Sine-Gordon Parametric Resonance

• Main Authors: Greene, Patrick B, Kofman, Lev, Starobinsky, Alexei A
• Format: Journal Article
• Language: English
• Published: 30.08.1998
• Subjects: Mathematics - Mathematical Physics; Physics - Astrophysics of Galaxies; Physics - Cosmology and Nongalactic Astrophysics; Physics - Earth and Planetary Astrophysics; Physics - High Energy Astrophysical Phenomena; Physics - High Energy Physics - Phenomenology; Physics - High Energy Physics - Theory; Physics - Instrumentation and Methods for Astrophysics; Physics - Mathematical Physics; Physics - Solar and Stellar Astrophysics
• DOI: 10.48550/arxiv.hep-ph/9808477

Nucl.Phys. B543 (1999) 423-443 We consider the instability of fluctuations in an oscillating scalar field which obeys the Sine-Gordon equation. We present simple closed-form analytic solutions describing the parametric resonance in the Sine-Gordon model. The structure of the resonance differs from that obtained with the Mathieu equation which is usually derived with the small angle approximation to the equation for fluctuations. The results are applied to axion cosmology, where the oscillations of the classical axion field, with a Sine-Gordon self-interaction potential, constitute the cold dark matter of the universe. When the axion misalignment angle at the QCD epoch, $\theta_0$, is small, the parametric resonance of the axion fluctuations is not significant. However, in regions of larger $\theta_0$ where axion miniclusters would form, the resonance may be important. As a result, axion miniclusters may disintegrate into finer, denser clumps. We also apply the theory of Sine-Gordon parametric resonance to reheating in the Natural Inflation scenario. The decay of the inflaton field due to the self-interaction alone is ineffective, but a coupling to other bosons can lead to preheating in the broad resonance regime. Together with the preheating of fermions, this can alter the reheating scenario for Natural Inflation.