Srijit Bhattacharjee, Parthasarathi Majumdar
Gravitons minimally coupled to Higgs fields in a background Minkowski spacetime is shown to develop an instability in their propagators in presence of a spacetime-independent Higgs field background, due to the appearance of a tachyonic pole. The one loop effective potential (for constant Higgs field backgrounds) is shown to develop an infrared instability in the form of acquiring an imaginary part, which can be traced to the tachyonic pole in the graviton propagator. This instability is analogous to the finite temperature infrared instability of a gas of gravitons coupled to fermions found by Gross et. al., even though it already exists at zero tempertature; it is thus reminiscent of the Jeans instability thought to be at the heart of structure formation in the early universe. A finite temperature analysis of the effective potential at one loop shows that in the high temperature limit, the zero-temperature instability is in fact reinforced by finite temperature effects. In the low temperature limit, the finite temperature contribution to the imaginary part of the effective potential exhibits a damped oscillatory behaviour; all thermal effects are damped out as the temperature vanishes, consistent with the zero-temperature result.
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http://arxiv.org/abs/1210.0497
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