Hubble parameter reconstruction from a principal component analysis:
  minimizing the bias
  A model-independent reconstruction of the cosmic expansion rate is essential
to a robust analysis of cosmological observations. Our goal is to demonstrate
that current data are able to provide reasonable constraints on the behavior of
the Hubble parameter with redshift, independently of any cosmological model or
underlying gravity theory. Using type Ia supernova data, we show that it is
possible to analytically calculate the Fisher matrix components in a Hubble
parameter analysis without assumptions about the energy content of the
Universe. We used a principal component analysis to reconstruct the Hubble
parameter as a linear combination of the Fisher matrix eigenvectors (principal
components). To suppress the bias introduced by the high redshift behavior of
the components, we considered the value of the Hubble parameter at high
redshift as a free parameter. We first tested our procedure using a mock sample
of type Ia supernova observations, we then applied it to the real data compiled
by the Sloan Digital Sky Survey (SDSS) group. In the mock sample analysis, we
demonstrate that it is possible to drastically suppress the bias introduced by
the high redshift behavior of the principal components. Applying our procedure
to the real data, we show that it allows us to determine the behavior of the
Hubble parameter with reasonable uncertainty, without introducing any ad-hoc
parameterizations. Beyond that, our reconstruction agrees with completely
independent measurements of the Hubble parameter obtained from red-envelope
galaxies.
