In this paper, the application of entropy cosmology in describing cosmic inflation is investigated. Our research is based on a new multi-parameter generalized entropy, which can generalize all the known entropies proposed so far, for suitable representations of the entropic parameters. We investigated a cosmological model of an inflationary universe under a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) metric by using different forms of thermodynamic parameters and bulk viscosity in the equation of state (EoS). We employ the holographic description based on generalized infrared cut-off proposed by Nojiri and Odintsov to solve the equations of motion for gravity, and calculate the scale factor and the infrared cut-off with the future or particle horizon as parameters. The representation of the energy conservation from the holographic point of view is obtained. The corrections in the energy conservation equation related to the multi-parameter generalized entropy function allow creating more detailed picture of the evolution of the universe. Finally, the correspondence between spectral indices, tensor-to-scalar ratio, and the recent astronomical observation data from the Planck satellite is also discussed.
Chen et al. (Thu,) studied this question.