Cosmological constraints on curved quintessence

TL;DR

This work analyzes a curved quintessence scenario with an exponential potential $V=V_0 e^{-\lambda\phi}$ in a non-flat FLRW universe. It combines a dynamical-systems treatment of the background with full cosmological constraints from Planck, DESI BAO, and multiple Type Ia SN datasets to constrain $\lambda$ and spatial curvature. The findings show a mild preference for nonzero $\lambda$ and an open curvature tendency that is not statistically significant, while typical string-theory motivated values $\lambda>\sqrt{2}$ are disfavored. Overall, exponential quintessence with curvature is mildly favored over $\Lambda$CDM but may be too simplistic to fully capture dark energy dynamics, motivating exploration of more complex string-inspired potentials and upcoming DESI data for tighter tests.

Abstract

Dynamical dark energy has gained renewed interest due to recent theoretical and observational developments. In the present paper, we focus on a string-motivated dark energy set-up, and perform a detailed cosmological analysis of exponential quintessence with potential $V=V_0 e^{-λφ}$, allowing for non-zero spatial curvature. We first gain some physical intuition into the full evolution of such a scenario by analysing the corresponding dynamical system. Then, we test the model using a combination of Planck CMB data, DESI BAO data, as well as recent supernovae datasets. For the model parameter $λ$, we obtain a preference for nonzero values: $λ= 0.48^{+0.28}_{-0.21},\; 0.68^{+0.31}_{-0.20},\; 0.77^{+0.18}_{-0.15}$ at 68% C.L. when combining CMB+DESI with Pantheon+, Union3 and DES-Y5 supernovae datasets respectively. We find no significant hint for spatial curvature. We discuss the implications of current cosmological results for the exponential quintessence model, and more generally for dark energy in string theory.

Figures (13)

• Figure 1: Left: a slice of the phase space for the dynamical system including quintessence, matter, radiation and positive spatial curvature, with the selection of variables $\bar{x}$, $\bar{y}$ and $\sqrt{\bar{\Omega}_m}$, for $\lambda=\sqrt{{8}/{3}}$. Plotted in red is the trajectory determined by the initial conditions set today by $\Omega_{k,0}=-0.005000423845$, $\Omega_{\phi,0}=0.684587702938$, $\Omega_{r,0}=0.000080007654$ and $w_{\phi,0}=-0.573508930813358$, with: $\bar{z}_0 = {1}/{\sqrt{1-\Omega_{k,0}}}$, $\bar{x}_0=\sqrt{\Omega_{\phi,0}\bar{z}_0^{\,2} (1+w_{\phi,0})/2}$, $\bar{y}_0=\sqrt{\Omega_{\phi,0}\bar{z}_0^{\,2} - \bar{x}_0^{\,2}}$, $\bar{u}_0 = \sqrt{\Omega_{r,0}} \bar{z}_0$. These values are taken from the run of CAMB described in the following section, with a large amount of precision necessary to ensure past radiation domination. Right: The corresponding evolution of density parameters, $\Omega_n$ ($\Omega_\phi$ in green, $\Omega_r$ in red, $\Omega_m$ in yellow, and $\Omega_k$ in blue) and equations of state ($w_\phi$ in brown and $w_{\rm eff}$ in purple), with respect to $N$, related to $\bar{N}$ as $dN = \bar{z} d\bar{N}$. See main text for more details.
• Figure 2: Upper panel: Curvature and scalar density parameter evolution for various values of $\lambda$ for an open universe $k<0$. Lower panel: angular power spectrum $D_{\ell}^{TT}$ and the residuals $\Delta D_{\ell}^{TT}$ with respect to $\Lambda$CDM , for the same values of $\lambda$ and $k<0$. The grey shaded regions represent the error bars on $D_{ \ell}^{TT}$ from PlanckPlanck:2019nip.
• Figure 3: Equations of state evolution for the same parameter values as in figure \ref{['fig:Omegas_Kneg']} computed from CAMB.
• Figure 4: Scalar field evolution for the open quintessence case.
• Figure 5: Curvature and scalar density parameter evolution for a closed universe, $k>0$ for various values of $\lambda$ (upper panel). Angular power spectrum $D_{\ell}^{TT}$ and residuals $\Delta D_{\ell}^{TT}$ for same values of $\lambda$ and $k>0$ (lower panel). The grey shaded regions represent the error bars on $D_{ \ell}^{TT}$ from PlanckPlanck:2019nip.