Confronting dark energy in Harada's Conformal Killing Gravity with observational data

TL;DR

This work tests Harada's Conformal Killing Gravity (CKG) as an alternative to $\Lambda$CDM by confronting its two proposed dark energy (DE) implementations with DESI DR1 BAO, Planck 2018 CMB, and Pantheon+ SN Ia data, incorporating the Trans-Planckian Censorship Conjecture (TCC) constraints. The analysis shows that a pure $\omega=-5/3$ phantom fluid is ruled out, while a hybrid scenario with a cosmological constant plus a subdominant $\omega=-5/3$ component remains only marginally compatible, yielding an effective density $\Omega_{\text{eff}}$ consistent with zero. A comprehensive MCMC with self-consistently computed $r_d$ and an AIC comparison finds $\Omega_{\text{eff}}$ tightly centered near zero and no statistical preference for CKG over $\Lambda$CDM, with $H_0$ around $67.4$ km s$^{-1}$ Mpc$^{-1}$. Consequently, current cosmological data effectively reduce CKG to $\Lambda$CDM, and the Hubble tension remains unresolved within this framework. These results underscore the robustness of the standard model and illustrate the importance of self-consistent Bayesian tests for modified gravity theories using full observational datasets.

Abstract

Based on a comprehensive analysis of recent observational data-a combination of DESI DR1, Planck CMB, and Pantheon+ SN Ia-this study critically evaluates the two dark energy (DE) proposals within Harada's Conformal Killing Gravity (CKG) model. The model in question predicts either a dominant phantom-type effective DE component with EoS $ω= -5/3$ or a hybrid scenario combining a cosmological constant ($ω= -1$) with a subdominant $ω= -5/3$ fluid (around $5\%$) to address the Hubble tension (HT) and late-time acceleration. An analysis based on the Trans-Planckian Censorship Conjecture (TCC) demonstrates that the pure CKG fluid scenario $ω= -5/3$ is excluded, whereas the hybrid model remains only marginally compatible. Our Markov Chain Monte Carlo (MCMC) analysis constrains the effective DE density parameter to $Ω_{\text{eff}} = 0.009^{+0.006}_{-0.007}$ ($68\%$ CL), consistent with zero and ruling out the around $5\%$ contribution required by Harada's CKG. The resulting Hubble expansion history $H(z)$ and effective EoS $ω_{\text{eff}}(z)$ are indistinguishable from those of $Λ$CDM. Bayesian model comparison via the Akaike Information Criterion (AIC) shows no statistical preference for CKG over $Λ$CDM ($Δ\text{AIC} = +2.6$), disfavoring the additional complexity of the CKG model. The key output of this study is that both DE proposals in Harada's CKG are ruled out by current cosmological data, and HT remains unresolved.

Figures (6)

• Figure 1: 1D marginalized posterior distributions, for the key parameters of the Harada's CKG model.
• Figure 2: 2D posterior distributions within 68%, and 95%, for the key parameters of the Harada's CKG model.
• Figure 3: The Hubble parameter $H(z)$ as a function of redshift for the best-fit CKG and $\Lambda$CDM models with error bars (red) from Cosmic Chronometer data (CCD). Goodness-of-fit to CCD for these two models are $\chi_{\Lambda CDM}=15.28$, and $\chi_{\text{CKG}}=15.17$ which leads to $\Delta \chi^2=-0.108$, meaning that them are indistinguishable.
• Figure 4: The effective EoS $\omega_{\text{eff}}(z)$ for the constrained CKG model, with a prominent red dashed line for the pure CKG case ($w = -5/3$) (right panel). The filled area (gray) in the right panel address the DESI DR1 preferred range ($\omega\sim~- 0.98~ \hbox{to}~ -0.94$).
• Figure 5: Comparison of $\chi^2_{min}$ for CKG and $\Lambda$CDM models (left panel). AIC evidence interpretation scale in right panel bookLiddle:2007fy.