Motor Inflation: Cosmological Consequences of the Motor Dimension

In this work, we investigate the cosmological consequences of the motor dimension modelproposed in [1] . In this model, the fifth compact dimension µ (the motor dimension) generatesmass, inertia, and the perception of time through motion along a circle of radius Rµ. We showthat the same geometric structure naturally provides a mechanism for cosmic inflation. Thefield Φ (the radion) or, more generally, the Wilson phase of a gauge field along the compactdimension can play the role of the inflaton. The inflationary potential arises from non-localeffects - quantum corrections due to particles propagating around the compact circle -and is therefore protected from ultraviolet (UV) corrections. We derive the inflationarypotential, calculate the slow-roll parameters, and compare predictions for the spectral indexns and the tensor-to-scalar ratio r with the latest observational data from Planck 2018 andBICEP/Keck. We find that under the slow-roll condition, the model predicts ns ≈ 0.965and r ≈ 0.0026, which agrees with the observed limits from Planck 2018 and BICEP/Keck.The model also predicts the production of superheavy Kaluza-Klein (KK) particles duringand after inflation via the Schwinger effect, which could constitute dark matter or dominatethe early Universe.