This paper studies the quantum corrections to the Higgs inflation model in
the context of the Einstein-Cartan (E-C) gravity in the large-$ N $ limit with
$N$ being the number of real scalar components in Higgs. Recently, it is
realized that the Higgs inflation in the E-C formalism smoothly connects those
in the metric and the Palatini formalisms in the presence of a non-minimal
coupling between the Higgs fields and the Nieh-Yan term. This motivates us to
investigate the quantum corrections to the E-C Higgs inflation and to clarify
how the Ricci curvature squared $ R^2 $ induced by the quantum corrections
succeeds in Ultraviolet (UV)-extending the Higgs inflation in metric formalism
while it fails in the Palatini case. We show that a generalized $ R^2 $-term
required for the renormalization in the E-C formalism induces a new scalar
degree of freedom (DoF), the scalaron, which gradually decouples with the
system due to its increasing mass as approaching the Palatini limit. The
presence of the scalaron extends the UV cutoff at vacuum of the original model
except for the parameter space close to the Palatini limit. This UV-extension
is expected to solve the strong coupling problem that may exist during
(p)reheating in the absence of the scalaron.
Quantum Corrections and Higgs Inflation in the Einstein-Cartan Gravity
This study explores the quantum corrections to the Higgs inflation model within the framework of the Einstein-Cartan (E-C) gravity. The research focuses on the large-$ N $ limit, where $N$ represents the number of real scalar components in the Higgs field. Recent findings have established a connection between Higgs inflation in the E-C formalism and those in the metric and Palatini formalisms, achieved through a non-minimal coupling between the Higgs fields and the Nieh-Yan term.
Motivation and Objectives
The primary motivation for this inquiry is to understand how quantum corrections affect E-C Higgs inflation and to determine the role played by the Ricci curvature squared term ($ R^2 $). Notably, this investigation seeks to explain why $ R^2 $ succeeds in UV-extending Higgs inflation within the metric formalism while failing to do so within the Palatini case.
Main Findings
The research demonstrates that a generalized $ R^2 $ term, necessary for renormalization in the E-C formalism, introduces a new scalar degree of freedom called the scalaron. As the system approaches the Palatini limit, this scalaron gradually decouples from the rest of the system due to its increasing mass. Consequently, the presence of the scalaron extends the UV cutoff at the vacuum of the original model, except for parameter space near the Palatini limit.
Implications and Opportunities
The identification of the scalaron and its role in extending the UV cutoff has crucial implications for solving the strong coupling problem potentially encountered during (p)reheating in the absence of the scalaron. By incorporating the scalaron in the E-C Higgs inflation model, the study opens up opportunities for exploring novel avenues to address and mitigate these strong coupling issues.
Roadmap for Future Research
While this study provides valuable insights into the quantum corrections and dynamics of the E-C Higgs inflation model, several challenges and opportunities lie ahead. Some potential areas of research include:
- Further investigating the specific properties and behavior of the scalaron, particularly concerning its interaction with other particles and fields.
- Examining the implications of the scalaron for cosmological scenarios and inflationary models beyond the Higgs field.
- Exploring the role of the scalaron in other gravitational theories and alternative frameworks.
- Investigating the experimental detectability of the scalaron and its potential observables.
- Developing methods to incorporate the scalaron in numerical simulations and computational models.
Addressing these research avenues will deepen our understanding of the E-C Higgs inflation model, contribute to resolving the strong coupling problem, and enable further advancements in particle physics, cosmology, and gravity theories.