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.

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