Supernova constraints on higher-dimensional cosmology with a phantom
  field
  We use observational data on the magnitude-redshift relation for Type Ia
supernovae together with constraints on the ages of the oldest stars to rule
out a higher-dimensional extension of General Relativity with a negative
kinetic-energy scalar field. This theory is of considerable physical interest
because it produces accelerated expansion at both early and late times with a
single new field, as in quintessential inflation scenarios. It is also of
mathematical interest because it is characterized by an analytic expression for
the macroscopic scale factor $a(t)$. We show that cosmological solutions of
this theory can be usefully parametrized by a single quantity, the lookback
time $\tau_{\text{tr}}$ corresponding to the transition from deceleration to
acceleration. Supernovae data from the recently released Supernova Cosmology
Project Union 2.1 compilation single out a narrow range of values for
$\tau_{\text{tr}}$. In the context of the theory, however, these same values of
$\tau_{\text{tr}}$ imply that the universe is much older than the oldest
observed stars.
