Constraints on the transition redshift from the calibrated Gamma-ray Burst $E_{\rm p}$-$E_{\rm iso}$ correlation

TL;DR

This paper uses model-independent techniques with calibrated gamma-ray burst correlations and observational data to constrain the epoch of transition from deceleration to acceleration in the universe, confirming compatibility with the Lambda-CDM model.

Contribution

It introduces a novel calibration of the $E_{p}$-$E_{iso}$ correlation using Bézier polynomial interpolation and applies it to constrain the transition redshift and jerk parameter.

Findings

Constraints on $z_{tr}$ are consistent with previous results.

Results support the $ ext{Lambda}$CDM model predictions.

The jerk parameter shows slight deviations from standard cosmology.

Abstract

We constrain the deceleration-acceleration epoch, namely the transition redshift $z_{tr}$, adopting model-independent techniques that utilize a calibrated $E_{\rm p}$-$E_{\rm iso}$ correlation for gamma-ray bursts (GRBs). To do so, in addition to real data points, we employ up to $1000$ simulated observational Hubble data (OHD) points. We then calibrate the $E_{\rm p}$-$E_{\rm iso}$ correlation by means of the well-consolidate B\'ezier polynomial technique, interpolating OHD up to the second order. Once GRB data have been calibrated, we consider two strategies of cosmographic expansions, i.e., first we take a direct Hubble rate expansion around $z_{tr}$, and second the expansion of the deceleration parameter around the same redshift, but with a different order. Employing type Ia supernovae, baryonic acoustic oscillations and GRB data sets, from Monte Carlo analyses we infer tight constraints on $z_{tr}$ and the jerk parameters at $z=z_{tr}$, namely $j_{tr}$. Our results are extremely compatible with previous outcomes and confirm the $\Lambda$CDM predictions, being slightly different in terms of the jerk parameter. In this respect, we conjecture which extensions of the concordance paradigm are possible and we compare our findings with expectations provided by generic dark energy models.