Slope evolution of GRB correlations and cosmology
  Gamma -ray bursts (GRBs) observed up to redshifts $z>9.4$ can be used as
possible probes to test cosmological models. Here we show how changes of the
slope of the {\it luminosity $L^*_X$ -break time $T^*_a$} correlation in GRB
afterglows, hereafter the LT correlation, affect the determination of the
cosmological parameters. With a simulated data set of 101 GRBs with a central
value of the correlation slope that differs on the intrinsic one by a $5\sigma$
factor, we find an overstimated value of the matter density parameter,
$\Omega_M$, compared to the value obtained with SNe Ia, while the Hubble
constant, $H_0$, best fit value is still compatible in 1$\sigma$ compared to
other probes. We show that this compatibility of $H_0$ is due to the large
intrinsic scatter associated with the simulated sample. Instead, if we consider
a subsample of high luminous GRBs ($HighL$), we find that both the evaluation
of $H_0$ and $\Omega_M$ are not more compatible in 1$\sigma$ and $\Omega_M$ is
underestimated by the $13\%$. However, the $HighL$ sample choice reduces
dramatically the intrinsic scatter of the correlation, thus possibly
identifying this sample as the standard canonical `GRBs' confirming previous
results presented in Dainotti et al. (2010,2011). Here, we consider the LT
correlation as an example, but this reasoning can be extended also for all
other GRB correlations. In literature so far GRB correlations are not corrected
for redshift evolution and selection biases, therefore we are not aware of
their intrinsic slopes and consequently how far the use of the observed
correlations can influence the derived `best' cosmological settings. Therefore,
we conclude that any approach that involves cosmology should take into
consideration only intrinsic correlations not the observed ones.
