Interacting DBI essence in viscous f(T) gravity for different choices of scale factor and thermodynamics with power-law and logarithmic entropy corrections

From the hydrodynamic viewpoint, the inclusion of viscosity in the theory of cosmic fluid may appear as an abstraction. Using modern observational results for the Hubble parameter and standard Friedmann formalism, we may have a description of the universe up to the inflationary era, or we may be able to analyse the probable ultimate fate of the universe. Inspired by this bulk viscosity formalism reviewed in Brevik et al., (2017) in this work, we report a study of the DBI essence scalar field model of dark energy (DE) interacting with pressureless dark matter (DM) in the presence of bulk viscous pressure of the form ξ=ξ0+ξ1H+ξ2(Ḣ+H2). We choose the scale factor in three forms: emergent, logamediate, and intermediate. We choose the interaction term Q in the form Q=3HδρΛ, where ρΛ denotes the density of the scalar field model of DE. We present a detailed cosmology of the interacting DE and observe a quintom behaviour of the equation of state (EoS). We conduct a statefinder analysis to attain ΛCDM fixed point by the interacting DE. Subsequently, we report a reconstruction scheme for f(T) gravity. Finally, we conduct thermodynamic analysis where we consider entropy’s logarithmic and power-law corrections.