Constraints on the redshift dependence of the dark energy potential

TL;DR

The paper develops a Horizon-flow–inspired formalism to reconstruct the redshift evolution of the dark energy potential $V(z)$ from observables, generalizing to multi-field quintessence and possible curvature corrections. It presents exact reconstruction relations for $V(z)$ and $K(z)$ in terms of $H(z)$, $\dot{H}(z)$, and the energy content, and offers parametric schemes including a Chebyshev expansion to handle non-ideal data. By applying differential ages of passively evolving galaxies and supernova data, the authors find the potential is consistent with a constant value at 1σ, while allowing small deviations that future data (e.g., ACT) could constrain much more tightly. The framework enables direct testing of dynamical dark energy against the cosmological constant and provides a practical path to compare models using $V(z)$ instead of solely $w(z)$.

Abstract

We develop a formalism to characterize the redshift evolution of the dark energy potential. Our formalism makes use of quantities similar to the Horizon-flow parameters in inflation and is general enough that can deal with multiscalar quintessence scenarios, exotic matter components, and higher order curvature corrections to General Relativity. We show how the shape of the dark energy potential can be recovered non parametrically using this formalism and we present approximations analogous to the ones relevant to slow-roll inflation. Since presently available data do not allow a non-parametric and exact reconstruction of the potential, we consider a general parametric description. This reconstruction can also be used in other approaches followed in the literature (e.g., the reconstruction of the redshift evolution of the dark energy equation of state w(z)). Using observations of passively evolving galaxies and supernova data we derive constraints on the dark energy potential shape in the redshift range 0.1 < z < 1.8. Our findings show that at the 1sigma level the potential is consistent with being constant, although at the same level of confidence variations cannot be excluded with current data. We forecast constraints achievable with future data from the Atacama Cosmology Telescope.

Figures (5)

• Figure 1: Left panel: the absolute age for the 32 passively evolving galaxies in our catalogue (see text for more detals) determined from fitting stellar population models is plotted as a function of redshift. Note that there is a clear age-redshift relation: the lower the redshift the older the galaxies. Right panel: the value of the Hubble parameter as a function of redshift as derived from the differential ages of galaxies in the left panel. The determination at $z\sim 0.1$ indicated by the '+' symbol is the hubble constant determination of $H$ from JVTS03. The dotted line is the value of $H(z)$ for the LCDM model.
• Figure 2: Regions in the $\lambda_1/\rho_{c}$ vs $\lambda_0/\rho_{c}$ (left panel) and $\lambda_2/\rho_{c}$ vs $\lambda_0/\rho_{c}$ (right panel) excluded at the $1-\sigma$ and $2-\sigma$ joint confidence level, by the priors and the constraints that the kinetic energy in the quintessence field must be positive and that at all redshifts $\rho_m+\rho_q$ must be positive.
• Figure 3: Constraints in the $\lambda_1/\rho_{c}$ vs $\lambda_0/\rho_{c}$ (left panel) and $\lambda_2/\rho_{c}$ vs $\lambda_0/\rho_{c}$ (righ panel) obtained from $H(z)$ measurement based on relative galaxy ages. Contour levels are 1$-\sigma$ marginalized, 1$-\sigma$ joint and 2$-\sigma$ joint. The diamon shows the location of the maximum of the marginalized likelihood.
• Figure 4: One and two sigma joint constraints in the $\lambda_1/\rho_{c}$ vs $\lambda_0/\rho_{c}$ plane and $\lambda_2/\rho_{c}$ vs $\lambda_0/\rho_{c}$ obtained from the Riess et al. (2004) supernovae data.
• Figure 5: Reconstruted $V(z)$ from relative galaxy ages (left) and from Supernovae (right). The gray regions represent the 1- and 2- $\sigma$ confidence regions. In the left panel the dotted line shows the constraint imposed by the prior.