Reheating in geometric Weyl-invariant Einstein-Cartan gravity

We study Weyl-invariant purely gravitational theories formulated within the Einstein-Cartan framework. In the Einstein-frame description, these models are dynamically equivalent to standard general relativity coupled to an axion-like pseudoscalar degree of freedom, which naturally drives a period of cosmic inflation. Without committing to a specific microscopic mechanism for reheating, we demonstrate that the post-inflationary reheating dynamics play a crucial role in shaping the inflationary predictions. In particular, we show that assumptions about the reheating temperature and the equation-of-state parameter can significantly affect the predicted values of inflationary observables, highlighting the necessity of consistently incorporating reheating effects in the phenomenological analysis of inflationary models.

💡 Research Summary

The paper investigates a class of purely gravitational theories that are invariant under local Weyl transformations and are formulated within the Einstein‑Cartan framework, where spacetime possesses both curvature and torsion. In this setting two independent curvature scalars can be built: the usual Ricci scalar R and the pseudoscalar Holst invariant \tilde R, the latter violating parity. Imposing Weyl invariance forbids any dimensionful couplings, so the most general action contains only quadratic curvature combinations, schematically S∼γR²+δ\tilde R²+εR\tilde R, with dimensionless constants γ, δ and ε. The parity‑odd term εR\tilde R is crucial: without it the scalar potential that emerges after moving to the Einstein frame grows exponentially and cannot support slow‑roll inflation.

By introducing two auxiliary scalars χ and ζ the quadratic action can be linearised. After fixing the Weyl gauge χ=M_P²/γ and solving the algebraic equations for the torsion components (the vector T_μ, the axial vector \hat T_μ and the pure tensor τ_μνρ) the torsion can be eliminated. The resulting on‑shell action is equivalent to Einstein‑Hilbert gravity minimally coupled to a single canonical pseudoscalar field ϕ with a potential \