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Linear Growth of Structure in the Symmetron Model

In the symmetron mechanism, the fifth force mediated by a coupled scalar field (the symmetron) is suppressed in high-density regions due to the restoration of symmetry in the symmetron potential. In this paper we study the background cosmology and large scale structure formation in the linear perturbation regime of the symmetron model. Analytic solutions to the symmetron in the cosmological background are found, which agree well with numerical results. We discuss the effect of the symmetron perturbation on the growth of matter perturbation, in particular the implications of the brief period of tachyonic instability caused by the negative mass-squared of the symmetron during symmetry breaking. Our analysis and numerical results show that this instability has only very small effects on the growth of structures on sub-horizon scales, and even at horizon scales its influence is not as drastic as naively expected. The symmetron fifth force in the non-tachyonic regime does affect the formation of structure in a nontrivial way which could be cosmologically observable.