- Article
30 Pages
We investigate the background dynamics of cubic Geometric Inflation coupled with radiation and a minimally coupled canonical scalar field with an exponential potential, using the cubic truncation as a minimal test of geometric-to-scalar inflationary cascades. We formulate the cosmological equations as an autonomous dynamical system and analyze its finite critical points and representative Hubble-flow trajectories. The cubic sector can generate an initial geometrically accelerated phase, but its duration grows only logarithmically with the initial curvature hierarchy and is insufficient to solve the horizon problem for moderate initial conditions. The subsequent scalar-field-dominated stage obeys the power-law relation
under the standard GR-based first-order mapping, placing it in strong tension with current bounds on primordial tensor modes. Moreover, no value of the constant exponential-potential slope yields a graceful exit into a standard radiation-dominated epoch. The regular branch requires trans-Planckian radiation densities in the asymptotic past, whereas the alternative branch contains a finite-curvature dynamical degeneracy. Thus, although cascade-like background trajectories exist, the minimal cubic model does not satisfy the basic background requirements of a viable inflationary cosmology.
Universe
15 October 2026






![A schematic HR Diagram for populations of evolved stars. Published with permission from Patrick [2]. Massive stars are those above
10
4
L
⊙
. The locations of the red, yellow and blue hypergiants and supergiants and the evolved OB and WN stars are identified. The dashed red line show the location of the Humphreys-Davidson Limit.](https://mdpi-res.com/cdn-cgi/image/width=281%2Cheight=192/https://mdpi-res.com/universe/universe-12-00229/article_deploy/html/images/universe-12-00229-g001-550.jpg)



