Sine-Gordon parametric resonance

We consider the instability of fluctuations in an oscillating scalar field which obeys the sine-Gordon equation. We present simple closed-form analyti c solutions describing the parametric resonance in the sine-Gordon model. T he structure of the resonance differs from that obtained with the Mathieu e quation which is usually derived with the small angle approximation to the equation for fluctuations. The results are applied to axion cosmology, wher e the oscillations of the classical axion field, with a sine-Gordon self-in teraction potential, constitute the cold dark matter of the universe. When the axion misalignment angle at the QCD epoch, theta(0), is small, the para metric resonance of the axion fluctuations is not significant. However, in regions of larger theta(0) where axion miniclusters would form, the resonan ce may be important. As a result, axion miniclusters may disintegrate into finer, denser clumps. We also apply the theory of sine-Gordon parametric re sonance to reheating in the Natural Inflation scenario. The decay of the in flaton field due to the self-interaction alone is ineffective, but a coupli ng to other bosons can lead to preheating in the broad resonance regime. To gether with the preheating of fermions, this can alter the reheating scenar io for Natural Inflation. (C) 1999 Elsevier Science B.V.