Constraints on tachyon inflationary models with an AdS/CFT correspondence

To study the effect of the anti–de Sitter/conformal field theory correspondence (AdS/CFT) on the primordial inflationary era, we consider a universe filled with a tachyon field in a slow-roll regime. In this context, the background and perturbative parameters characterizing the inflationary era are related to the standard one by correction terms. We show a clear agreement between the theoretical prediction and the observational data for the above-mentioned model. The main results of our work are illustrated for an exponential potential. We show that, for a suitable conformal anomaly coefficient, AdS/CFT correspondence might leave its imprints on the spectrum of the gravitational waves amplitude with a tensor to scalar ratio, $r$, of the perturbations compatible with Planck data.

Figure 1

Evolution of the dimensionless parameter $x$ versus the conformal anomaly coefficient $c$ for different values of the tensor-scalar ratio $r$ and for $A_s^2=2.20\times {10}^{-9}$.

Figure 2

Evolution of the tensor-scalar ratio $r$ versus the dimensionless parameter $x$ for different values of the conformal anomaly coefficient $c$.

Figure 3

Evolution of the correction term $G_{r,c}$ versus the conformal anomaly coefficient $c$ for different values of the tensor-scalar ratio $r$.

Figure 4

Evolution of the correction term $G_{r,c}$ versus the tensor-scalar ratio $r$ for different values of the conformal anomaly coefficient $c$.

Figure 5

Evolution of the correction term $C_{r,c}$ versus the conformal anomaly coefficient $c$ for different values of the tensor-scalar ratio $r$.

Figure 6

Evolution of the correction term $C_{r,c}$ versus the tensor-scalar ratio $r$ for different values of the conformal anomaly coefficient $c$.

Figure 7

Evolution of the potentials $V_{hc}$ (blue curve) and $V_{\max }$ (black curve) versus the conformal anomaly coefficient $c$ for $r=0.08$.

Figure 8

Evolution of the $e$-folding number $N$ versus the conformal anomaly coefficient $c$ for different values of the $\alpha$ parameter and for the tensor-scalar ratio $r=0.08$. We set ${\alpha }^{\prime }=\alpha /{\widehat{m}}_p$.

Figure 9

Evolution of the $e$-folding number $N$ versus the conformal anomaly coefficient $c$ for different values of the tensor-scalar ratio $r$ and for ${\alpha }^{\prime }=\alpha /{\widehat{m}}_p=1.22\times {10}^{-5}$.

Figure 10

Evolution of the scalar spectral index $n_s$ versus the number of $e$-folds $N$ for different values of $c$, for $r=0.08$ and $\alpha =6\times {10}^{-6}{\widehat{m}}_p$.

Figure 11

Evolution of the running spectral index ${\alpha }_s$ versus the number of $e$-folds $N$, for different values of $c$, for $r=0.08$ and $\alpha =6\times {10}^{-6}{\widehat{m}}_p$.

Figure 12

Plot of the parameter $r$ as a function of the scalar spectral index $n_s$ for two values of the $\alpha$ parameter, $\alpha =0.8\times {10}^{-5}{\widehat{m}}_p$ (green dashed line) and $\alpha =0.6\times {10}^{-5}{\widehat{m}}_p$ (black solid line), and for the conformal anomaly coefficient $c=2.5\times 10^7$. The marginalized joint 68% and 95% confidence level contours $(n_s,r)$ using Planck $\mathrm{TT}+\text{low}\mathrm{P}$, Planck TT, TE, $\mathrm{EE}+\text{low}\mathrm{P}$ data release are shown [3].

Figure 13

Plot of the parameter $r$ as a function of the scalar spectral index $n_s$ for two values of the conformal anomaly coefficient, $c=3\times 10^7$ (green dashed line) and $c=2\times 10^7$ (black solid line), and for the $\alpha$-parameter $\alpha =0.6\times {10}^{-5}{\widehat{m}}_p$. The marginalized joint 68% and 95% confidence level contours $(n_s,r)$ using Planck $\mathrm{TT}+\text{low}\mathrm{P}$, Planck TT, TE, $\mathrm{EE}+\text{low}\mathrm{P}$ data release are shown [3].

Figure 14

Plot of the running spectral index ${\alpha }_s$ as a function of the scalar spectrum index $n_s$, for different two values of the $\alpha$ parameter, $\alpha =0.8\times {10}^{-5}{\widehat{m}}_p$ (green dashed line) and $\alpha =0.6\times {10}^{-5}{\widehat{m}}_p$ (black solid line), and for the conformal anomaly coefficient $c=2.5\times 10^7$. The marginalized joint 68% and 95% confidence level contours $(n_s,dns/d\ln k)$ using Planck $\mathrm{TT}+\text{low}\mathrm{P}$, Planck TT, TE, $\mathrm{EE}+\text{low}\mathrm{P}$ data release are shown [3].

Figure 15

Plot of the running spectral index ${\alpha }_s$ as a function of the scalar spectrum index $n_s$, for two values of the conformal anomaly coefficient $c=3\times 10^7$ (green dashed line) and $c=2\times 10^7$ (black solid line), and for the $\alpha$-parameter $\alpha =0.6\times {10}^{-5}{\widehat{m}}_p$. The marginalized joint 68% and 95% confidence level contours $(n_s,dns/d\ln k)$ using Planck $\mathrm{TT}+\text{low}\mathrm{P}$, Planck TT, TE, $\mathrm{EE}+\text{low}\mathrm{P}$ data release are shown [3].