Geometrical origin of inflation in Weyl-invariant Einstein-Cartan gravity (2501.16416v1)

Abstract: It is shown that the scalar degree of freedom built-in in the quadratic Weyl-invariant Einstein-Cartan gravity can drive inflation and with predictions in excellent agreement with observations.

• The paper demonstrates that cosmological inflation can originate geometrically from a scalar field within the Weyl-invariant Einstein-Cartan framework, which incorporates torsion in addition to the metric.
• Using auxiliary fields, the authors show equivalence to General Relativity with a massive spin-0 field and find numerically that a plateau potential at large coupling supports sufficient inflationary dynamics.
• The model's predictions for the spectral index and tensor-to-scalar ratio align well with cosmic microwave background observational data, comparable to predictions from other successful inflation models.

An Exploration of Inflation Mechanisms within Weyl-Invariant Einstein-Cartan Gravity

The paper investigates a comprehensive framework for understanding the origin of inflation within the Weyl-invariant Einstein-Cartan (EC) formulation of general relativity. Unlike conventional approaches grounded solely in the metric framework, this work exploits the EC formulation, which incorporates torsion as a supplementary geometric entity alongside the metric. The principal objective is to demonstrate that inflation can be driven by a scalar degree of freedom inherently embedded in the quadratic Weyl-invariant EC theory, ensuring the applicability and relevance of this approach given its alignment with observational data.

The central theoretical construct is a unique ghost-free action expressed in terms of a quadratic curvature formulation. The action incorporates scalar and pseudoscalar (Holst) curvatures, which are linked to a torsionful, metric-compatible affine connection. The action sets the stage for introducing auxiliary fields to facilitate translation from a torsion-inclusive to a purely metric description. This transition highlights the equivalence of the formulated EC theory to general relativity complemented by a massive spin-0 field — a pivotal aspect of driving inflation.

An essential component of the investigation is the use of numerical models to demonstrate the potential characteristics of the scalar field. The potential exhibits a plateau-like behavior for large values of the coupling parameter $q$, which turns out to be paramount for supporting robust inflationary dynamics. This behavior allows for a sufficient period of exponential expansion matching the observational constraints imposed by cosmic microwave background data.

The implications of achieving inflation via geometric origins within the Weyl-invariant EC framework are significant, paralleling the traditional Starobinsky model while leveraging the inherent symmetry properties of the underlying theory. Most notably, the paper illustrates the inherently geometric nature of the inflaton, augmented by non-minimal coupling effects arising from torsion, further differentiating it from purely metric-based formulations.

Numerical results underpin the viability of the model, presenting compatibility with the latest observational data. Specific predictions concerning the spectral index $n_s$ and tensor-to-scalar ratio $r$ align well with observationally constrained values, similar to those derived from other successful inflationary models. As the calculations indicate, the required number of e-foldings and the dynamics of inflation are well-supported through the integration of parameter space extended by large $q$ values.

Future avenues of research suggested by this work include coupling the Weyl-invariant EC gravity to the Standard Model of particle physics. While intriguing insights were hinted at, such as the potential for gravitational solutions to the strong-CP problem, pragmatic challenges persist regarding match-ups with observed cosmological constants and gravitationally induced scalar masses. This underscores a potential tension between simultaneously solving inflationary dynamics and other Standard Model issues, such as the strong-CP problem or Higgs mass fine-tuning, indicating that further explorations might necessitate alternative approaches or compromises.

In conclusion, this paper contributes a significant step towards understanding inflation through a refined geometric lens. By leveraging the unique properties of Weyl invariance in the EC framework, the research illustrates how fundamental extensions of our geometric understanding of spacetime can provide suitable mechanisms for inflation. It opens doors for reconciling diverse theoretical components across cosmological theories and tensor frameworks, posing fresh questions and challenges for future research in both theoretical and observational domains.