EFT of Dark Energy with Cosmic Chronometers: Reconstructing Background EFT Functions

Abstract

The effective field theory (EFT) of dark energy provides a model-independent framework for studying cosmology within scalar-tensor theories. In this work, we explore how the time evolution of the cosmological background, inferred from cosmic chronometer measurements of the Hubble parameter, can be used to reconstruct the relevant EFT functions. Our approach enables the direct determination of these EFT functions from observational data without assuming any specific cosmological model. This makes it possible to test the background evolution of a wide range of dark energy models, including the $Λ$CDM model. We further demonstrate how the reconstructed EFT functions can be applied to constrain concrete theories, such as the quintessence model.

Figures (9)

• Figure 1: Summary of 32 CC data used in Ref. Jalilvand:2022lfb, taken from the following references, each indicated by a different label: Jimenez et al. (2003) Jimenez:2003iv, Simon et al. (2005) Simon:2004tf, Stern et al. (2010) Stern:2009ep, Moresco et al. (2012) Moresco:2012jh, Zhang et al. (2014) 2014RAA....14.1221Z, Moresco (2015) Moresco:2015cya, Moresco et al. (2016) Moresco:2016mzx, Ratsimbazafy et al. (2017) Ratsimbazafy:2017vga, and Borghi et al. (2022) Borghi:2021rft.
• Figure 2: Plots of $H(z)$ and $dH/dz$ reconstructed by GP with several kernel functions. Each colored band represents the $1\sigma$ uncertainty. We used $m(z)=0$ in this GP reconstruction. The black dots and error bars in the left panel represent the CC data shown in Fig. \ref{['fig:CC_data']}.
• Figure 3: Plots of $H(z)$ and $dH/dz$ reconstructed by GP with several mean functions. Each colored band represents the $1\sigma$ uncertainty. We used the Matérn kernel with $\nu=3.5$ in this GP reconstruction. The black dots and error bars in the left panel represent the CC data shown in Fig. \ref{['fig:CC_data']}.
• Figure 4: Plots of $H(z)$ and $dH/dz$ reconstructed by GP using the method of Ref. Shafieloo:2012ht. Each colored band represents the $1\sigma$ uncertainty. The black dots and error bars in the left panel represent the CC data shown in Fig. \ref{['fig:CC_data']}.
• Figure 5: Plots of $\Lambda(z)/(M_{\rm Pl}^2H_0^2)$ reconstructed from CC data using Eq. \ref{['eq:Lambda_z_simple']} for $\Omega_{{\rm m}0} \in \{0.25,0.30,0.35\}$. The black dashed line represents the constant value in the $\Lambda$CDM model, $3(1-\Omega_{{\rm m}0})$, evaluated at the central Planck 2018 value $\Omega_{{\rm m}0}=0.315\,(\pm 0.007)$Planck:2018vyg.