  We study the inflationary scenario in the Tsallis entropy-based cosmology.
The Friedmann equations in this setup can be derived by using the first law of
thermodynamics. To derive the relations of the power spectra of the scalar and
tensor perturbations in this setup, we reconstruct an $f(R)$ gravity model
which is thermodynamically equivalent to our model in the slow-roll
approximation. In this way, we find the inflationary observables, including the
scalar spectral index and the tensor-to-scalar ratio in our scenario. Then, we
investigate two different potentials in our scenario, including the quadratic
potential and the potential associated with the natural inflation in which the
inflaton is an axion or a pseudo-Nambu-Goldstone boson. We examine their
observational viability in light of the Planck 2018 CMB data. We show that
although the results of these potentials are in tension with the observations
in the standard inflationary setting, their consistency with the observations
can be significantly improved within the setup of the Tsallis entropy-based
inflation. Moreover, we place constraints on the parameters of the considered
inflationary models by using the current observational data.
