Assessment of the cosmic distance duality relation using Gaussian Process

TL;DR

This work tests the cosmic distance duality relation in a model-independent way by reconstructing $H(z)$, $d_L(z)$, and $D_V(z)$ from Pantheon SN-Ia, BAO, and CC data using Gaussian Processes with multiple kernels. The key quantity, $\eta(z)=\dfrac{d_L}{d_A(1+z)^2}$, is derived directly from reconstructed functions, and the study finds no evidence for CDDR violation up to $z\approx2$, with unity lying within $2\sigma$ across kernels. The authors also constrain nuisance and cosmological parameters ($M_B$, $\Omega_{m0}$, $r_d$) in a fully non-parametric framework, demonstrating consistency across kernel choices while noting the impact of high-$z$ data sparsity and $r_d$ uncertainties. Overall, the results reinforce Etherington’s reciprocity in the late-time universe and illustrate the viability and limitations of GP-based cosmography for testing fundamental distance relations.

Abstract

Two types of distance measurement are important in cosmological observations, the angular diameter distance $d_A$ and the luminosity distance $d_L$. In the present work, we carried out an assessment of the theoretical relation between these two distance measurements, namely the cosmic distance duality relation, from type Ia supernovae (SN-Ia) data, the Cosmic Chronometer (CC) Hubble parameter data, and baryon acoustic oscillation (BAO) data using Gaussian Process. The luminosity distance curve and the angular diameter distance curve are extracted from the SN-Ia data and the combination of BAO and CC data respectively using the Gaussian Process. The distance duality relation is checked by a non-parametric reconstruction using the reconstructed $H$, $d_L$, and the volume-averaged distance $D_v$. We compare the results obtained for different choices of the covariance function employed in the Gaussian Process. It is observed that the theoretical distance duality relation is in well agreement with the present analysis in 2$σ$ for the overlapping redshift domain $0 \leq z \leq 2$ of the reconstruction.

Figures (8)

• Figure 1: Plots for $H(z)$ (in units of km Mpc$^{-1}$ s$^{-1}$) reconstructed from CC data using the Matérn 9/2, Matérn 7/2, Matérn 5/2 and Squared Exponential covariance function (from left to right) respectively. The solid black line is the best fitting curve and the associated 1$\sigma$, 2$\sigma$ and 3$\sigma$ confidence regions are shown in lighter shades.
• Figure 2: Plots for marginalized likelihood of absolute magnitude $M_B$ using the Matérn 9/2, Matérn 7/2, Matérn 5/2 and Squared Exponential covariance function (from left to right) respectively.
• Figure 3: Plots for marginalized likelihood of matter density parameter $\Omega_{m0}$ using the Matérn 9/2, Matérn 7/2, Matérn 5/2 and Squared Exponential covariance function (from left to right) respectively.
• Figure 4: Plots for marginalized likelihood of comoving sound horizon at drag epoch $r_d$ (in units of Mpc) using the Matérn 9/2, Matérn 7/2, Matérn 5/2 and Squared Exponential covariance function (from left to right) respectively.
• Figure 5: Plots for the reconstructed dimensionless or normalized luminosity distance $D_L$ considering the Matérn 9/2, Matérn 7/2, Matérn 5/2 and Squared Exponential (from left to right) covariance function. The black solid lines represent the best fitting curves. The associated 1$\sigma$, 2$\sigma$ and 3$\sigma$ confidence levels are shown by the shaded regions.