**1. Introduction**

Gamma-ray bursts (GRBs) represent powerful extra-galactic transient that emit in *γ*-rays [1,2]. They are commonly associated with the death of massive stars or with binary compact object mergers. As expected, due to their enormous luminosity, after the aforementioned processes, there would be the presence a newborn stellar mass black hole (BH) that provides particle accelerations and emits a relativistic collimated outflow, in the form of jets. At the same time, this new system furnishes non-thermal emissions at almost all wavelengths. The above picture lies on the standard model describing GRBs and requires isotropic energies in the range 1044–10<sup>47</sup> J, or 1051–10<sup>54</sup> erg, mostly larger than the brightest supernova (SN) emission, lying on 10<sup>42</sup> J, or 10<sup>49</sup> erg [3,4]. Thereby, the need of singling out GRB progenitors is essential to disclose their fundamental properties as well as the physical conditions that permit relativistic jets to form and accelerate. Even though a clear landscape for GRB progenitor is still unclear, in view of their duration, it is plausible to classify GRBs into long and short ones.

**Citation:** Luongo, O.; Muccino, M. A Roadmap to Gamma-Ray Bursts: New Developments and Applications to Cosmology. *Galaxies* **2021**, *9*, 77. https://doi.org/10.3390/ galaxies9040077

Academic Editors: Elena Moretti and Francesco Longo

Received: 30 June 2021 Accepted: 7 October 2021 Published: 12 October 2021

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Clearly, in our *Precision Cosmology*, epoch GRBs could open new windows<sup>1</sup> toward the universe description at intermediate redshifts<sup>2</sup> [5–7], i.e., much larger than SN ones [8]. Thus, several new observations have been developed, with always better accuracy, trying to standardize GRBs and to handle their emissions in analogy to SNe. In general, the most tricky challenge for cosmology is measuring distances and arguing luminosity in the cosmic scenario, understanding from astronomical emission at which distance the emitter is placed [9].

Unfortunately, this is not exactly the case of GRBs that are not standard candles, i.e., they do not provide the above requirement on distance and luminosity [10,11]. In fact, their highly variable *γ*-ray emission, mostly evident during the prompt phase, is thought to be associated with jet internal energy dissipation. However, the jet kinematics, among all its speed, collimation, energy, magnetization, etc., are all properties not well clarified, as well as energy dissipation mechanisms and/or shock acceleration efficiency. Hence, it is hard to relate luminosity to GRB distances as their microphysics is not well understood. Although the above caveats plague the overall GRB scenario, both short and long GRBs have relativistic outflows and share analogous properties<sup>3</sup> and many attempts have been spent to standardize GRBs for both clarifying their nature, internal structure, and origin together with employing these objects for cosmological purposes [12,13].

In this review, we first introduce the concept of GRB and their main observable quantities. As stated above, according to time duration, we introduce the role of the *t*<sup>90</sup> duration to classify GRBs following the standard guidelines and underline the issues related to such a classification, e.g., ultra-long GRBs and X-ray flashes. To this end, we introduce the concepts of GRB progenitor, showing quantitatively the physical reasons that limit GRBs to be fully considered as genuine standard candles. However, we also emphasize how using luminosity correlations found in prompt and afterglow phases would be useful to characterize some sort of standardization technique. In this respect, we portray the main observable quantities coming from GRBs and deeply introduce the standard picture of GRB formation and evolution, dubbed the *fireball model*.

From all the above aspects, we expect GRBs to able to reconcile the cosmic expansion history at small and intermediate redshifts, connecting de facto late with early times, trying to open new windows toward the comprehension of cosmology. We therefore explain how GRBs serve as complementary probes to frame DE and cosmic expansion throughout the universe evolution, together with other standard candles, e.g., type Ia SN (SNeIa), baryonic acoustic oscillation (BAO), cosmic microwave background (CMB), Hubble differential data, etc. We show how to combine such data sets with GRBs and write the main features of experimental analysis for cosmological purposes. Great emphasis will be devoted to the circularity problem that essentially plagues cosmology with GRBs. Once introduced, we also underline strategies that do not take into account its role for fitting cosmological models with GRBs.

Hence, we provide how to challenge the standard cosmological model, namely the ΛCDM paradigm, with GRBs. To do so, we provide the main and evident features of cosmology with GRBs by showing how to perform error analyses, Bayesian treatments, and how to handle systematics for several GRB correlations. We therefore develop model dependent and independent techniques of calibrations and report a few numerical outcomes related to GRBs, showing the most recent cosmological bounds, found with distinct procedures.

The review is split as follows. After this short introduction, in Section 2, we classify GRBs and we report the most interesting properties, among all the classification, the progenitors, and the main observable quantities coming from GRBs. In Section 3, we work out the standard GRB model, namely the fireball paradigm. Here, we also discuss about particle and radiative processes, giving emphasis to the possible emissions coming from GRBs. In Section 4, we start introducing the concept of cosmology with GRBs. We thus highlight distance indicators and the concept of standard candles. In Section 5, we explain in detail the experimental tools useful for getting Bayesian analysis with GRBs. Finally, in Section 6, we provocatively report the concept of standardizing GRBs to permit those

objects to be used in the same manner as other probes. Several issues have been raised in Section 7, although likely the most serious one, the circularity problem, is described in detail in Section 8, where we also stress the opposite view in which one can also avoid calibration. Last but not least, we report the most recent developments of cosmology with GRBs in Section 9, while we conclude our journey in Section 10 with our final outlooks and perspectives of this work.
