Constraints on the dark energy using multiple observations : snare of principal component analysis

TL;DR

This paper investigates the limitations of principal component analysis in accurately reconstructing the dynamic behavior of dark energy's equation of state from multiple cosmological observations, revealing significant drawbacks.

Contribution

It extends previous work by analyzing PCA's effectiveness with multiple data types and demonstrates its inability to resolve rapidly varying dark energy models.

Findings

PCA tends to produce nearly constant $$ even for rapidly changing models.

The resolution of $$'s dynamics is significantly degraded when using PCA with multiple observations.

PCA's limitations are highlighted in the context of dark energy parameter estimation.

Abstract

We explore snares in determining the equation of state of dark energy ($\omega$) when one uses the so-called principal component analysis for multiple observations. We demonstrated drawbacks of principal component analysis in an earlier paper. We used the Hubble parameter data generated from a fiducial model using the so-called Chevallier-Polarski-Linder parameterization. We extend our previous consideration to multiple observations, the Hubble parameter and the luminosity distance. We find that the principal component analysis produces the almost constant $\omega$ even when a fiducial model is a rapidly varying $\omega$. Thus, resolution of dynamical property of $\omega$ through PCA is degraded especially when one fits to several observations.