  21 cm intensity mapping (IM) has the potential to be a strong and unique
probe of cosmology from redshift of order unity to redshift potentially as high
as 30. For post-reionization 21 cm observations, the signal is modulated by the
thermal and dynamical reaction of gas in the galaxies to the passage of
ionization fronts during the Epoch of Reionization. In this work, we
investigate the impact of inhomogeneous reionization on the post-reionization
21 cm power spectrum and the induced shifts of cosmological parameters at
redshifts $3.5 \lesssim z \lesssim 5.5$. We make use of hydrodynamics
simulations that could resolve small-scale baryonic structure evolution to
quantify HI abundance fluctuation, while semi-numerical large box 21cmFAST
simulations capable of displaying inhomogeneous reionization process are
deployed to track the inhomogeneous evolution of reionization bubbles. We
discussed the prospects of capturing this effect in two post-reionization 21 cm
intensity mapping experiments: SKA1-LOW and PUMA. We find the inhomogeneous
reionization effect could impact the HI power spectrum up to tens of percent
level and shift cosmological parameters estimation from sub-percent to tens
percent in the observation of future post-reionization 21 cm intensity mapping
experiments such as PUMA, while SKA1-LOW is likely to miss this effect at the
redshifts of interest given the considered configuration. In particular, the
shift is up to 0.0206 in the spectral index $n_s$ and 0.0192 eV in the sum of
the neutrino masses $\sum m_\nu$ depending on the reionization model and the
observational parameters. We discuss strategies to mitigate and separate these
biases.
