Quantum Gravity Effects on the Tachyon Inflation from Thermodynamic Perspective

Abstract: By considering the Friedmann equations emerging from the entropy-area law of black hole thermodynamics in the context of the generalized uncertainty principle, we study tachyon inflation in the early universe. The presence of a minimal length modifies the Friedmann equations and hence the slow-roll and perturbation parameters in the tachyon model. These modifications, though small, affect the viability of the tachyon inflation in confrontation with observational data. We compare the numerical results of the model with Planck2018 TT, TE, EE +lowE+lensing+BAO+BK14(18) data and Planck2018 TT, TE,EE +lowE+lensing+BK14(18) +BAO+LIGO $&$ Virgo2016 data at $68\%$ and $95\%$ CL. We show that while the tachyon inflation with power-law, inverse power-law and inverse exponential potentials is not observationally viable in comparison with the $1\sigma$ and $2\sigma$ confidence levels of the new joint data, in the presence of the minimal length the model becomes observationally viable.