Abstract
In this work, we investigate gravitational resonances in both single and double mimetic thick branes, which can provide a new way to detect the extra dimension. For the single brane model, we apply the relative probability proposed in [Phys. Rev.D 80 (2009) 065019]. For the double brane model, we investigate the resonances quasi-localized on the double brane, on the sub-branes and between the sub-branes, respectively. To investigate the resonances quasi-localized on the double brane, we introduce two different definitions of the relative probability and find that the corresponding mass spectra of gravitational resonances are almost the same. For the gravitational resonances quasi-localized on sub-branes and between the sub-branes, the influence of the distance between the two sub-branes and the thickness of the sub-branes are analyzed and new features are found in both cases.
Highlights
JHEP04(2019)154 scalar field φ as gμν = −gμνgαβ∂αφ∂βφ
In this work, we investigate gravitational resonances in both single and double mimetic thick branes, which can provide a new way to detect the extra dimension
For the double brane model, we investigate the resonances quasi-localized on the double brane, on the sub-branes and between the sub-branes, respectively
Summary
We briefly introduce the mimetic thick brane model and the linear perturbation of the brane system, which were given in ref. [61] in detail. The mimetic scalar field φ = φ(y) is used to generate the thick brane. The equations of motion can be obtained by varying the action with respect to the physical metric gMN , the mimetic scalar field φ. Where Lφ = λ gMN ∂M φ∂N φ − U (φ) − V (φ) is the lagrangian of the mimetic scalar field. When the mimetic scalar φ(y) is set to be constant, the potentials V (φ) and U (φ) and the Lagrange multiplier λ(y) become constants, and the theory turns to general relativity. 1 a(y) dy, the perturbed metric in the new coordinate is given by ds2 = a(z) (ημν + hμν )dxμdxν + dz2 ,. The mimetic scalar field generates more types of thick brane, which could lead to new type of potential of the tensor perturbation. In the cosmological context, the scalar perturbation of mimetic gravity has no terms of ∇2δφ (see eq (64) of ref. [48]), which implies that the sound speed is identically zero
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