Luminosity distance and anisotropic sky-sampling at low redshifts: a
  numerical relativity study
  Most cosmological data analysis today relies on the
Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, providing the basis of the
current standard cosmological model. Within this framework, interesting
tensions between our increasingly precise data and theoretical predictions are
coming to light. It is therefore reasonable to explore the potential for
cosmological analysis outside of the exact FLRW cosmological framework. In this
work we adopt the general luminosity-distance series expansion in redshift with
no assumptions of homogeneity or isotropy. This framework will allow for a full
model-independent analysis of near-future low-redshift cosmological surveys. We
calculate the effective observational 'Hubble', 'deceleration', 'curvature' and
'jerk' parameters of the luminosity-distance series expansion in numerical
relativity simulations of realistic structure formation, for observers located
in different environments and with different levels of sky-coverage. With a
'fairly-sampled' sky, we find 0.6% and 4% cosmic variance in the 'Hubble' and
'deceleration' parameters for scales of 200 Mpc/h (corresponding to density
contrasts of ~0.05 in the simulated model universe), respectively. On top of
this, we find that typical observers measure maximal sky-variance of 2% and
120% in the same parameters, as compared to their analogies in the large scale
FLRW model. Our work suggests the inclusion of low-redshift anisotropy in
cosmological analysis could be important for drawing correct conclusions about
our Universe.
