  The cosmic expansion history, mapped by the Hubble parameter as a function of
redshift, offers the most direct probe of the dark energy equation of state.
One way to determine the Hubble parameter at different redshifts is essentially
differentiating the cosmic age or distance with respect to redshift, which may
incur large numerical errors with observational data. Taking the scenario that
the Hubble parameter increases monotonically with redshift as a reasonable
prior, we propose to enforce the monotonicity when reconstructing the Hubble
parameter at a series of redshifts. Tests with mock type Ia supernova (SN Ia)
data show that the monotonicity prior does not introduce significant biases and
that errors on the Hubble parameter are greatly reduced compared to those
determined with a flat prior at each redshift. Results from real SN Ia data are
in good agreement with those based on ages of passively evolving galaxies.
Although the Hubble parameter reconstructed from SN Ia distances does not
necessarily provide more information than the distances themselves do, it
offers a convenient way to compare with constraints from other methods.
Moreover, the monotonicity prior is expected to be helpful to other probes that
measure the Hubble parameter at multiple redshifts (e.g., baryon acoustic
oscillations), and it may be generalized to other cosmological quantities that
are reasonably monotonic with redshift.
