Inflationary generalized Chaplygin gas and dark energy in light of the Planck and BICEP2 experiments

In this work, we study an inflationary scenario in the presence of generalized Chaplygin gas (GCG). We show that in Einstein gravity, GCG is not a suitable candidate for inflation; but in a five-dimensional brane-world scenario, it can work as a viable inflationary model. We calculate the relevant quantities such as $n_s$, $r$, and $A_s$ related to the primordial scalar and tensor fluctuations, and using their recent bounds from Planck and BICEP2, we constrain the model parameters as well as the five-dimensional Planck mass. But as a slow-roll inflationary model with a power-law type scalar primordial power spectrum, GCG as an inflationary model cannot resolve the tension between results from BICEP2 and Planck with a concordance $\mathrm{\Lambda }\mathrm{CDM}$ Universe. We show that by going beyond the concordance $\mathrm{\Lambda }\mathrm{CDM}$ model and incorporating more general dark energy behavior, we may ease this tension. We also obtain the constraints on the $n_s$ and $r$ and the GCG model parameters using $\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$ data considering the CPL dark energy behavior.

Figure 1

Allowed region in the ($\alpha -N_{*}$) plane. The region inside the solid lines is for the $n_s$ constraint from $\text{Planck}+\mathrm{WP}$; the region inside the dashed lines is for the $r$ constraint from BICEP2. The constraints are for the $\mathrm{\Lambda }\mathrm{CDM}$ model. The shaded region satisfies both the constraints.

Figure 2

Allowed region in ($\alpha -\beta$) parameter space for different values of $N_{*}$. Here we have used best fit values and bounds of $n_s$ and $r$ given by $\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$. The cosmological model is assumed to be $\mathrm{\Lambda }\mathrm{CDM}$. The region inside the solid lines satisfies the constraint on $n_s$ from $\text{Planck}+\mathrm{WP}$ and the region inside the dashed lines satisfies the constraint on $r$ from BICEP2. The shaded region satisfies both the constraints. The dotted lines satisfy the constraint on $A_s$ from Planck for $V_0=7.0\times 10^{62}{\mathrm{GeV}}^4$ (for the top panel), $8.0\times 10^{62}{\mathrm{GeV}}^4$ (bottom left), and $9.5\times 10^{62}{\mathrm{GeV}}^4$ (bottom right). The dots are for the $M_5=1.47\times 10^{-2}{M}_{\text{Pl}}$ (top), $M_5=1.54\times 10^{-2}{M}_{\text{Pl}}$ (bottom left), and $M_5=1.58\times 10^{-2}{M}_{\text{Pl}}$ (bottom right).

Figure 3

Behavior of $C_l^{TT}$ (left) and $C_l^{BB}$ (right) with angular scale $l$ for different cases. For the left panel, top to bottom, Power Law PPS $(\mathrm{\Lambda }\mathrm{CDM})+r$ ($\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$), Power Law PPS $(\mathrm{DE}1)+r$ ($\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$), Power Law PPS $(\mathrm{DE}2)+r$ ($\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$). The error bars are for Planck low-$l$ data points. For the right panel, bottom to top, Power Law PPS $(\mathrm{\Lambda }\mathrm{CDM})+r$ ($\text{Planck}+\mathrm{WP}$), Power Law PPS $(\mathrm{\Lambda }\mathrm{CDM})+r$ ($\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$), Power Law PPS $(\mathrm{DE}1)+r$ ($\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$), Power Law PPS $(\mathrm{DE}2)+r$ ($\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$). The error bars are for BICEP2 data points.

Figure 4

Likelihood functions for $n_s$ and $r$ using $\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$ with the CPLDE model.

Figure 5

Likelihood function for $\alpha$ and $\beta$ for different values of $N_{*}$ using $\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$ with the CPLDE model. The thick black lines in both panels represent $N_{*}=55$ while the dotted lines in both panels correspond to likelihood for $N_{*}=60$.

Figure 6

Allowed region in ($\alpha -\beta$) parameter space for different values of $N_{*}$ using $\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$ with the CPLDE model. The region inside the solid lines satisfies the constraint on $n_s$ and the region inside the dashed lines satisfies the constraint on $r$. The shaded region satisfies both the constraints. The dotted lines satisfies the constraint on $A_s$ from Planck for $V_0=1.6\times 10^{63}{\mathrm{GeV}}^4$ (for the top panel), $1.9\times 10^{63}{\mathrm{GeV}}^4$ (bottom left), and $2.1\times 10^{63}{\mathrm{GeV}}^4$ (bottom right). The dots are for the $M_5=1.68\times 10^{-2}{M}_{\text{Pl}}$ (top), $M_5=1.8\times 10^{-2}{M}_{\text{Pl}}$ (bottom left), and $M_5=1.83\times 10^{-2}{M}_{\text{Pl}}$ (bottom right).

Figure 7

68% and 95% contour regions in the $r-n_s$ plane allowed by $\text{Planck}+\mathrm{WP}$ data (solid contours), and by $\text{Planck}+\mathrm{WP}+\mathrm{BICEP}2$ data (dashed contours) using CPLDE. Dotted, continuous, and dashed lines correspond to $\alpha =-1.016$, $\alpha =-1.025$, and $\alpha =-1.028$, respectively. For each of these cases, the upper line is for $N_{*}=50$ and the lower one is for $N_{*}=60$. From top to bottom, circle points correspond to $\beta =0.0085$, $\beta =0.0368$, $\beta =0.2572$, $\beta =0.5013$, $\beta =0.3894$, and $\beta =0.6420$, respectively. From top to bottom, star points correspond to $\beta =0.0053$, $\beta =0.0230$, $\beta =0.1714$, $\beta =0.3342$, $\beta =0.2596$, and $\beta =0.5707$, respectively.