Observational constraints on conformal time symmetry, missing matter and double dark energy

The current concordance model of cosmology is dominated by two mysterious ingredients: dark matter and dark energy. In this paper, we explore the possibility that, in fact, there exist two dark-energy components: the cosmological constant Lambda, with equation-of-state parameter w(Lambda) = -1, and a 'missing matter' component X with w(X) = -2/3, which we introduce here to allow the evolution of the universal scale factor as a function of conformal time to exhibit a symmetry that relates the big bang to the future conformal singularity, such as in Penrose's conformal cyclic cosmology. Using recent cosmological observations, we constrain the present-day energy density of missing matter to be Omega(X,0) = -0.034 +/- 0.075. This is consistent with the standard Lambda CDM model, but constraints on the energy densities of all the components are considerably broadened by the introduction of missing matter; significant relative probability exists even for Omega(X,0) similar to 0.1, and so the presence of a missing matter component cannot be ruled out. As a result, a Bayesian model selection analysis only slightly disfavours its introduction by 1.1 log-units of evidence. Foregoing our symmetry requirement on the conformal time evolution of the universe, we extend our analysis by allowing w(X) to be a free parameter. For this more generic 'double dark energy' model, we find w(X) = -1.01 +/- 0.16 and Omega(X,0) = -0.10 +/- 0.56, which is again consistent with the standard Lambda CDM model, although once more the posterior distributions are sufficiently broad that the existence of a second dark-energy component cannot be ruled out. The model including the second dark energy component also has an equivalent Bayesian evidence to Lambda CDM, within the estimation error, and is indistuingishable according to the Jeffreys guideline.