  In this {\sl Letter} we construct the Hubble diagram (HD) for the standard
Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological model after enforcing
it with the general relativistic energy conditions, heeding to investigate
whether it still stands on as the leading scenario for cosmology in face of the
distance modulus-redshift relation of a sample of GRBs that had their redshifts
properly estimated and corrected upon applying on the data analysis the {\sl
Ghirlanda relation} (Ghirlanda et al. 2004) and the recently discovered {\sl
Firmani et al. relation} (Firmani et al. 2006a). Our $\chi^2$ analysis support
the view that FLRW plus the strong energy condition (SEC) is what better fits
the GRB data. But this is not the whole story, since for a cosmological
constant $\Lambda \neq 0$ the FLRW+SEC analysis with undefined $p=p(\rho)$
suggests that $\Lambda$ is not constant anyhow, because it does not follows the
$p= \omega \rho$ HD, with $\omega=-1$. Thenceforth, one concludes that either
the cosmological constant does not exist at all, and consequently one is left
with the FLRW+SEC which fits properly the GRBs HD and there is no late-time
acceleration, or it does exist but should be time-varying. This all is contrary
to current views based on SNIa observations that advogate for an actual
constant $\Lambda$ and an accelerating universe. In connection to the results
above, this last argumentation would imply that either there is something wrong
with the SNIa interpretation regarding cosmic late-time acceleration
(Middleditch 2006) or we will have to move away from general relativity. We
would better to think that general relativity is still the most correct theory
of gravity.
