D-term inflation in braneworld models: Consistency with cosmic-string bounds and early-time Hubble tension resolving models

We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $\mathrm{\Lambda }$CDM model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=\lambda =0.1$) can be achieved in the case of D-term inflation on the brane.