Figure 1

The scalar (thick, blue) and tensor (dashed, red) PPS in the punctuated inflation model, an example of a sandwich model. Notice the sharp spike in scalar PPS and tensor power overtaking scalar power for a range of modes near it.Reuse & Permissions

Figure 2

The trajectories of mode function of $R_k$ in complex plane. The dots on the trajectory are uniform in expansion e-folds, crowding of dots indicates that $R_k$ freezes. The thin trajectory corresponds to power law inflation which never crosses the origin. Notice that when $R_k$ freezes, the tangent vector to its trajectory points radially in. The other two trajectories show the behavior of $R_k$ in the complex plane for two different modes in the punctuated inflation model. The mode denoted by the continuous (thick) purple curve freezes once, then unfreezes, evolves radially in and freezes again before crossing the origin. The dashed gray curve corresponds to a mode with larger $k^2$, it undergoes large radial super-Hubble evolution, crosses the origin and then freezes undergoing super-Hubble enhancement of power compared with the other mode that undergoes suppression. In between would lie a mode (not shown) that ends up right at the origin leading to a null in PPS.Reuse & Permissions

Figure 3

Typical behavior of $z^{\prime \prime }/z$ against conformal time, $\eta$, in any sandwich model (blue curve). The horizontal red line is $k^2$ while the dashed curve is an alternative modified $z^{\prime \prime }/z$ that may be needed to ensure that the mode of interest becomes super-Hubble (as explained in the text).Reuse & Permissions

Figure 4

The behavior of the mode in $(r\equiv |v_k|,r^{\prime }\equiv |v_k{|}^{\prime })$ phase space for a given mode in the Starobinsky model for different strengths of the delta function in $z^{\prime \prime }/z$. Stage I of the evolution shall make sure that ${\theta }^{\prime }$ has already become zero. For low strengths of the delta function, blue (thick) and black (dashed), there is no origin crossing, while for high strengths, purple (dotted) and red (continuous thin), $v_k$ passes through the origin (leading to a discontinuity in $r^{\prime }$). Notice that since this is not an autonomous system, the trajectories do cross each other. The thick arrow illustrates that stage II is expected to take $(|v_k|,|v_k{|}^{\prime })$ to regions with sufficiently negative $|v_k{|}^{\prime }$.Reuse & Permissions