We study the possibility of having HDE as the source of inflation in the
frame of $f(R,T)$ gravity theory. The length scale of the energy density is
taken as the GO cutoff, which is a combination of the Hubble parameter and its
time derivative. It is found that for a specific range of the free parameters
of the model, the scalar spectral index and the tensor-to-scalar ratio stand in
good agreement with data. Also, by reconstructing the potential in terms of the
scalar field, the validity of the swampland criteria is considered. The results
indicate that to have a scalar field below the Planck mass, the parameter
$\lambda$ should be at least of the order of $\mathcal{O}(10^2)$. The same
order of $\lambda$ is required to keep the gradient of the potential greater
than one and satisfy the second conjecture of the swampland criteria.
