Cosmic bubble and domain wall instabilities I: parametric amplification of linear fluctuations
Abstract
This is the first paper in a series where we study collisions of nucleated bubbles taking into account the effects of small initial (quantum) fluctuations in a fully 3+1dimensional setting. In this paper, we consider the evolution of linear fluctuations around highly symmetric though inhomogeneous backgrounds. In particular, we demonstrate that a large degree of asymmetry develops over time from tiny initial fluctuations superposed upon planar and SO(2,1) symmetric backgrounds. These fluctuations are inevitable consequences of zeropoint vacuum oscillations, so excluding them by enforcing a high degree of spatial symmetry is inconsistent in a quantum treatment. To simplify the analysis we consider the limit of two colliding planar walls, with mode functions for the fluctuations characterized by the wavenumber transverse to the collision direction and a longitudinal shape along the collision direction x, which we solve for. In the linear regime, the fluctuations obey a linear wave equation with a time and spacedependent mass m_{eff}(x,t). In situations where the walls collide multiple times, m_{eff} oscillates in time. We use Floquet theory to study the evolution of the fluctuations and generalize the calculations familiar from the preheating literature to the case with many coupled degrees of freedom. The inhomogeneous case has bands of unstable transverse wavenumbers k_{⊥} whose corresponding mode functions grow exponentially. By examining the detailed spatial structure of the mode functions in x, we identify both broad and narrow parametric resonance generalizations of the homogeneous m_{eff}(t) case of preheating. The unstable k_{⊥} modes are longitudinally localized, yet can be described as quasiparticles in the Bogoliubov sense. We define an effective occupation number and show they are created in bursts for the case of welldefined collisions in the background. The transverselongitudinal coupling accompanying nonlinearity radically breaks this localized particle description, with nonseparable 3D modes arising that will be studied in subsequent papers.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 March 2015
 DOI:
 10.1088/14757516/2015/03/007
 arXiv:
 arXiv:1412.5591
 Bibcode:
 2015JCAP...03..007B
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 37 pages + references, 20 figures, submitted to JCAP