$w_0w_a$ or $bc$: DESI constraints on relative baryon-CDM perturbations

We carry out a search for the relative baryon-cold dark matter (CDM) density and velocity modes in the DESI full-shape (FS) data, and investigate whether DESI's preference for evolving dark energy can be affected by these relative perturbations, which are a known contaminant of the baryon acoustic oscillations. For the first time, we use a holistic effective field theory (EFT) treatment of the power spectrum and bispectrum both for the standard terms (without relative perturbations), modeled in EFT to one-loop order, and for the relative perturbations. For the latter we implement an efficient computation of the one-loop power spectrum that allows us to scan over different cosmologies. We obtain robust constraints on the relative density and velocity bias parameters $b_{δ_{bc}}$, and $b_{v^2_{bc}}$ for all the DESI DR1 tracers, finding e.g. $b_{δ_{bc}}=5 \pm 6$, $b_{v^2_{bc}}=-0.031\pm 0.023$ (at 68% CL) for the LRG2 sample in a DESI FS-only analysis within $Λ$CDM, supplemented by CMB priors on the baryon density and spectral tilt. Assuming instead a $w_0w_a$CDM cosmological model, and combining DESI FS with the CMB primary anisotropies, CMB lensing, and Pantheon+ supernovae, our LRG2 constraints read $b_{δ_{bc}}=2 \pm 5$, $b_{v^2_{bc}}=-0.032\pm 0.022$. Adding the relative velocity divergence biases we find $b_{δ_{bc}}=-17_{-17}^{+19}$, $b_{θ_{bc}}=-760_{-680}^{+700}$, $b_{v^2_{bc}}=-0.032\pm 0.024$ for the same sample. The constraints on the dark energy equation of state parameters are virtually unchanged when marginalizing over the baryon-CDM modes. We conclude that DESI's preference for evolving dark energy is robust with respect to the baryon-CDM relative perturbations.