Probing cosmic curvature with Alcock-Paczynski data

The Alcock-Paczynski (AP) parameter $F_{AP}$ is independent of the sound horizon $r_d$, making the Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) AP measurements particularly well suited for cosmological applications. We propose a novel null test of cosmic curvature tailored to DESI BAO data that combines $F_{AP}$ with the ratios $D_V'/D_V$ or $D_M'/D_M$. This null test can also be performed using a joint dataset of DESI BAO and type Ia supernova (SNe Ia) observations. Additionally, we use the test to assess the internal consistency and mutual compatibility of these datasets. We find that the data are compatible. Although the results show that a spatially flat universe is inconsistent with the data at low redshift $z\lesssim 0.5$, we cannot draw the conclusion that the observational data prefers $Ω_k\neq 0$ because there is no observational data in that region.