Possible relationship between initial conditions for inflation and past geodesic incompleteness of the inflationary spacetime

According to the Borde-Guth-Vilenkin (BGV) theorem an expanding region of spacetime cannot be extended past beyond some boundary \mathcal{B}. Therefore, inflationary universe must have had kind beginning. However, BGW says nothing about conditions on \mathcal{B}, or even its location. Here we present a single-scalar field model Two-Measure Theory, where non-Riemannian volume element $\Upsilon d^4x$ is in action. As result dynamics, upper bound \varphi_0 admissible values scalar \varphi appears, which sets position \mathcal{B} form spacelike hypersurface \Upsilon(x)=0 with condition: \Upsilon\to 0^+ as \varphi\to\varphi_0^-. A detailed study has established that if initial kinetic energy density \rho_{kin}^{(in)} prevails over gradient \rho_{grad}^{(in)} then there interval \varphi_{in}^{(min)}\leq\varphi_{in}<\varphi_0, and exceed potential hence necessary for onset inflation are satisfied. It shown under almost all possible left-handed 0^-, metric tensor Einstein frame jump discontinuity so Christoffel connection coefficients not defined \Upsilon=0. Thus, \varphi_{in}^{(min)}\leq \varphi_{in}<\varphi_0 \rho_{kin}^{(in)}>\rho_{grad}^{(in)}, was stage history our Universe congruence timelike geodesics