Frequentist Cosmological Constraints from Full-Shape Clustering Measurements in DESI DR1

We present a frequentist analysis of clustering measurements from Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI) using the standard profile likelihood method. While Bayesian inferences for effective field theory models of galaxy clustering can be highly sensitive to prior choices for extended cosmological models, frequentist inferences are not susceptible to such effects. We compare frequentist and Bayesian constraints for the parameter set $\{\sigma_8, H_0, \Omega_{\rm{m}}, w_0, w_a\}$ using the full-shape power spectrum multipoles, post-reconstruction baryon acoustic oscillation (BAO) measurements, and external datasets from the CMB and type Ia supernovae measurements. The frequentist confidence intervals are significantly shifted relative to the Bayesian credible intervals for the $w_0w_a$CDM model, unless supernovae data are included. When DESI full-shape and BAO data are fit jointly, we obtain the following $1\sigma$ frequentist confidence intervals for $\Lambda$CDM ($w_0w_a$CDM): $\sigma_8 = 0.863^{+0.048}_{-0.040} , \ H_0 = 68.96^{+0.81}_{-0.80} \ \rm{km \ s^{-1}Mpc^{-1}} , \ \Omega_{\rm{m}} = 0.3034\pm0.0110$ ($\sigma_8 = 0.782^{+0.060}_{-0.036} , \ H_0 = 63.7^{+4.2}_{-2.0} \ \rm{km \ s^{-1}Mpc^{-1}} , \ \Omega_{\rm{m}} = 0.378^{+0.024}_{-0.047} , \ w_0 = -0.16^{+0.10}_{-0.50} , \ w_a = -3.0^{+1.7}_{}$), corresponding to 0.8$\sigma$, 0.3$\sigma$, 0.7$\sigma$ (2.1$\sigma$, 4.1$\sigma$, 6.5$\sigma$, 6.3$\sigma$, 6.6$\sigma$) shifts between the maximum likelihood estimate and the Bayesian posterior mean for $\Lambda$CDM ($w_0w_a$CDM) respectively.