Tachyon inflation with steep potentials

Within the framework of tachyon inflation, we consider different steep potentials and check their viability in light of the Planck 2015 data. We see that in this scenario, the inverse power-law potential $V(\varphi )=V_0(\varphi /{\varphi }_0{)}^{-n}$ with $n=2$ leads to the power-law inflation with the scale factor $a(t)\propto t^q$ where $q>1$, while with $n<2$, it gives rise to the intermediate inflation with the scale factor $a(t)\propto \exp (A{t}^f)$ where $A>0$ and $0<f<1$. We find that, although the inverse power-law potential with $n\le 2$ is completely ruled out by the Planck 2015 data, the result of this potential for $n>2$ can be compatible with the 95% CL region of Planck 2015 TT, TE, $\mathrm{EE}+\mathrm{lowP}$ data. We further conclude that the exponential potential $V(\varphi )=V_0{e}^{-\varphi /{\varphi }_0}$, the inverse cosh potential $V(\varphi )=V_0/\cosh (\varphi /{\varphi }_0)$, and the mutated exponential potential $V(\varphi )=V_0[1+(n-1{)}^{-(n-1)}(\varphi /{\varphi }_0{)}^n]e^{-\varphi /{\varphi }_0}$ with $n=4$, can be consistent with the 95% CL region of Planck 2015 TT, TE, $\mathrm{EE}+\mathrm{lowP}$ data. Moreover, using the $r-n_s$ constraints on the model parameters, we also estimate the running of the scalar spectral index $d{n}_s/d\ln k$ and the local non-Gaussianity parameter $f_{\mathrm{NL}}^{\text{local}}$. We find that the lower and upper bounds evaluated for these observables are compatible with the Planck 2015 results.

Figure 1

Predictions of different steep potentials in $r-n_s$ plane in the tachyon inflationary scenario in comparison with the observational results. The marginalized joint 68% and 95% CL regions from Planck 2013, Planck 2015 $\mathrm{TT}+\mathrm{lowP}$ and Planck 2015 TT, TE, $\mathrm{EE}+\mathrm{lowP}$ data ($\mathrm{\Lambda }\mathrm{CDM}+r+d{n}_s/d\ln k$) [9] are specified by gray, red and blue, respectively.