Abstract
We investigate the existence and behavior of oscillons in theories in which higher derivative terms are present in the Lagrangian, such as galileons. Such theories have emerged in a broad range of settings, from higher-dimensional models, to massive gravity, to models for late-time cosmological acceleration. By focusing on the simplest example---massive galileon effective field theories---we demonstrate that higher derivative terms can lead to the existence of completely new oscillons (quasi-breathers). We illustrate our techniques in the artificially simple case of 1 + 1 dimensions, and then present the complete analysis valid in 2 + 1 and 3 + 1 dimensions, exploring precisely how these new solutions are supported entirely by the non-linearities of the quartic galileon. These objects have the novel peculiarity that they are of the differentiability class $C^1$.
Highlights
All of modern physics is described by nonlinear partial differential equations (PDEs)
The Vainshtein mechanism and nonrenormalization theorems that Galileon theories enjoy [8,33] mean that the higher-derivative operators are within the regime of validity of the effective field theory (EFT) in contrast to Pðφ; XÞ theories. One example where this is problematic for solitons is Skyrmion theories where higherderivative operators are required for stability so that such objects are outside the regime of validity of the EFT
The decoupling limit of many IR modifications of gravity such as ghost-free massive gravity or braneworld models are described by higher-derivative EFTs, in particular massless Galileons [8,19,20,61]
Summary
All of modern physics is described by nonlinear partial differential equations (PDEs). When the conserved charge results from a global U(1) symmetry [or an unbroken U(1) of some higher gauge group], these objects are typically referred to as Q-balls [1] Another class of interesting nonlinear solitary objects are oscillons, sometimes called breathers. Oscillons are stable, extended, quasiperiodic (in time) particlelike excitations These are objects with no conserved charges at all and for this reason are typically found in real scalar field theories. The Vainshtein mechanism and nonrenormalization theorems that Galileon theories enjoy [8,33] mean that the higher-derivative operators are within the regime of validity of the effective field theory (EFT) in contrast to Pðφ; XÞ theories One example where this is problematic for solitons is Skyrmion theories where higherderivative operators are required for stability so that such objects are outside the regime of validity of the EFT. There is a no-go theorem for static solitons [34] but the existence and stability of timedependent solitons is still unexplored
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