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Gamma -ray bursts (GRBs) observed up to redshifts $z>9.4$ can be used aspossible probes to test cosmological models. Here we show how changes of theslope of the {\it luminosity $L^*_X$ -break time $T^*_a$} correlation in GRBafterglows, hereafter the LT correlation, affect the determination of thecosmological parameters. With a simulated data set of 101 GRBs with a centralvalue 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 Hubbleconstant, $H_0$, best fit value is still compatible in 1$\sigma$ compared toother probes. We show that this compatibility of $H_0$ is due to the largeintrinsic scatter associated with the simulated sample. Instead, if we considera subsample of high luminous GRBs ($HighL$), we find that both the evaluationof $H_0$ and $\Omega_M$ are not more compatible in 1$\sigma$ and $\Omega_M$ isunderestimated by the $13\%$. However, the $HighL$ sample choice reducesdramatically the intrinsic scatter of the correlation, thus possiblyidentifying this sample as the standard canonical `GRBs' confirming previousresults presented in Dainotti et al. (2010,2011). Here, we consider the LTcorrelation as an example, but this reasoning can be extended also for allother GRB correlations. In literature so far GRB correlations are not correctedfor redshift evolution and selection biases, therefore we are not aware oftheir intrinsic slopes and consequently how far the use of the observedcorrelations can influence the derived `best' cosmological settings. Therefore,we conclude that any approach that involves cosmology should take intoconsideration only intrinsic correlations not the observed ones.

Slope evolution of GRB correlations and cosmology