Monodromic Dark Energy and DESI

Recent baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) collaboration have renewed interest in dynamical dark energy models, particularly those that cross the "phantom divide" ($w_{\rm DE} = -1$). We present the first observational constraints on monodromic k-essence, a physically motivated scalar field dark energy scenario capable of realizing rapid oscillations about the phantom divide. Using cosmic microwave background (CMB) information, DESI DR2 BAO measurements, and Type Ia supernovae observations, we constrain the amplitude, frequency, phase, and power-law index describing the monodromic k-essence scenario at the background level. We find that the monodromic dark energy scenario can fit these datasets with a $χ^2$ that is comparable to the phenomenological $w_0$-$w_a$ parametrization. While the CMB and BAO data alone are consistent with the standard $Λ$CDM model, the inclusion of DESY5 supernovae shows a preference for a non-zero amplitude, $A=0.44^{+0.16}_{-0.12}$ (fully marginalized 68% C.L.). Conversely, inclusion of the Pantheon-Plus supernovae provides no evidence for monodromic k-essence, with $A<0.43$ (95% C.L.). We show that constraints on both monodromic dark energy and $w_0$-$w_a$ models are sensitive to the DESI DR2 LRG2 BAO distance, especially in the absence of supernovae data.