  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.
