Title: The role of LRG1 and LRG2's monopole in inferring the DESI 2024 BAO cosmology

Abstract: Dark Energy Spectroscopic Instrument (DESI) collaboration recently release the first year data (DR1) of baryon acoustic oscillations (BAO) in galaxy, quasar and Lyman-$\alpha$ forest tracers. When combined the CMB and SNIa data with DESI BAO, its cosmological implication shows a hint of thawing dark energy behavior. The official distance measurements for cosmology analysis are given in terms of the comoving distances along ($D_H$), and perpendicular to ($D_M$), the line of sight to the observer. We notice that there are $1\sim2\sigma$ deviations in $D_M$ and $D_H$ from the values of Planck cosmology in the luminous red galaxies (LRG) bin 1 and bin 2, namely LRG1 and LRG2. In this paper, we want to study the role of LRG1 and LRG2 in driving the DESI 2024 BAO osmology away from Planck cosmology. Since the angle-averaged distance $D_V$ and the ratio of transverse and line-of-sight comoving distances $F_{\rm AP}=D_M/D_H$ are more directly related with the measured monopole and quadrupole components of galaxy power spectrum or correlation function, we use $D_V$ and $F_{\rm AP}$ instead of the officially adopted $D_M$ and $D_H$. The purpose of this data vector transformation is to isolate the influence of monopoles in LRG1 and LRG2 in driving the deviation from $w=-1$. We find that by removing the $D_V$ data point in LRG2, the DESI + CMB + SNIa data compilation recovers $w=-1$ within $2\sigma$ contour.Similarly, the exclusion of the $D_V$ data point from LRG1 shifts the contour in the $w_0/w_a$ plane toward $w=-1$, though no intersection is observed. This underscores the preference of both the LRG1 and LRG2 BAO monopole components for the thawing dark energy model, with LRG2 exhibiting a stronger preference compared to LRG1. Alongside this paper, we provide the $D_V$ and $F_{\rm AP}$ data as well as their covariance.