*3.4. Variation of Micro-Physical Parameters with Time*

Thanks to the increasing number of available observations on a wide range of frequencies (from radio to TeV) and times (from seconds to weeks), the basic assumption that micro-physical parameters (such as *e<sup>e</sup>* , *e<sup>e</sup>* , *p* and *ξe*) are constant over the whole afterglow evolution can be tested. We comment on the hints (inferred from afterglow modeling) for temporal evolution of these parameters.

In case of well-sampled multi-wavelength light-curves, the modeling with synchrotron spectra is able not only to identify the location of the spectral breaks at a certain time but also evaluate their evolution in time. As a result, hints that micro-physical parameters *e<sup>e</sup>* and *e<sup>B</sup>* may vary with time have been found in some events with well-detailed multi-wavelength follow-up campaigns.

In [115], broad-band (from near infrared up to X-ray) afterglow data from GRB 091127 were interpreted in the standard external forward shock scenario assuming a constantdensity medium. The good quality of the data allows one to identify the breaks in the light-curves and associate them with the synchrotron spectral breaks. As a result, the time evolution of the synchrotron breaks was estimated. In particular, it was calculated that the cooling break frequency *νcool* evolves as *νcool* ∝ *t* −1.2, which is in contrast with synchrotron predictions for which a less steeper decay *νcool* ∝ *t* <sup>−</sup>0.5 is expected. As a result, some assumptions of the standard model must be relaxed to remove the tension between observations and theoretical predictions. The most likely option able to explain the cooling break observational behavior without affecting the general interpretation of the data is to let the *e<sup>B</sup>* parameter variate with time. Assuming that *e<sup>B</sup>* ∝ *t* 0.49 the time evolution of *νcool* can be explained successfully.

In [116] for GRB 130427A modeling, in order to explain the observed fast evolution of the injection frequency *ν<sup>m</sup>* ∝ *t* <sup>−</sup>1.9, a temporal evolution of *e<sup>e</sup>* is claimed. Considering that *ν<sup>m</sup>* ∝ *e* 2 *e* , a modest evolution of *e<sup>e</sup>* following the trend *e<sup>e</sup>* ∝ *t* <sup>−</sup>0.2 is able to satisfactorily describe the observed light-curves.

A time-dependent evolution of the micro-physical parameters has also been proposed in order to explain the features observed in the early afterglow phase, which are not predicted by the external forward shock scenario such as X-ray afterglow plateaus, chromatic breaks, and afterglow rebrightenings [117–120].

Information from TeV observations can be certainly exploited in order to reduce the uncertainty on the values of the micro-physical parameters. The expansion of the broad band afterglow observations to a new spectral window will be a further test and a challenge for the multi-wavelength modeling based on the standard external forward shock scenario. In particular, the time evolution of the different energetic components, also including TeV emission, will give new insights useful to investigating the evolution of the micro-physical parameters. A first proof is provided by the well-sampled multiwavelength emission observed for GRB 190114C, one of the few GRBs detected so far at TeV energies. The broadband emission can be explained only by invoking the evolution of the micro-physical parameters with time [121], as will be discussed in the next section.
