  Most of current cosmological theories are built combining an isotropic and
homogeneous manifold with a scale factor that depends on time. If one supposes
a hyperconical universe with linear expansion, an inhomogeneous metric can be
obtained by an appropriate transformation that preserves the proper time. This
model locally tends to a flat Friedman-Robertson-Walker metric with linear
expansion. The objective of this work is to analyse the observational
compatibility of the inhomogeneous metric considered. For this purpose, the
corresponding luminosity distance was obtained and was compared with the
observations of 580 SNe Ia, taken from the Supernova Cosmology Project (SCP).
The best fit of the hyperconical model obtains \chi_0^2 = 562, the same value
that the standard \LambdaCDM model. Finally, a possible relationship is found
between both theories.
