f(Q, Lm) gravity fits OHD+DES+BAO data with quintessence-to-phantom transition

The authors derive modified Friedmann equations in f(Q, Lm) and insert four dark-energy equation-of-state forms (CPL, JBP, BA, LOG). They perform a joint MCMC fit to 31 OHD points, 1829 DES supernovae, and BAO measurements, obtaining best-fit values that keep the models inside current 1-sigma contours. All four cases produce a smooth shift from q>0 at high redshift to q<0 today, with w crossing -1 at low redshift except in the BA parametrization.

Energy-condition analysis shows the null and weak conditions are marginally violated at late times, consistent with phantom-like behavior, while the models remain stable under scalar perturbations. The study does not, however, report Bayesian evidence ratios against flat Lambda-CDM, leaving open whether the extra degrees of freedom are justified by the data.

Because the work is a purely theoretical exploration with no direct observational test proposed, its near-term relevance to cosmology is limited to providing additional functional forms that future surveys such as Euclid or LSST could falsify through tighter w(z) measurements.

Next steps require a full nested-sampling comparison with Lambda-CDM on the same likelihood and an explicit forecast for how Stage-IV surveys would tighten the parameter space.