Frequentist cosmological constraints from full-shape clustering measurements in DESI DR1

We perform a frequentist analysis using the standard profile likelihood method for clustering measurements from Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI). While Bayesian inferences for Effective Field Theory models of galaxy clustering can be highly sensitive to the choice of priors for extended cosmological models, frequentist inferences are not susceptible to such effects. We compare Bayesian and frequentist constraints for the parameter set $\{\sigma_8, H_0, \Omega_{\rm{m}}, w_0, w_a\}$ when fitting to the full-shape of the power spectrum multipoles, the post-reconstruction Baryon Acoustic Oscillation (BAO) measurements, as well as external datasets from the CMB and type Ia supernovae measurements. Bayesian prior effects are very significant for the $w_0w_a$CDM model; while the $1 \sigma$ frequentist confidence intervals encompass the maximum a posteriori (MAP), the Bayesian credible intervals almost always exclude the maximum likelihood estimate (MLE) and the MAP - indicating strong prior volume projection effects - unless supernovae data are included. We observe limited prior effects for the $\Lambda$CDM model, due to the reduced number of parameters. When DESI full-shape and BAO data are jointly fit, we obtain the following $1\sigma$ frequentist confidence intervals for $\Lambda$CDM ($w_0w_a$CDM): $\sigma_8 = 0.867^{+0.048}_{-0.041} , \ H_0 = 68.91^{+0.80}_{-0.79} \ \rm{km \ s^{-1}Mpc^{-1}} , \ \Omega_{\rm{m}} = 0.3038\pm0.0110$ ($\sigma_8 = 0.793^{+0.069}_{-0.048} , \ H_0 = 64.9^{+4.8}_{-2.8} \ \rm{km \ s^{-1}Mpc^{-1}} , \ \Omega_{\rm{m}} = 0.369^{+0.029}_{-0.059}$ , $w_0 = -0.24^{+0.17}_{-0.64}$ , $w_a = -2.5^{+1.9}_{}$), corresponding to 0.7$\sigma$, 0.3$\sigma$, 0.7$\sigma$ (1.9$\sigma$, 3.4$\sigma$, 5.6$\sigma$, 5.5$\sigma$, 5.6$\sigma$) shifts between the MLE relative to the Bayesian posterior mean for $\Lambda$CDM ($w_0w_a$CDM) respectively.