Inflationary Cosmology with Quantum Gravitational Effects and Swampland Conjectures *

Qiang Wu,Tao Zhu

Fig. 1 (Color online) The schematic plots of function $g(y)$ in Eq. (9) for four representative cases. The number and nature of the turning points for each case are different. Case (a): three single real turning points ($y_0 \ll y_1 < y_2$); Case (b): one single real turning point ($y_0$) and one double real turning point $y_1=y_2 \gg y_0$; Case (c): one single real turning point ($y_0$) and two complex conjugated turning points ($y_1=y_2^*$ and $y_0 \ll {\rm Re}(y_0) = {\rm Re}(y_2) $); Case (d): one single real turning point $y_0$. Noe that for all cases $b_2>0$.