Correspondence between particle creation and dark components interaction in the context of f(𝒢) gravity

In this paper, we explore the particle creation scenario in the context of [Formula: see text] gravity in flat-FLRW metric. For this purpose, from the perspective of thermodynamics and considering an adiabatic universe, we obtain the modified continuity equation in terms of the dynamic number of particles [Formula: see text]. On the other hand, we obtain Friedmann’s equations in [Formula: see text] gravity and then write down the continuity equations of the components of matter and dark energy, taking into account the interaction between them. In what follows, by establishing a correspondence between the particle production scenario and [Formula: see text] gravity, we obtain the cosmological parameters in terms of [Formula: see text]. After that, we find cosmological solutions using power-law cosmology and compare them with Hubble parameter data. Finally, we fit the current model with Hubble data and plot the best fit in terms of the redshift parameter.