Bias of reconstructing the dark energy equation of state from the Pad$\acute{e}$ cosmography

TL;DR

This paper reveals that using Padé cosmography to reconstruct dark energy's equation of state can introduce biases at high redshift, potentially misleading conclusions about dark energy's nature.

Contribution

The study demonstrates that Padé cosmography inherently biases the reconstructed dark energy equation of state at high redshift, highlighting limitations of this method.

Findings

Padé approximant better describes cosmic evolution than standard cosmography.

Reconstructed w(z) approaches 1/3 or 0 at high redshift, regardless of parameters.

Bias in dark energy property inference when using Padé cosmography at z>2.

Abstract

Pad$\acute{e}$ cosmography has been widely used to probe the cosmic evolution and to investigate the nature of dark energy. In this paper, we find that the Pad$\acute{e}$ approximant can describe the cosmic evolution better than the standard cosmography, and if the luminosity distance $d_L(z)$ described by the Pad$\acute{e}$ approximant is used to reconstruct the dark energy equation of state $w(z)$, then the reconstructed $w(z)$ will approach a constant, i.e. $1/3$ or $0$, when the redshift is very high. This result is general since it is independent of the coefficients in the Pad$\acute{e}$ approximant and the value of the present dimensionless matter density parameter. This intrinsic character will bias the $w(z)$ reconstruction and lead to misconception of the property of dark energy. Therefore, one must exercise caution in investigating the property of dark energy from Pad$\acute{e}$ cosmography when the high redshift data, i.e. $z>2$, are included.