We present an Effective Field Theory based reconstruction of quintessence models of dark energy directly from cosmological data. We show that current cosmological data possess enough constraining power to test several quintessence model properties fo
r redshifts $zin [0,1.5]$ with no assumptions about the behavior of the scalar field potential. We use measurements of the cosmic microwave background, supernovae distances, and the clustering and lensing of galaxies to constrain the evolution of the dark energy equation of state, Swampland Conjectures, the shape of the scalar field reconstructed potential, and the structure of its phase space. The standard cosmological model still remains favored by data and, within quintessence models, deviations from its expansion history are bounded to be below the 10% level at 95% confidence at any redshift below $z=1.5$.
Of the many proposed extensions to the $Lambda$CDM paradigm, a model in which neutrinos self-interact until close to the epoch of matter-radiation equality has been shown to provide a good fit to current cosmic microwave background (CMB) data, while
at the same time alleviating tensions with late-time measurements of the expansion rate and matter fluctuation amplitude. Interestingly, CMB fits to this model either pick out a specific large value of the neutrino interaction strength, or are consistent with the extremely weak neutrino interaction found in $Lambda$CDM, resulting in a bimodal posterior distribution for the neutrino self-interaction cross section. In this paper, we explore why current cosmological data select this particular large neutrino self-interaction strength, and by consequence, disfavor intermediate values of the self-interaction cross section. We show how it is the $ell gtrsim 1000$ CMB temperature anisotropies, most recently measured by the Planck satellite, that produce this bimodality. We also establish that smaller scale temperature data, and improved polarization data measuring the temperature-polarization cross-correlation, will best constrain the neutrino self-interaction strength. We forecast that the upcoming Simons Observatory should be capable of distinguishing between the models.
