Hubble diagram of gamma-ray bursts and prevalence of energy conditions   in Friedmann-Lema\^itre-Robertson-Walker Cosmology
  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. 
Herman J. Mosquera Cuesta, Carlos A. Bonilla Quintero, M. Habib Dumet,   Cristina Furlanetto, Jefferson Morais, Rodrigo Turcati