Observational constraints on a damped harmonic oscillator model of dark energy

Abstract: 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 $w_{\rm m}$ 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 $z&lt;0.6$, 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., $c_s² =1$. We show that reducing the rest-frame sound speed removes this obstruction while leaving the observables unchanged at the $10<sup>{-3}$ level, and therefore treat it as a numerical prescription rather than a physical modification of the model. The model yields $H_0 = 67.53<sup>{+1.22}_{-1.18}$ km/s/Mpc for Pantheon+, $H_0 = 69.08<sup>{+1.23}_{-1.16}$ km/s/Mpc for DES-Dovekie, and $H_0 = 70.67<sup>{+1.89}_{-1.87}$ km/s/Mpc for Union3. The present-day equation-of-state parameter is constrained to $w_0 = -0.521<sup>{+0.891}_{-0.414}$, $-3.01<sup>{+1.14}_{-1.21}$, and $-3.16<sup>{+1.11}_{-1.16}$ for Pantheon+, DES-Dovekie, and Union3, respectively.