Observational constraints on new exact inflationary scalar-field solutions

An algorithm is used to generate new solutions of the scalar-field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalizations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. Furthermore other closed-form solutions which provide inflationary universes are presented. We also show how the Hubble slow-roll parameters can be calculated using the solution algorithm and we compare these inflationary solutions with the observational data provided by the Planck 2015 collaboration in order to constrain and rule out some of these models.

Figure 1

Diagrams $r=r(n_s)$ (left) and $n_s^{\prime }=n_s^{\prime }(n_s)$ (right) for the generalized Chaplygin gas I model for the number of $e$-folds in the range $N_e\in [50,60]$.

Figure 2

Left: $n_s-r$ diagram for the generalized Chaplygin gas II model. Right: $n_s-n_s^{\prime }$ diagram for the same model. The plots are for $N_e\in [50,60]$ and $\lambda \in [-0.5,0.5]$.

Figure 3

Left: $n_s-r$ diagram for the generalized Chaplygin gas III model. Right: $n_s-n_s^{\prime }$ diagram for the same model. The plots are for $N_e\in [50,60]$ and $\lambda \in [-1.03,-1.01]$, with $F_1=-1.0001$.

Figure 4

Diagrams $r=r(n_s)$ (left) and $n_s^{\prime }=n_s^{\prime }(n_s)$ (right) for the generalized Chaplygin gas IV model for the number of $e$-folds in the range $N_e\in [50,60]$, for $A=1$ and free parameter $B$ in the range $B\in [-10,100]$.

Figure 5

Left: $n_s-r$ diagram for the model generalized Chaplygin gas V. Right: $n_s-n_s^{\prime }$ diagram for the same model. The plots are for $N_e\in [50,60],\overline{B}=-0.002$ and $\lambda \in [-1,0)$.

Figure 6

Left: $n_s-r$ diagram for the model “Lambert function II.” Right: $n_s-n_s^{\prime }$ diagram for the same model. The plots are for $N_e\in [50,60]$ and $q\in [65,100]$.

Figure 7

Left: $n_s-r$ diagram for the model error function. Right: $n_s-n_s^{\prime }$ diagram for the same model. The plots are for $N_e\in [50,60]$ and $AB\in [-100,-0.02]$.