  Dirac, in 1937 proposed the variation of coupling constants derived from his
large number hypothesis. Efforts have continued since then to constrain their
variation by various methods. We briefly discuss several methods used for the
purpose while focusing primarily on the use of supernovae type 1a, quasars, and
gamma-ray bursts (GRBs) as cosmological probes for determining cosmological
distances. Supernovae type Ia (SNeIa) are considered the best standard candles
since their intrinsic luminosity can be determined precisely from their light
curves. However, they have only been observed up to about redshift $z=2.3$,
mostly at $z<1.5$. Quasars are the brightest non-transient cosmic sources in
the Universe. They have been observed up to $z=7.5$. Certain types of quasars
can be calibrated well enough for their use as standard candles but with a
higher degree of uncertainty in their intrinsic luminosity than the SNeIa. GRBs
are even brighter than quasars, observed up to $z=9.4$. Their radiation lasts
from 10s of milliseconds to several minutes and, in rare cases, for a few
hours. However, they are even more challenging to calibrate as standard candles
than quasars. What if the standard candles' intrinsic luminosities are affected
when the coupling constants become dynamic? This paper uses our earlier finding
that the speed of light c, the gravitational constant G, the Planck constant h,
and the Boltzmann constant k variations are correlated as $G\thicksim
c^{3}\thicksim h^{3}\thicksim k^{3/2}$ with
$(\dot{G}/G)_{0}=3(\dot{c}/c)_{0}=(\dot{h}/h)_{0}=1.5 (\dot{k}/k)_{0}=5.4H_{0}
=3.90(\pm 0.04)\times 10^{-10} yr^{-1}$ corroborates it with SNeIa, quasars,
and GRBs observational data. Also, we show that this covarying coupling
constant model may be better than the standard {\Lambda}CDM model for using
quasars and GRBs as standard candles and predict the mass of the GRBs scales as
$((1+z)^{1/3}-1)$.
