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.
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