Probing cosmic curvature with Alcock-Paczynski data

Abstract

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.

Figures (5)

• Figure 1: The reconstructed $D_H/r_d$ along with the $1\sigma$ error from DESI BAO DR2 data. We imposed the constraint $D_M(z=0)=0$. The green lines labeled as $D_M'=D_H$ are reconstructed with the data $D_M/r_d$, $D_H/r_d$ and their correlations by taking the data $D_H/r_d$ as $D_M'/r_d$. The blue lines labeled as MG are reconstructed with the data $D_M$, $D_H$ and their correlations. The red lines are reconstructed separately from the respective data alone. The solid lines are for $D_H/r_d$ and the dashed lines are for $D_M'/r_d$.
• Figure 2: The reconstructed $\mathcal{O}_k$ with its $1\sigma$ uncertainty from DESI BAO measurements of $F_{\rm AP}$ and $D_V/r_d$. Solid curves show the posterior mean; shaded regions indicate the $1\sigma$ uncertainties. Gray regions correspond to reconstructing $F_{\rm AP}$ and $D_V/r_d$ separately from the respective data sets $F_{\rm AP}$ and $D_V/r_d$. Red regions show the reconstruction when $F_{\rm AP}$ and $D_V/r_d$ are analyzed jointly, using the combined data and their full covariance.
• Figure 3: The reconstructed $\mathcal{O}_k$ along with the $1\sigma$ error from DESI BAO AP and SNe Ia.
• Figure 4: The reconstructed $F_{AP}$ along with the $1\sigma$ error from DESI BAO DR2 data. We imposed the constraint $D_M(z=0)=0$ and $F_{AP}(z=0)=0$. The blue lines labeled as $D_M/D_H$ are reconstructed from the joint data $D_M/r_d$, $D_H/r_d$ and their correlations. The black lines labeled as MG are reconstructed from the joint data $F_{AP}$, $D_V/r_d$ and their correlations. The red lines are reconstructed from the data $F_{AP}$ only.
• Figure 5: The reconstructed $D_M/D_M'$ along with the $1\sigma$ error from DESI BAO and SNe Ia. The blue lines labeled as $D_M$ are reconstructed from the data $D_M$ only, the purple lines labeled as MG are reconstructed from the joint data $D_M$, $D_H$ and their correlations.