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 Penroses conformal cyclic cosmology. Using recent cosmological observations, we constrain the present-day energy density of missing matter to be $Omega_{X,0}=-0.034 pm 0.075$. 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 $Omega_{X,0} sim 0.1$, 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 $w_X = -1.01 pm 0.16$ and $Omega_{X,0} = -0.10 pm 0.56$, 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 indistinguishable according to the Jeffreys guideline.
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