Addressing the High-$f$ Problem in Pseudo-Nambu-Goldstone Boson Dark Energy Models with Dark Matter - Dark Energy Interaction

We consider a dark energy scenario driven by a scalar field $phi$ with a pseudo Nambu Goldstone boson (pNGB) type potential $V(phi)=mu^4 left( 1+ {rm cos}(phi/f) right)$. The pNGB originates out of breaking of spontaneous symmetry at a scale $f$ close to Planck mass $M_{rm{pl}}$. We consider two cases namely the quintessence dark energy and the other, where the standard pNGB action is modified by the terms related to Slotheon cosmology. We demonstrate that for this pNGB potential, high-$f$ problem is better addressed when interaction between dark matter and dark energy is taken into account and that Slotheon dark energy scenario works even better over quintessence in this respect. To this end, a mass limit for dark matter is also estimated.