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 zero-point 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 timeand space-dependent mass m ef f (x, t). In situations where the walls collide multiple times, m ef f 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 ef f (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 well-defined collisions in the background. The transverse-longitudinal coupling accompanying nonlinearity radically breaks this localized particle description, with nonseparable 3D modes arising that will be studied in subsequent papers.

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“…arXiv:1806.06069v1 [hep-th] 15 Jun 2018 with a tenth-order accurate Gauss-Legendre time integrator [21,22]. The spatial Laplacian is computed using a Fourier collocation stencil, resulting in periodic boundary conditions.…”

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“…[30][31][32] and the references therein), these studies have not included the effect of inhomogeneities, which would be interesting to explore. See [33][34][35] for related work suggesting that domain walls (neglecting self-gravity) are unstable to perturbations. extent, and not properties of the nonlinear interaction in gravitational wave scattering.…”