Unbiased constraints on the clumpiness of universe from standard candles
  We perform unbiased tests for the clumpiness of universe by confronting the
Zel'dovich-Kantowski-Dyer-Roeder luminosity distance which describes the effect
of local inhomogeneities on the propagation of light with the observational one
estimated from measurements of standard candles, i.e., type Ia supernovae (SNe
Ia) and gamma-ray bursts (GRBs). Methodologically, we first determine the
light-curve fitting parameters which account for distance estimation in SNe Ia
observations and luminosity/energy relations which are responsible for distance
estimation of GRBs in the global fit to reconstruct the Hubble diagrams in the
context of a clumpy universe. Subsequently, these Hubble diagrams allow us to
achieve unbiased constraints on the matter density parameter $\Omega_m$ as well
as clumpiness parameter $\eta$ which quantifies the fraction of homogeneously
distributed matter within a given light cone. At 1$\sigma$ confidence level,
the constraints are $\Omega_m=0.34\pm0.02$ and $\eta=1.00^{+0.00}_{-0.02}$ from
the joint analysis. The results suggest that the universe full of
Friedman-Lema\^{i}tre-Robertson-Walker fluid is favored by observations of
standard candles with very high statistical significance. On the other hand,
they may also indicate that the Zel'dovich-Kantowski-Dyer-Roeder approximation
is a sufficient accurate form to describe the effects of local homogeneity in
the expanding universe.
