Reheating constraints on k-inflation

In this work we revisit constraints on k-inflation with a Dirac-Born-Infeld (DBI) kinetic term and a power-law kinetic term from reheating. For the DBI kinetic term we choose monomial potentials, V proportional to phi(n) with n = 2/3, 1, 2, and 4, and natural inflaton potential, and for the power-law kinetic term we choose quadratic, quartic, and exponential potentials. The phase of reheating can be parametrized in terms of the reheating temperature, T-re, the number of e-folds during reheating N-re, and the effective equation of state during reheating w(re). These parameters can be related to the spectral index n(s) and other inflationary parameters depending on the choice of inflaton kinetic term and potential. By demanding that wre should have a finite range and T-re should be above the electroweak scale, one can obtain bounds on ns that can provide bounds on the tensor-to-scalar ratio, r. We find, for k-inflation with a DBI kinetic term, and quadratic and quartic potentials, that the upper bound on r for the physically plausible value of 0 <= w(re) <= 0.25 is slightly larger than the Planck 2018 and BICEP2/Keck array bound, and for n = 2/3 and 1, the reheating equation of state should be less than 0 to satisfy Planck 2018 joint constraints on ns and r. However, natural inflation with the DBI kinetic term is compatible with Planck 2018 bounds on r and joint constraints on ns and r for the physically plausible range 0 <= w(re) <= 0.25. The quadratic and quartic potential with a power-law kinetic term are also compatible with Planck 2018 joint constraints on ns and r for 0 <= w(re) <= 1. However, for an exponential potential with a power-law kinetic term, the equation of state during reheating, wre, should be greater than 1 for r - n(s) predictions to lie within 68% C.L. of joint constraints on n(s) and r from Planck 2018 observations.