Geometrical scalar back-reaction effects in inflation

Starting with the Lagrangian formulation of General Relativity, we will conduct an investigation into the production of spacetime waves, due to a geometric boundary term of a closed extended manifold, within the tensor and scalar sectors. This scheme will be studied in an inflationary universe. We explore two distinct scenarios: Cold Inflation and Warm Inflation. The scalar modes $Z_{k}^{\mathbb{R}}$ and $Z_{k}^{\mathbb{I}}$ oscillate within the horizon, and they become constant at (or right after) horizon crossing $k\simeq aH$ and they remain so when radiation starts to dominate. The larger $k/k_{0}$ the $Z_{k}$'s amplitudes increase too. In general we can notice that radiation reduces the size of the $Z_{k}$'s amplitudes, hence yielding smaller signals of such modes. The tensor sector shows an irregular journey due to their abruptly growth just as they cross the horizon. This upshot hinders any probable observational hint or signal. However, we expect this novel mechanism of spacetime waves production brings new cosmological sources, for which no astrophysical source has been identified.