Conformal Holographic Dark Energy

TL;DR

The paper addresses hints from DESI that dark energy may evolve rather than be a cosmological constant, and it confronts this with a conformal holographic dark energy (CHDE) model in which the DE density scales with conformal time as $\mathcal{M} \propto \eta^n$. The authors derive the CHDE in the Einstein equations, show an explicit DM–CHDE interaction with $\rho'_{dm} + 3\mathcal{H}\rho_{dm} = -n\, (\rho_c^{(0)}/\eta_0) \Omega_{\mathcal{M}}^{(0)} (\eta/\eta_0)^{n-1}$, and impose $w_{\mathcal{M}} = -1$, with $\Lambda$CDM recovered at $n=0$. They perform extensive MCMC analyses using combinations of DESI BAO, Planck CMB, ACT, and SN data under flat and curved geometries, finding that $\Lambda$CDM is not preferred when CMB data are included and that the best-fit CHDE exponent lies around $n \sim -0.3$, while $\Omega_m$ is generally lower with DESI data and neutrino masses lie near the terrestrial bounds. The results highlight dataset-dependent tensions but show CHDE remaining compatible with neutrino-mass constraints, suggesting CHDE as a viable dynamical DE alternative. The work advances the exploration of dynamical DE models compatible with current large-scale structure and CMB observations.

Abstract

Recent results from the DESI collaboration suggest a preference for an evolving dark energy (DE) component rather than a cosmological constant, motivating the exploration of alternative models for the background expansion. These data also reveal tension in the inferred matter density parameter -- lower in DESI and higher in Planck -- as well as a neutrino mass posterior that approaches the lower bounds permitted by oscillation experiments. In this work, we propose and test a conformal holographic DE (CHDE) model in which the DE density depends on a power law of the conformal time, characterized by an exponent (n). This formulation introduces a single additional parameter relative to LambdaCDM and reduces to it in the limit n = 0. We confront the CHDE model with BAO, CMB, and supernova datasets, following the same combinations used by DESI, and perform parameter inference under both flat and non-flat cosmologies. Our analyses show that LambdaCDM is not favored as the best-fit model when using CMB data alone or in joint analyses including BAO and SNla, and it is disfavored at the 4.4 sigma level for non-flat model and 4.5 sigma for the flat model. We obtain consistent values of n= -0.28 to -0.32 with uncertainties less than +-0.1 across multiple data combinations. Similar to LambdaCDM, the CHDE model predicts a lower matter density when employing DESI data instead of Planck data. This, in turn, influences the neutrino mass constraints, yielding values close to the minimal allowed range. Despite these dataset-dependent tensions, both the flat and curved CHDE models remain compatible with neutrino mass constraints from terrestrial experiments and yield posterior distributions that peaks at positive values. This behavior avoids the issue encountered in the LambdaCDM model, where the posterior peaks at negative mass values.

Figures (9)

• Figure 1: Contours plots of the CHDE model parameters: the density parameter of DE ($\Omega_{\mathcal{M}}^{(0)}$) and the power law exponent ($n$) , cf. eq. (\ref{['eq:HF2']}). The cosmological parameters and data of each plot are combination of the different sets: the left panel correspond to results of BAO and Planck with the curvature as free parameter; the right panel corresponds to BAO, Planck, and ACT, also for free curvature; and the panel below corresponds to BAO, Planck, and ACT for a flat model. Our results exclude the $\Lambda$CDM model ($\Omega_{\mathcal{M}}^{(0)}$ = $\Omega_\Lambda$, $n=0$, dashed lines) as a best fit when CMB data are included.
• Figure 2: Contours plots of matter density parameter vs the Hubble constant for the CHDE model (left) and the marginalized 1D posteriors probabilities (P) for different datasets. As a reference, the black dashed line points to the best fit values for the $\Lambda$CDM model using Planck data.
• Figure 3: Contours plots of matter density parameter vs the Hubble constant for the flat CHDE model. As a reference, the black dashed line points to the best fit values for the $\Lambda$CDM model using Planck data.
• Figure 4: Contours plots of the curvature and matter density parameters for the CHDE model.
• Figure 5: Posterior probabilities of the sum of the neutrino masses for nonflat (left panel) and flat (right panel) models for the CHDE model. Both plots show a maximum probability in the positive neutrino masses. For reference vertical dashed lines indicate the NH and IH experimental limits from terrestrial experiments, at $0.059$ eV and $0.1$ eV, respectively.