- \tosc \right) \right)  &, \,\,  t_{i} < t \leq  \tosc \\
                                    \dfrac{\cos^{2} \left[\omega \left(t - \tosc \right) \right] }{\left(\frac{15}{2\omega }+6(t-\tosc)-\frac{9}{2\omega } \cos [2\omega (t-\tosc)]\right)}  & , \,\, \tosc \leq t \, ,
                    \end{dcases}$$ where $\tosc = t_{i} + (3/2\omega^2) H_{i} - (1/2\omega)$. We show the details to obtain these solutions in the appendix. Thus, after the long inflationary plateau, $H(t)$ decreases linearly and reaches to the oscillation period. The approximate solutions for the scale factor $a$ are obtained from $H$s in Eqs.(\[Htiosc\]) $$\label{attiosc} a(t) = \begin{dcases} a_{i} e^{H_{i}\left(t - t_{i}\right) - (\omega^2/3) \left( t -t_{i} \right)^2} &, \,\, t_{i} < t \leq t_{\text{osc}}  \\
             a_{\osc} \left( 1 + \dfrac{\omega \left(t - \tosc \right)}{4} \right)^{2/3}  &, \,\, \tosc \leq t \, , 
             \end{dcases}$$ where one can obtain the $a(t)$ in the oscillatory phase by integrating the $H$ averaged over a few cycles. During the corresponding periods, the Ricci scalar evolves as $$\label{Rtiosc} 
    R(t) = \begin{dcases} -4 \omega (\omega -1) - 8\omega ^2 \left( t-t_{i} \right) &, \,\, t_{i} < t \leq t_{\text{osc}} \, , \\ 
                                              \frac{-4 \omega  \cos \left[\left(t-t_{\text{osc}}\right) \omega \right]}{\left(5+4 \omega \left( t - t_{\text{osc}} \right) -3 \cos \left[2 \left(t-t_{\text{osc}}\right) \omega \right]\right){}^2} \times & \\ 
                                              \Biggl( \Bigl(-7+\left(4-8 t+8 t_{\text{osc}}\right) 