On Inflation with Non-minimal Coupling (1002.2995v4)

Abstract: A simple realization of inflation consists of adding the following operators to the Einstein-Hilbert action: (partial phi)^2, lambda phi^4, and xi phi^2 R, with xi a large non-minimal coupling. Recently there has been much discussion as to whether such theories make sense quantum mechanically and if the inflaton phi can also be the Standard Model Higgs. In this note we answer these questions. Firstly, for a single scalar phi, we show that the quantum field theory is well behaved in the pure gravity and kinetic sectors, since the quantum generated corrections are small. However, the theory likely breaks down at ~ m_pl / xi due to scattering provided by the self-interacting potential lambda phi^4. Secondly, we show that the theory changes for multiple scalars phi with non-minimal coupling xi phi dot phi R, since this introduces qualitatively new interactions which manifestly generate large quantum corrections even in the gravity and kinetic sectors, spoiling the theory for energies > m_pl / xi. Since the Higgs doublet of the Standard Model includes the Higgs boson and 3 Goldstone bosons, it falls into the latter category and therefore its validity is manifestly spoiled. We show that these conclusions hold in both the Jordan and Einstein frames and describe an intuitive analogy in the form of the pion Lagrangian. We also examine the recent claim that curvature-squared inflation models fail quantum mechanically. Our work appears to go beyond the recent discussions.

• The paper establishes that single-field non-minimal coupling yields controlled quantum corrections in gravity and kinetic sectors.
• It demonstrates that multi-field interactions trigger significant quantum corrections, leading to theoretical breakdowns at energies around ∼1/ξ.
• These findings challenge the viability of the Standard Model Higgs as an inflaton and encourage refinements in inflationary model frameworks.

On Inflation with Non-minimal Coupling: An Academic Overview

The paper "On Inflation with Non-minimal Coupling" investigates theories of inflation characterized by non-minimal coupling terms in the scalar field-gravity interaction. This analysis integrates scalar fields into the cosmological inflation paradigm through the Einstein-Hilbert action, particularly focusing on operators $(\partial\phi)^2$, $\lambda\phi^4$, and $\xi\phi^2\mathcal{R}$. The author, Mark P. Hertzberg, explores whether such models are quantum mechanically viable and evaluates the Higgs boson’s role within these inflationary frameworks.

The research scrutinizes the inflation models by differentiating between single and multiple scalar fields with non-minimal coupling. The core objective is to ascertain the validity of the quantum field theories underpinning these models and the implications for the Standard Model Higgs as a potential inflaton. Notably, the paper highlights specific conditions and limitations fundamental to each scenario.

Single Field Case

For a single scalar field $\phi$, the paper confirms that the quantum theory remains well-behaved in the gravity and kinetic sectors. This conclusion stems from the minor nature of quantum corrections inherent to these sectors. However, complications arise with higher energy scattering induced by the $\lambda\phi^4$ potential, indicating a probable breakdown around $\sim/\xi$. This presents a challenge for developing a UV-complete framework.

Multi-field Case

The analysis notably shifts with multiple scalar fields $\vec{\phi}$, introducing qualitatively new interactions. Such interactions generate substantial quantum corrections even in the gravity and kinetic levels, leading to theoretical inconsistencies for energies above $\sim /\xi$. When applied to the Standard Model Higgs, composed of multiple fields, this finding indicates a breakdown in its applicability within non-minimal inflation models. The multi-field problems are corroborated by tree-level $2 \to 2$ scattering processes, emphasizing quantum effects that void the theory's robustness in inflationary contexts.

Theoretical Models: Frames and Analogy

The robustness of the paper extends to both Jordan and Einstein frames, ensuring the conclusions' consistency across theoretical frameworks. The research also draws a parallel with the pion Lagrangian, highlighting analogous breakdowns in multi-scalar field theories. This comparison aids in contextualizing the distinctive quantum behaviors between single and multiple field systems.

Additionally, the paper discusses the scalar-tensor formulation of curvature-squared models. The analysis here demonstrates that, contrary to recent criticisms, these formulations are perturbatively sound. This reassessment further shapes the narrative regarding gravitational interactions and potential quantum constraints at varying energy scales.

Implications and Speculation

This examination underscores significant implications for non-minimally coupled inflation models. The findings question the viability of embedding inflaton candidates within multi-field contexts like the Standard Model Higgs. Theoretical gaps identified through perturbative and loop-level analyses offer future avenues for refining inflationary models or reevaluating fundamental gravitational interaction paradigms.

Fundamentally, this work advances the dialogue on inflationary quantum field theories, exposing potential pathways and hurdles for unifying early universe cosmology with particle physics frameworks. Future explorations could refine these models or explore alternative scalar field configurations, potentially informing new inflation paradigms or gravitation theories.

In summary, “On Inflation with Non-minimal Coupling” provides a comprehensive examination of non-minimal coupling in inflation, offering pivotal insights that challenge current theoretical models. This research necessitates cautious interpretation of scalar fields' roles and encourages continued effort towards reconciling high-energy physics with early cosmological observations.