New general parametrization of quintessence fields and its observational constraints

We present a new parameterization of quintessence potentials for dark energy based directly upon the dynamical properties of the equations of motion. Such parameterization arises naturally once the equations of motion are written as a dynamical system in terms of properly defined polar variables. We have identified two different classes of parameters, and we dubbed them dynamical and passive parameters. The dynamical parameters appear explicitly in the equations of motion, but the passive parameters play just a secondary role in their solutions. The new approach is applied to the so-called thawing potentials, and it is argued that only three dynamical parameters are sufficient to capture the evolution of the quintessence fields at late times. This work reconfirms the arbitrariness of the quintessence potentials as the recent observational data fail to constrain the dynamical parameters.

Figure 1

Plots of $1+w_{\varphi }$ as a function of the redshift $z$ for the values indicated of the dynamical parameters ${\alpha }_0$ (top), ${\alpha }_1$ (middle) and ${\alpha }_2$ (bottom). Notice that the curves deviate from the cosmological constant value ($w=-1$) for $z<3$, in general the curves grow monotonically as $z\to 0$ but a small bump appears if the dynamical parameters take on negative values.

Figure 2

Fitting of the proposed parametrization in Eq. (17) to the numerical solutions obtained using the class code corresponding to the Table 3. These plots are for $(1+w_{\varphi })/(1+w_{\varphi 0})a^3$ as a function of the scale factor $a$ in the range [0.1: 1]. Top-left plot corresponds to the class Ia where ${\alpha }_i=0$. Top-right corresponds to class II where ${\alpha }_1={\alpha }_2=0$. In bottom-left, the plots are for the class IIIa, ${\alpha }_0={\alpha }_2=0$ and in bottom-right the plots are for ${\alpha }_0={\alpha }_1=0$ which belongs to class I.

Figure 3

Posterior distributions (solid lines) and mean likelihood (dashed line) for the constrained cosmological parameters using $\mathrm{BAO}+\mathrm{JLA}$ data set plus a PLANCK15 prior. The data sets considered do not show any preference for a particular quintessence potential. See the text, Sec. 4, for more details.

Figure 4

(Top) Posterior distributions (solid lines) and mean likelihood (dashed lines) for the constrained cosmological parameters corresponding to the quadratic potential in class Ia. (Bottom) Same as above for the axion potential in class IIa (${\alpha }_1={\alpha }_2=0$). As anticipated from Fig. 3, the dynamical variable ${\alpha }_0=3/({\kappa }^2{f}_{\varphi }^2)$ remains unconstrained, whereas there appears an upper bound for the passive parameter $m_{\varphi }^2{f}_{\varphi }^2<3.66\times {10}^{-10}{\mathrm{eV}}^4$. See the text for more details.