High dissipative nonminimal warm inflation

Abstract

We study a model of warm inflation in which both inflaton field and its derivatives are coupled nonminimally to curvature. We survey the spectrum of the primordial perturbations in high dissipative regime. By expanding the action up to the third order, the amplitude of the non-Gaussianity is studied both in the equilateral and orthogonal configurations. Finally, by adopting four sort of potentials, we compare our model with the Planck 2015 released observational data and obtain some constraints on the model’s parameters space in the high dissipation regime.

Appendix

$$\begin{aligned} S_{3} =& \int dt d^{3}x a^{3} \biggl[3M_{pl}^{2}H^{2} \biggl(1-\frac{\xi\varphi^{2}}{2M_{pl}^{2}} \biggr)-\frac{\dot{\varphi}^{2}}{2} \\ &{}- 6\xi H\varphi\dot{\varphi}+15\frac{H^{2}}{M^{2}}\dot{ \varphi}^{2} \biggr]\varPhi^{3}-\frac{2\dot{\varphi}^{2}}{a^{2}M^{2}} \partial^{2}\varPsi \\ &{}+ \biggl[ \biggl(-9M_{pl}^{2}H^{2} \biggl(1-\frac{\xi\varphi^{2}}{M_{pl}^{2}} \biggr)+ \frac{3\dot{\varphi}^{2}}{2}+18\xi H\varphi\dot{ \varphi} \\ &{}- \frac{27H^{2}}{M^{2}}\dot{\varphi}^{2} \biggr)\varPsi \\ &{}+ \biggl(-6M_{pl}^{2}H \biggl(1-\frac{\xi\varphi^{2}}{M_{pl}^{2}} \biggr)-6\xi H\varphi\dot{\varphi}-\frac{18H}{M^{2}}\dot{\varphi}^{2} \biggr)\dot{\varPsi} \\ &{}+ \biggl(2M_{pl}^{2}H \biggl(1-\frac{\xi\varphi^{2}}{M_{pl}^{2}} \biggr)-2\xi \varphi\dot{\varphi}+\frac{6H}{M^{2}}\dot{\varphi}^{2} \biggr)\frac{\partial^{2}{\mathcal{B}}}{a^{2}} \biggr]\varPhi^{2} \\ &{}+ \biggl[ \biggl(18M_{pl}^{2}H \biggl(1-\frac{\xi\varphi^{2}}{2M_{pl}^{2}} \biggr)-18\xi \varphi\dot{\varphi} \\ &{}-\frac{27H}{M^{2}}\dot{\varphi}^{2} \biggr)\dot{\varPsi}\varPsi- \frac{2M_{pl}^{2} (1-\frac{\xi\varphi^{2}}{2M_{pl}^{2}} )+ \frac{\dot{\varphi}^{2}}{M^{2}}}{a^{2}}\varPsi\partial^{2}\varPsi \\ &{}+ \biggl(-2M_{pl}^{2} \biggl(1-\frac{\xi\varphi^{2}}{M_{pl}^{2}} \biggr)+2\xi\varphi\dot{\varphi}+ \frac{3}{M^{2}}\dot{\varphi}^{2} \biggr)\frac{\partial_{i}\varPsi \partial_{i}{\mathcal{B}}}{a^{2}} \\ &{}+ \frac{-M_{pl}^{2}(1-\frac{\xi\varphi^{2}}{2M_{pl}^{2}})+ \frac{\dot{\varphi}^{2}}{2M^{2}}}{a^{2}}\bigl(\partial^{2}\varPsi\bigr) \\ &{}+ \frac{ (-2M_{pl}^{2} (1-\frac{\xi\varphi^{2}}{M_{pl}^{2}} )+2\xi\varphi\dot{\varphi}+ \frac{3}{M^{2}}\dot{\varphi}^{2} )}{a^{2}}\varPsi\partial^{2}{\mathcal{B}} \\ &{}+ \biggl(3M_{pl}^{2} \biggl(1-\frac{\xi\varphi^{2}}{2M_{pl}^{2}} \biggr)- \frac{9\dot{\varphi}^{2}}{2M^{2}} \biggr)\dot{\varPsi}^{2} \biggr]\varPhi \\ &{}+ \frac{M_{pl}^{2} (1-\frac{\xi \varphi^{2}}{2M_{pl}^{2}} )+\frac{\dot{\varphi}^{2}}{2M^{2}}}{a^{2}}\varPsi(\partial\varPsi)^{2} \\ &{}+ \biggl(-9M_{pl}^{2} \biggl(1-\frac{\xi \varphi^{2}}{M_{pl}^{2}} \biggr)+\frac{\dot{\varphi}^{2}}{2M^{2}} \biggr)\dot{\varPsi}^{2}\varPsi \\ &{}+ \frac{2M_{pl}^{2} (1-\frac{\xi \varphi^{2}}{M_{pl}^{2}} )-\frac{2\dot{\varphi}^{2}}{M^{2}}}{a^{2}}\dot{\varPsi}\partial_{i}\varPsi \partial_{i}{\mathcal{B}} \\ &{}+ \frac{2M_{pl}^{2} (1-\frac{\xi \varphi^{2}}{M_{pl}^{2}} )-\frac{\dot{\varphi}^{2}}{M^{2}}}{a^{2}}\dot{\varPsi}\varPsi\partial^{2}{\mathcal{B}} \\ &{}+ \frac{-2M_{pl}^{2} (1-\frac{\xi \varphi^{2}}{M_{pl}^{2}} )+\frac{\dot{\varphi}^{2}}{M^{2}}}{ a^{2}}\partial_{i}\varPsi\partial_{i}{ \mathcal{B}}\partial^{2}{\mathcal{B}} \\ &{}+ \frac{3}{2}\frac{ (M_{pl}^{2} (1 {-} \frac{\xi \varphi^{2}}{M_{pl}^{2}} ) {+} \frac{\dot{\varphi}^{2}}{2M^{2}} )\varPsi (\partial_{i}\partial_{j}{\mathcal{B}}\partial_{i}\partial_{j}{\mathcal{B}} {-} \partial^{2}{\mathcal{B}}\partial^{2}{\mathcal{B}} )}{a^{4}}, \end{aligned}$$

