Towards the geometry of the universe from data
  We present a new algorithm that can reconstruct the full distributions of
metric components within the class of spherically symmetric dust universes that
may include a cosmological constant. The algorithm is capable of confronting
this class of solutions with arbitrary data and opens a new observational
window to determine the value of the cosmological constant. In this work we use
luminosity and age data to constrain the geometry of the universe up to a
redshift of $z = 1.75$. We show that, although current data are perfectly
compatible with homogeneous models of the universe, simple radially
inhomogeneous void models that are sometimes used as alternative explanations
for the apparent acceleration of the late time universe cannot yet be ruled
out. In doing so we reconstruct the density of cold dark matter out to $z =
1.75$ and derive constraints on the metric components when the universe was
10.5 Gyr old within a comoving volume of approximately 1 Gpc$^{3}$.
