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A signature of trans-Planckian physics which does not depend upon nonlinear unknown quantum effects is the one induced by resonant production of the particle during inflation leaving an imprint in the form of sharp features in the primordial power spectrum. This effect has been discussed in D.J. Chung, E.W. Kolb, A. Riotto, and I.I. Tkachev, Phys. Rev. D 62, 043508 (2000).
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85038274340
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Notice that (Formula presented) is the value of the scale factor at (Formula presented) not its present value.
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Notice that (Formula presented) is the value of the scale factor at (Formula presented) not its present value.
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85038319309
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This equation admits the solution (Formula presented) for any value of (Formula presented) In the limit of small (Formula presented) the solutions of Eq. (22) are (Formula presented) with p ranging over the non-negative integers. Indeed, in the limit (Formula presented) the space is not warped (Formula presented) and we recover the usual equally spaced Kaluza-Klein eigenvalues. The solutions for (Formula presented) are plotted in Fig. 11.
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This equation admits the solution (Formula presented) for any value of (Formula presented) In the limit of small (Formula presented) the solutions of Eq. (22) are (Formula presented) with p ranging over the non-negative integers. Indeed, in the limit (Formula presented) the space is not warped (Formula presented) and we recover the usual equally spaced Kaluza-Klein eigenvalues. The solutions for (Formula presented) are plotted in Fig. 11.
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85038344460
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See, e.g., A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, Cambridge, England, 2000).
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See, e.g., A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, Cambridge, England, 2000).
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38
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85038295199
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Notice that if we defined the effective four-dimensional Planck mass during inflation by integrating the background gravitational action over y, we would obtain a different result, (Formula presented) However, we are interested here in the effective gravitational coupling of the zero Kaluza-Klein mode of the tensor perturbation, which is properly defined by Eq. (39).
-
Notice that if we defined the effective four-dimensional Planck mass during inflation by integrating the background gravitational action over y, we would obtain a different result, (Formula presented) However, we are interested here in the effective gravitational coupling of the zero Kaluza-Klein mode of the tensor perturbation, which is properly defined by Eq. (39).
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40
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