(76)

$$\begin{aligned} n_{s}-1 =&\frac{2V''\varepsilon H}{V'H'} \\ &{}- \frac{ (\varGamma'H+H'\varGamma+\frac{36H^{3}H'}{M^{2}} ) (V'+\xi R \varphi )}{2 (\varGamma H+9\frac{H^{4}}{M^{2}} )^{2}} \\ &{}+ 2 \biggl[-\eta+ \frac{H'' (\xi R\varphi+V' )}{H' (\varGamma H+9\frac{H^{4}}{M^{2}} )} \\ &{}+ \frac{27H^{2}H' (\xi R\varphi+V' )}{M^{2}H (9\frac{H^{3}}{M^{2}} )^{2}}-\frac{\varGamma' (\xi R\varphi+V' )}{H (9\frac{H^{3}}{M^{2}}+\varGamma )^{2}} \\ &{}- \frac{ (V'+\xi R\varphi )}{2H^{2} (\varGamma +9\frac{H^{3}}{M^{2}} )^{2}} \\ &{}\times \frac{\kappa^{2} (1+3\frac{H^{2}}{M^{2}}-2\xi-\frac{\varGamma' (\xi R \varphi+V' )}{48H^{2} (9\frac{H^{3}}{M^{2}}+\varGamma )}+\frac{\varGamma}{4H} )}{ (1-\kappa^{2}\xi \varphi^{2} )} \\ &{}\times \biggl[\frac{-18H^{3} (\xi R \varphi+V' )}{M^{2} (9\frac{H^{3}}{M^{2}}+\varGamma )}-2\xi R\varphi-2V' \\ &{}-3\varGamma \dot{\varphi} \biggr] \biggr]. \end{aligned}$$

(77)