The consequences of using a smooth cosmic distance in a lumpy universe:
  I
  How do we appropriately fit a model based on an idealised
Friedmann-Lema{\i}tre Robertson-Walker (FLRW) spacetime to observations made
from a single location in a lumpy Universe? We address this question for
surveys that measure the imprints of the Baryon Acoustic Oscillation (BAO) in
galaxy distribution and the peak apparent magnitude of the type 1A supernova
(SN1A). These observables are related to the cosmological model through the
Alcock-Paczynski parameters and the distance-redshift relation. Using the
corresponding inhomogeneous spacetime expressions of these as observed data, we
perform a parameter inference assuming that the background FLRW model is the
correct model of the universe. This process allows us to estimate the best fit
Hubble rate and the deceleration parameter. We find that the inferred Hubble
rate from the monopole of the Alcock-Paczynski parameters is in tension with
the Hubble rate determined using the distance-redshift relation. The latter
gives the best fit Hubble rate for the cosmological expansion. The constraint
on the Hubble rate from the Alcock-Paczynski parameters is contaminated by the
environment. When the environmental contribution is restricted to modes in the
Hubble flow, we find about (9-12)\% discrepancy in the Hubble rate. Finally, we
comment on the insufficiency of the method of cosmography in constraining the
deceleration parameter.
