Abstract
Coleman–Weinberg (CW) phenomena for the case of gravitons minimally coupled to massless scalar field is studied. The one-loop effect completely vanishes if there is no self-interaction term present in the matter sector. The one-loop effective potential is shown to develop an instability in the form of acquiring an imaginary part, which can be traced to the tachyonic pole in the graviton propagator. The finite temperature counterpart of this CW potential is computed to study the behaviour of the potential in the high and low temperature regimes with respect to the typical energy scale of the theory. Finite temperature contribution to the imaginary part of gravitational CW potential exhibits a damped oscillatory behaviour; all thermal effects are damped out as the temperature vanishes, consistent with the zero-temperature result.
Highlights
Physics at Tev scale appears to be adequately described by the standard strong and electroweak theory
We have shown that gravitational analog of CW potential exhibits instability
A constant scalar field background resembles a thermal bath which backreacts to the gravitons to produce the instability in the system
Summary
Physics at Tev scale appears to be adequately described by the standard strong and electroweak theory. In [5], finite temperature corrections to the effective potential, calculation of tunneling rates and the nature of cosmological phase transitions are discussed These results are applied to the standard model to derive stringent bounds on Higgs and fermion passes. In spirit one can ask the question whether any similar phenomenon occurs when spin-2 graviton is minimally coupled to a massless Higgs field It may not have practical applications as in the case for standard model but it may reveal certain interesting features of unique nature of gravity as a fundamental interaction. The low temperature limit, on the other hand, shows a rather interesting behaviour : in the physically relevant region the temperature dependent imaginary part oscillates with a damping amplitude This oscillation may be a reminiscence of the instability of flat background under perturbation in presence of interaction between gravitons and thermally excited matter fields [15]. The concluding section contains a critical look at our results and future outlook
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