Dynamical symmetries and observational constraints in scalar field cosmology

We propose to use dynamical symmetries of the field equations, in order to classify the dark energy models in the context of scalar field (quintessence or phantom) Friedmann-Lemaître-Robertson Walker cosmologies. Practically, symmetries provide a useful mathematical tool in physical problems since they can be used to simplify a given system of differential equations as well as to determine the integrability of the physical system. The requirement that the field equations admit dynamical symmetries results in two potentials, one of which is the well-known unified dark matter potential and another new potential. For each hyperbolic potential we obtain the corresponding analytic solution of the field equations. The proposed analysis suggests that the requirement of the contact symmetry appears to be very competitive to other independent tests used to probe the functional form of a given potential and thus the associated nature of dark energy. Finally, in order to test the viability of the above scalar field models we perform a joint likelihood analysis using some of the latest cosmological data.

Figure 1

Left: Equation of state $w_{\varphi }(a)$ evolution for scalar field with scale factor (55). Right: Deceleration parameter $q(a)$ for scale factor (55). We use $({\omega }_{m0},c_{Q1})=(0.12,0.36)\times 10^4$, ${ϵ}_{\theta }=-1$; the solid line is for ${\theta }_1=0.01$, the dotted line is for ${\theta }_1=0.1$ and the dashed-dotted line is for ${\theta }_1=0$.

Figure 2

In the left panel we give the equation of state $w_{\varphi }(a)$ evolution of the scalar field with Lagrangian (65) and in the right panel we give the deceleration parameter $q(a)$ of the scale factor with Lagrangian (65) where in (69) we considered the sign minus. For the numeric solution we use ${(u,v)}_{t\to 0}=(0.01,0.0998)$, $({\rho }_{m0},c_1,c_2)=(0.33,1,0.8)\times 10^4$; the solid line is for ${\mathrm{\Phi }}_0=0$, the dotted line is for ${\mathrm{\Phi }}_0=10^3$ and the dashed-dotted line is for ${\mathrm{\Phi }}_0=10^4$.

Figure 3

Likelihood contours of $1\sigma (\mathrm{\Delta }{\chi }^2=2.3)$, $2\sigma (\mathrm{\Delta }{\chi }^2=6.18)$ and $3\sigma (\mathrm{\Delta }{\chi }^2=11.83)$ in the plane $({\omega }_{m0},c_{(Q,P)1})$ for the scalar field with potential (41). The left panel is for the quintessence field whereas the right panel is for the phantom field. The filled areas are for the $\mathrm{SnIa}+\mathrm{BAO}+\mathrm{H}(\mathrm{z})$ test, the best fit values are marked with a dot; the dotted lines are for the $\mathrm{SnIa}+\mathrm{BAO}$ test and the best fit values are marked with cross.

Figure 4

Likelihood contours of $1\sigma (\mathrm{\Delta }{\chi }^2=2.3)$, $2\sigma (\mathrm{\Delta }{\chi }^2=6.18)$ and $3\sigma (\mathrm{\Delta }{\chi }^2=11.83)$ in the plane $({\omega }_{m0},c_{(Q,P)1})$ for the scalar field with potential (46). The left panel is for the quintessence field whereas the right panel is for the phantom field. The filled areas are for the $\mathrm{SnIa}+\mathrm{BAO}+\mathrm{H}(\mathrm{z})$ test, the best fit values are marked with a dot; the dotted lines are for the $\mathrm{SnIa}+\mathrm{BAO}$ test and the best fit values are marked with cross.