a;Silva et al 2007). In the limit of extremely low redshifts (z 1), we have η = 1 and D L = D A as should be expected, and, more important for our subsequent analysis, the value η 0 = 0 must be favored by the Etherington result.…”

“Expansion” around the vacuum: how far can we go fromΛ?

“…3 also shows that almost no constraint can be placed on the additional parameter α from the available sets of observational data, which hampers any definitive answer to our initial question. Such a conclusion may also be generalized for other EOS parametrizations as, for instance, the so-called Chaplygin gas EOS (Kamenshchik et al 2001;Bilic et al 2002;Bento et al 2002;Dev et al 2003) or still for EOS parametrizations that explicitely depend on time/redshift (Goliath et al 2001;Efstathiou 1999;Chevallier & Polarski 2001;Linder 2003;Padmanabhan & Choudhury 2003;Jain et al 2006; see also Maor et al 2002, for a discussion of this topic). For the analysis performed here, the best-fit model is found for values ofà = 0.03 and α = 0.98, which corresponds to a 13.6-Gyr-old, currently accelerated Fig.…”