Model-independent constraints on Lorentz invariance violation:
  implication from updated Gamma-ray burst observations
  Astrophysical observations provide a unique opportunity to test possible
signatures of Lorentz Invariance Violation (LIV), due to the high energies and
long distances involved. In quantum theory of gravity, one may expect the
modification of the dispersion relation between energy and momentum for
photons, which can be probed with the time-lag (the arrival time delay between
light curves in different energy bands) of Gamma-ray bursts (GRBs). In this
paper, by using the detailed time-delay measurements of GRB 160625B at
different energy bands, as well as 23 time-delay GRBs covering the redshifts
range of $z=0.168-2.5$ (which were measured at different energy channels from
the light curves), we propose an improved model-independent method (based on
the newly-compiled sample of $H(z)$ measurements) to probe the energy-dependent
velocity due to the modified dispersion relation for photons. In the framework
of a more complex and reasonable theoretical expression to describe the time
delays, our results imply that the intrinsic time lags can be better described
with more GRBs time delay data. More importantly, through direct fitting of the
time-delay measurements of a sample of GRBs, our limit on the LIV energy scale
is comparable to that with unknown constant for the intrinsic time lag, much
lower than the Planck energy scale in both linear LIV and quadratic LIV cases.
