Cosmology of axion dark energy in supersymmetric models and constraints on high-scale parameters

An analysis is given of interacting dark energy and dark matter where the dark energy is assumed to be an ultralight axionic field with a pseudo-Nambu-Goldstone boson potential, which is in general a superposition of $N$ number of cosine terms motivated by supergravity and string models with a $U(1)$ global symmetry, where the symmetry is broken by instanton effects. The case $N=2$ is investigated in detail and a fit to cosmological data is performed, where it is found that a better fit is obtained in comparison with the $N=1$ case. The fits also constrain high-scale parameters, i.e., the axion decay constant which is determined to be sub-Planckian, a result consistent with string theory that disfavors the trans-Planckian axion decay constant. Furthermore, the dark energy--dark matter interaction strength is constrained to be feeble, i.e., $\ensuremath{\lambda}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\text{ }{\mathrm{m}}_{\mathrm{Pl}}^{\ensuremath{-}2}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}2}$. We study possible implications of this type of potential on the Hubble tension and on the dynamics of the dark energy equation of state using the Dark Energy Spectroscopic Instrument DR2 data. For the cases $N=3$, 4, the analysis exhibits the phenomenon of transmutation even in the absence of coupling to dark matter, where thawing quintessence transmutes to freezing quintessence. The analysis is internally consistent in its treatment of the dark energy--dark matter interaction, as it is based on an underlying Lagrangian, in contrast with several previous works where the sources are chosen in an ad hoc manner to satisfy energy conservation.