  LambdaCDM, for the currently preferred cosmological density Omega_0 and
cosmological constant Omega_Lambda, predicts that the Universe expansion
decelerates from early times to redshift z~0.9 and accelerates at later times.
On the contrary, the cosmological model based on conformal gravity predicts
that the cosmic expansion has always been accelerating. To distinguish between
these two very different cosmologies, we resort to gamma-ray bursts (GRBs),
which have been suggested to probe the Universe expansion history at z>1, where
identified type Ia supernovae (SNe) are rare. We use the full Bayesian approach
to infer the cosmological parameters and the additional parameters required to
describe the GRB data available in the literature. For the first time, we use
GRBs as cosmological probes without any prior information from other data. In
addition, when we combine the GRB samples with SNe, our approach neatly avoids
all the inconsistencies of most numerous previous methods that are plagued by
the so-called circularity problem. In fact, when analyzed properly, current
data are consistent with distance moduli of GRBs and SNe that can respectively
be, in a variant of conformal gravity, ~15 and ~3 magnitudes fainter than in
LambdaCDM. Our results indicate that the currently available SN and GRB samples
are accommodated equally well by both LambdaCDM and conformal gravity and do
not exclude a continuous accelerated expansion. We conclude that GRBs are
currently far from being effective cosmological probes, as they are unable to
distinguish between these two very different expansion histories.
