Observational constraints on a damped harmonic oscillator model of dark energy

We constrain a damped harmonic oscillator (DHO) dark-energy equation of state using the full cosmic microwave background (CMB) likelihoods in combination with DESI BAO and three distinct Type Ia supernova compilations: Pantheon+, DES-Dovekie, and Union3. The equation of state obeys a second-order damped oscillator equation in number of e-folds, so that its frequency f, damping rate b, and equilibrium value w m fully specify the late-time dynamics. The model exhibits oscillatory behavior only at low redshifts, around the equilibrium value w=-1, with distinct characteristics for the different supernova compilations: an underdamped solution for DES-Dovekie and Union3, and an overdamped solution for Pantheon+. At higher redshifts, the model closely mimics Λ CDM and deviates significantly only at z<0.6, with the magnitude of the deviation depending on the supernova compilation. We further identify a region of the (f,b) parameter space, corresponding to rapid variation of the equation of state at low redshift, in which the perturbation equations become numerically stiff and cannot be integrated with a canonical dark-energy sound speed i.e., c s squared =1. We show that reducing the rest-frame sound speed removes this obstruction while leaving the observables unchanged at the 10-3 level, and therefore treat it as a numerical prescription rather than a physical modification of the model. The model yields H 0 = 67.53+1.22-1.18 km/s/Mpc for Pantheon+, H 0 = 69.08+1.23-1.16 km/s/Mpc for DES-Dovekie, and H 0 = 70.67+1.89-1.87 km/s/Mpc for Union3. The present-day equation-of-state parameter is constrained to w 0 = -0.521+0.891-0.414, -3.01+1.14-1.21, and-3.16+1.11-1.16 for Pantheon+, DES-Dovekie, and Union3, respectively.