*5.7. Binning Procedure*

In several cases, it is useful to get constraints directly on the universe equation of state. Thus, fitting it for the late-time universe constituents is extremely important to understand the dark energy evolution. In particular, pointing out a possible variation of the equation of state of dark energy is essential to *disentangle* the standard model predictions from possible theoretical extensions and, in this respect, GRBs can be seen as intermediate redshift probes to disclose such an evolution.

To do that, an intriguing strategy consists of binning the dark energy equation of state, say *w*, in short intervals of *z* and then fit *w* in each bin, assuming it is constant in each bin. Indicating with a generic function *f*(*z*) the dark energy evolution, we have

$$f(z\_{n-1} < z \le z\_n) = (1+z)^{3(1+w\_n)} \prod\_{i=0}^{n-1} (1+z\_i)^{3(w\_i - w\_{i+1})},\tag{38}$$

where *w<sup>i</sup>* is the barotropic factor within the *i* th redshift bin. The bin is built up by an upper boundary at *z<sup>i</sup>* , whereas the zeroth bin is defined as *z*<sup>0</sup> = 0.

Therefore, uncorrelated sub-equations of state in every bin can be experimentally refined adding data points and, in particular, GRBs, being calibrated as we will discuss later. Several indications have shown good agreement with the standard paradigm, up to *z* ' 9, albeit relevant deviations have been found, indicating that the situation is not still clear.

## **6. Standardizing GRBs**

Being successful in standardizing GRB data is of utmost importance to characterize new data catalogs up to high redshifts. In particular, getting redshifts, or more generally spectroscopic observations, is essential for GRB-related science, as we summarized below:


#### *6.1. GRB Correlations and Related Issues*

Since the first discovery of GRBs independent groups has found different correlations that represent a key to using GRBs for cosmological purposes, the basic idea is to intertwine different quantities of such objects among them. The observable quantities of interest are in relation with the cosmological model that lies on the background. This fact permits GRBs to be distance indicators at a first glance but limits their use because it requires postulating the underlying cosmological model, providing a circularity in the process itself, which is known as the circularity problem.

The widest majority of GRB correlations prompts the same requirement: the GRB standardization in terms of cosmological tools. Attempts for new correlations have been severely investigated, relating different observable quantities with each other. The way in which this is realized provides the theoretical interpretation behind the relation itself. In other words, evidence for a given correlation leads to interpreting particular physical processes. Thus, achieving the goal of standardizing GRBs brings the certainty of getting feasible bounds on cosmological parameters. Intriguingly, a narrow set of correlations enables one to also estimate GRB redshifts. Even though this is still under speculation, in general, a wide number of correlations could provide information about GRB progenitors.

More precisely, standardizing GRBs for cosmological purposes aims at reaching further hints toward progenitors of *different groups of GRBs*. Multi-wavelength instruments of recently-adopted satellites have significantly increased the number of GRBs that could be observed to check the validity of a given relation. Thus, it is even possible that a few correlations may be derived from experimental evidence, instead of theoretically. Unfortunately, this could open further issues related to data processing whose outputs can be biased in the overall computations.

Going ahead, it is certainly possible to constantly observe new hints undertaking novel correlations to allow free theoretical speculations that deeply probe into new physics beyond the standard comprehension of GRBs.
