[Paper Review] Light Scalars in Cosmology

R. D. Peccei|ArXiv.org|Sep 4, 2000

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates the cosmological implications of light scalar fields—axions and quintessence—focusing on how quantum and gravitational corrections destabilize their near-masslessness. It shows that gravitational interactions, via Planck-scale suppressed operators, induce large mass shifts and explicit symmetry breaking unless couplings to matter are unnaturally small, challenging the naturalness of these models in quantum field theory and gravity.

ABSTRACT

I discuss here some of the constraints imposed by quantum and gravitational corrections on two hypothetical excitations, axions and quintessence, which have important cosmological implications. Although these corrections can be kept under control, the resulting constraints are not too natural. In particular, to keep the quintessence field light one must essentially decouple it from ordinary matter. Some possible suggestions of how to avoid these troubles are briefly touched upon.

Motivation & Objective

• To assess the viability of axions and quintessence as light scalar fields in cosmology from a quantum and gravitational field theory perspective.
• To analyze how gravitational corrections, particularly via Planck-scale suppressed operators, destabilize the lightness of these fields.
• To evaluate whether the observed near-masslessness of axions and quintessence can be naturally maintained in the presence of quantum and gravitational effects.
• To explore whether the extreme smallness of couplings required to preserve lightness implies observable signatures in precision tests of gravity and constants.

Proposed method

• Analyzes the axion as a pseudo-Goldstone boson arising from spontaneous U(1)PQ symmetry breaking, with mass generated by anomalies via the effective potential $ V(a) = -\Lambda^{4}_{\text{QCD}} \cos(a/f_a) $.
• Introduces gravitational corrections to the axion Lagrangian via non-renormalizable operators $ \mathcal{L}_{\text{eff}} = \mathcal{L}_{\text{PQ}} + \sum_M \frac{1}{M_P^n} O_n $, leading to modified potential $ V(a) = -\Lambda^{4}_{\text{QCD}} \cos(a/f_a) - K \frac{f_a^{n+4}}{M_P^n} \cos(a/f_a + \delta) $.
• Evaluates the resulting mass shift $ m_a^2 \simeq \frac{\Lambda^4_{\text{QCD}}}{f_a^2} + K \frac{f_a^{n+2}}{M_P^n} $ and vacuum misalignment $ \theta_{\text{eff}} \simeq K \sin\delta \frac{f_a^{n+4}}{M_P^n \Lambda^4_{\text{QCD}}} $, showing large corrections unless $ K \ll 1 $.
• Applies similar analysis to quintessence, deriving a mass shift $ \mu^2_\phi \to \mu^2_\phi + \beta_e^2 m_e^2 $ from gravitational corrections, implying $ \beta_e \sim 10^{-40} $ to preserve $ \mu_\phi \sim 10^{-31} $ eV.
• Uses experimental constraints from equivalence principle tests and time-variation of fine structure constant to bound couplings $ \beta_{G^2}, \beta_{F^2}, \beta_{F\tilde{F}} $, finding $ \beta_{F^2} < 10^{-6} $ and $ \beta_{F\tilde{F}} < 3 \times 10^{-2} $.
• Considers alternative mechanisms such as extra dimensions or suppressed global symmetry breaking to stabilize light scalar masses.

Experimental results

Research questions

• RQ1 Can the near-masslessness of axions and quintessence be naturally maintained in the presence of gravitational corrections?
• RQ2 What are the implications of gravitational interactions for the vacuum misalignment angle $ \theta_{\text{eff}} $ in axion models?
• RQ3 How do Planck-scale suppressed operators affect the effective potential and mass of light scalar fields?
• RQ4 What constraints do precision gravity and coupling variation experiments place on the couplings of quintessence to gauge and matter fields?
• RQ5 Are there mechanisms—such as extra dimensions or suppressed global symmetries—that can naturally stabilize light scalar masses against quantum and gravitational corrections?

Key findings

• Gravitational corrections induce large mass shifts for axions and quintessence unless the coupling constants in the gravitational operators are unnaturally small, with $ K \ll 1 $ required to avoid large $ \theta_{\text{eff}} $.
• The required coupling of quintessence to matter fields is so small—$ \beta_e \sim 10^{-40} $—that it implies the field is effectively decoupled from ordinary matter.
• Experimental bounds on composition-dependent forces and time-variation of the fine-structure constant constrain the couplings of quintessence to $ \beta_{F^2} < 10^{-6} $ and $ \beta_{F\tilde{F}} < 3 \times 10^{-2} $, but these are still far from the values needed to avoid gravitational destabilization.
• The no-hair theorem implies that black holes can absorb global charges, leading to explicit breaking of global symmetries like U(1)PQ through Planck-scale operators, which destabilizes the axion mass and vacuum alignment.
• Supersymmetry does not resolve the issue, as it is broken at the Fermi scale, not at the sub-eV scale required for quintessence, leading to large radiative corrections.
• Alternative mechanisms such as extra dimensions or enhanced suppression in the dynamics of global symmetry breaking may provide a way out, but require new physics beyond the Standard Model.