A new diagnostic for the null test of dynamical dark energy in light of DESI 2024 and other BAO data

We introduce a new diagnostic for the null tests of dynamical dark energy alongside two other combined equivalent diagnostics. These diagnostics are useful, especially when we include anisotropic baryon acoustic oscillation (BAO) data in an analysis, to quantify the deviations from the standard Lambda CDM model. We also consider another diagnostic for isotropic BAO observations. These null tests are independent of any late-time dark energy model or parametrization. With these diagnostics, we study the evidence for dynamical dark energy in light of Dark Energy Spectroscopic Instrument (DESI) 2024 data combined with cosmic microwave background (CMB) observations of the Planck 2018 mission and local H-0 measurements. We find no strong evidence for dynamical dark energy. The exclusion of the individual deviations at the effective redshift 0.51 of the DESI 2024 data makes the evidence even weaker. We get nearly similar results for other non-DESI BAO data. Both for DESI 2024 and other non-DESI BAO data, the evidence is almost independent of early-time physics. The evidence corresponding to the SHOES value of H0 0 is higher than the corresponding tRGB value of H(0 )for all combinations of data, but still not strong enough to reject the flat Lambda CDM model.