The KSVZ Axion Model with Quasi-Degenerate Minima: A Unified Model for Dark Matter and Dark Energy

We consider the possibility that dark matter and dark energy can be explained by the minimal KSVZ axion model. This is possible if the lowest energy metastable minimum of the scalar potential has zero energy density, which is possible in theoretical models of vacuum energy cancellation based on spacetime averaging and in models based on energy parity. Dark energy is then understood as being due to the energy density of the metastable electroweak vacuum relative to a second quasi-degenerate metastable minimum. The requirement of quasi-degenerate minima is a non-trivial condition which completely determines the form of the potential for a given value of the axion decay constant, $f_{a}$, and the PQ scalar self-coupling, $\lambda_{\phi}$. The existence of the second quasi-degenerate minimum imposes a new lower bound on the axion decay constant, $f_{a} \geq 2.39 \times 10^{10} \, \lambda_{\phi}^{-1/4}$ GeV. If the PQ symmetry is broken after inflation then the lower bound on $f_{a}$ implies a lower bound on the amount of axion dark matter, $\Omega_{a}/\Omega_{dm} \geq (0.28-0.46)\,\lambda_{\phi}^{-0.291}$, where the range is due to the uncertainty in the amount of axion dark matter produced by vacuum realignment, cosmic strings and domain walls, therefore at least 30$\%$ of dark matter must be due to axions if $\lambda_{\phi} \lesssim 1$. When axions constitute all of the dark matter and the PQ symmetry is broken after inflation, $f_{a}$, and so the form of the scalar potential, is completely fixed for a given value of $\lambda_{\phi}$, with only a weak dependence on $\lambda_{\phi}$. This will allow the inflation and post-inflation evolution of the model to be quantitatively studied for a given inflation model and dimensionally natural values of $\lambda_{\phi}$.