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 $\Omega_{X,0}=-0.034 \pm 0.075$. 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.
