Arbitrariness of potentials in interacting quintessence models

Though we have entered an era of high precision cosmology the form of the quintessence potentials still remain arbitrary. In this work we explore the interacting quintessence models considering a parametrization of the quintessence potentials and tried to constrain the form of potentials using the recent cosmological observations. The particular parametrization which we have used includes many popular quintessence potentials. By constraining the parameters in the parametrization one can find which class of potentials are more favorable. Our findings reconfirm the arbitrariness of the quintessence potentials even for the interacting dark energy models as the recent cosmological observations are not able to put any constraint on the parameters in the parametrization. As a result, it is shown that the current observations are able to put an upper bound to the interaction parameter for both of the interactions we consider, although it is not possible to constrain the form of the potentials.

Figure 1

Plot of ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_{\varphi }$ for different values of $\beta$ parameters for the interaction A. All the $\alpha$ parameters are set to unity (${\alpha }_0={\alpha }_1={\alpha }_2=1$) and the present value of the EOS of scalar field is chosen to be $w_{\varphi }=-0.95$.

Figure 2

Plot of ratio of ${\rho }_{\varphi }$ and ${\rho }_m$ and in the inset of the plot is for the interaction variable $q$ for different values of $\beta$ parameters for the interaction A. All the $\alpha$ parameters are set to unity (${\alpha }_0={\alpha }_1={\alpha }_2=1$) and the present value of the EOS of scalar field is chosen to be $w_{\varphi }=-0.95$.

Figure 3

Plot of Posterior (1D and 2D) distributions of the constrained cosmological parameters for interaction A. The datasets used are $\mathrm{BAO}+\mathrm{JLA}+\mathrm{RSD}+\mathrm{H}(\mathrm{z})$ and a PLANCK15 prior is imposed on ${\omega }_b$ and ${\omega }_{cdm}$.

Figure 4

Plot of ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_{\varphi }$ for different values of $\beta$ parameters for the interaction B. All the $\alpha$ parameters are set to unity (${\alpha }_0={\alpha }_1={\alpha }_2=1$) and the present value of the EOS of scalar field is chosen to be $w_{\varphi }=-0.95$.

Figure 5

Plot of ratio of ${\rho }_{\varphi }$ and ${\rho }_m$ and in the inset the plot is for the interaction variable $q$ for different values of $\beta$ parameters for the interaction B. All the $\alpha$ parameters are set to unity (${\alpha }_0={\alpha }_1={\alpha }_2=1$) and the present value of the EOS of the scalar field is chosen to be $w_{\varphi }=-0.95$.

Figure 6

Plot of Posterior (1D and 2D) distributions of the constrained cosmological parameters for interaction B. The datasets used are $\mathrm{BAO}+\mathrm{JLA}+\mathrm{RSD}+\mathrm{H}(\mathrm{z})$ and a PLANCK15 prior is imposed on ${\omega }_b$ and ${\omega }_{cdm}$.

Figure 7

Comparison of posterior of different cosmological parameters from the two classes of the interaction. The datasets used are $\mathrm{BAO}+\mathrm{JLA}+\mathrm{H}(\mathrm{z})+\mathrm{RSD}$ and a PLANCK15 prior is imposed on ${\omega }_b$ and ${\omega }_{cdm}$.