field space.

Another popular inflaton potential is the Starobinsky model [@Starobinsky; @Mukhanov], which has the general form V =  ( 1 - e\^[-/M\_]{})\^ 2  . The same structure appears also in Higgs inflation [@higgsflation]. In Fig.(\[starobinsky\])-b we plot $\chi$ as a function of the canonical field in units of Planck mass. Essentially the same thing happens for the Starobinsky model. the simplest version of it would be inconsistent with the Strong SWGC, since at some points in field space the condition is violated. It needs to be modified at large trans-Planckian distances. Adding a perturbation may possibly make it consistent.

![ a) The value of $\chi$ for $A=1$ and $B=0.2,0.5,1.0$. The SSWGC implies $\chi \geq 0$. b) The value of $\chi$ for the Starobinsky potential.[]{data-label="starobinsky"}](laraiz.pdf "fig:") ![ a) The value of $\chi$ for $A=1$ and $B=0.2,0.5,1.0$. The SSWGC implies $\chi \geq 0$. b) The value of $\chi$ for the Starobinsky potential.[]{data-label="starobinsky"}](starobinsky_chi.pdf "fig:")

These are just a couple of examples, just to show that the constraint is potentially very strong. It would be interesting to study these and other examples in more detail.

Constraints on the SM from its 3D compactification
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Consider the SM compactified in a circle of radius 