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arXiv · 2107.14215

A new nonlinear instability for scalar fields

Farbod Hassani·Pan Shi·Julian Adamek·Martin Kunz·Peter Wittwer
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Abstract

In this letter we introduce the non-linear partial differential equation (PDE) $\partial^2_{\tau} \pi \propto (\vec\nabla \pi)^2$ showing a new type of instability. Such equations appear in the effective field theory (EFT) of dark energy for the $k$-essence model as well as in many other theories based on the EFT formalism. We demonstrate the occurrence of instability in the cosmological context using a relativistic $N$-body code, and we study it mathematically in 3+1 dimensions within spherical symmetry. We show that this term dominates for the low speed of sound limit where some important linear terms are suppressed.

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Farbod Hassani, Pan Shi, Julian Adamek, Martin Kunz, Peter Wittwer. 2021-07-29. A new nonlinear instability for scalar fields. https://doi.org/10.1103/physrevd.105.l021304

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