Abstract
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 analyze 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. The best fit of the hyperconical model obtains ${\ensuremath{\chi}}_{0}^{2}=562$, the same value as the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Finally, a possible relationship is found between both theories.
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