Abstract
We study effects of a rippling gravitational background on a scalar field with a double well potential, focusing on the analogy with the well known dynamics of the Kapitza's pendulum. The ripples are rendered as infinitesimal but rapidly oscillating perturbations of the scale factor. We find that the resulting dynamics crucially depends on a value of the parameter $\xi$ in the $\xi \,R\, \phi^2$ vertex. For the time-dependent perturbations of a proper form the resulting effective action is generally covariant, and at a high enough frequency at $\xi<0$ and at $\xi>1/6$ the effective potential has a single minimum at zero, thereby restoring spontaneously broken symmetry of the ground state. On the other side, at $0<\xi< 1/6$ spontaneous symmetry breaking emerges even when it is absent in the unperturbed case.
Highlights
Oscillating gravitational backgrounds attract attention of theoretical physicists in various contexts starting from quantum decoherence [1,2] and finishing some cosmological [3] and extra dimensional constructions [4,5,6]
As we show below already at classical level small but rapidly oscillating perturbations of the scale factor may affect the ground states of physically relevant models in a quite interesting way
We find that at ξ < 0 and at ξ > 1/6 the correction μ2 is always negative, and at the high enough frequency ω it can compensate the bare mass parameter, what quite naturally implies that the effect of the rapid oscillations is similar to an increase in temperature: the effective potential has just a single minimum at φ = 0, and spontaneous symmetry breaking of the bare theory vanishes
Summary
Oscillating gravitational backgrounds attract attention of theoretical physicists in various contexts starting from quantum decoherence [1,2] and finishing some cosmological [3] and extra dimensional constructions [4,5,6]. Where δφ is a rapidly oscillating and small correction, which approaches to zero as ω−1 in the high frequency limit, while the dynamics of the slowly varying field φis described by the classical action, which we establish. The most interesting result is related to the situation, when the oscillating metric takes the simple form (2) in the comoving frame.. The most interesting result is related to the situation, when the oscillating metric takes the simple form (2) in the comoving frame.4 In such a case the effective action has exactly the same structure (1), where the quantities gμν and φ are replaced correspondingly by gμν and φ, Sgeff φ =. The correction μ2 ≡ μ2eff − μ2 becomes positive, and even when the mass parameter is absent in the bare theory, it appears in the effective one.
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