We use the spectral lag data of 32 long GRBs detected by Fermi/GBM, which has been recently collated in Liu et al. (2022) to quantify the statistical significance of a transition in the spectral lag data based on Lorentz invariance violation (LIV) (for both sub-luminal and super-luminal propagation) using Bayesian model selection. We use two different parametric functions to model the null hypothesis of only intrinsic emission: a smooth broken power law model (SBPL) (proposed in Liu et al. (2022)) as well as a simple power law model, which has been widely used before in literature. We find that for sub-luminal propagation, when we use the SBPL model as the null hypothesis, five GRBs show “decisive evidence” based on Jeffreys' scale for linear LIV and quadratic LIV. When we use the simple power-law model as the null hypothesis, we find that 10 and 9 GRBs show Bayesian “decisive evidence” for linear and quadratic LIV, respectively. However these results should not be construed as evidence for LIV, as they would be in conflict with the most stringent upper limits. When we did a test for super-luminal LIV, we find that only four and two GRBs show Bayesian “decisive evidence” for linear and quadratic LIV, respectively, assuming a simple power law for the intrinsic emission. When we use the SBPL model, one GRB shows Bayesian “decisive evidence” for linear and quadratic LIV. This underscores the importance of adequately modeling the intrinsic emission while obtaining constraints on LIV using spectral lags, since inadequate modeling could masquerade as a signature of LIV.
Interacting dark energy models may play a crucial role in explaining several important observational issues in modern cosmology and also may provide a solution to current cosmological tensions. Since the phenomenology of the dark sector could be extremely rich, one should not restrict the interacting models to have a coupling parameter which is constant in cosmic time, rather allow for its dynamical behaviour, as it is common practice in the literature when dealing with other dark energy properties, as the dark energy equation of state. We present here a compendium of the current cosmological constraints on a large variety of interacting models, investigating scenarios where the coupling parameter of the interaction function and the dark energy equation of state can be either constant or dynamical. For the most general schemes, in which both the coupling parameter of the interaction function and the dark energy equation of state are dynamical, we find 95% CL evidence for a dark energy component at early times and slightly milder evidence for a dynamical dark coupling for the most complete observational data set exploited here, which includes CMB, BAO and Supernova Ia measurements. Interestingly, there are some cases where a dark energy component different from the cosmological constant case at early times together with a coupling different from zero today, can alleviate both the and tension for the full dataset combination considered here. Due to the energy exchange among the dark sectors, the current values of the matter energy density and of the clustering parameter are shifted from their ΛCDM-like values. This fact makes future surveys, especially those focused on weak lensing measurements, unique tools to test the nature and the couplings of the dark energy sector.