Abstract
In this paper, we represent a resolution for the hierarchy problem where the inverse size of the extra dimension and the fundamental Planck scale would all be of the order of the TeV scale by proposing a fiber fabric of spacetime. The origin of the large hierarchy is essentially due to the cosh function which is physically originated from the dynamics of the horizontal metric in the vacuum of non-zero energy. In addition, the fiber fabric of spacetime allows us to resolve elegantly and naturally the problems of the chirality fermions and stabilizing potential for the size of the extra dimension, which are usually encountered in the higher dimensional theories. Then, we explore the inflation with the modulus of the extra dimension identified as the inflaton where our slow-roll inflationary model belongs to the E-model class with n=1. We calculate the main inflationary observables which are consistent with the present experiments. Finally, we study how the geodesic motion of neutral test particles gets modified from the extension of spacetime. We compute the radius of the photon sphere, the innermost stable circular orbit, the perihelion shift, the light bending angle, and the observables of the strong gravitational lensing and the retrolensing phenomenon. By comparing the predicted values with the experimental observations, we determine the constraints on the fiber fabric of spacetime.
Highlights
Tions that the spacetime picture described by General Relativity (GR) should be broken down at short distances or high energies
In the scenario of the large extra dimensions proposed by Arkani-Hamed, Dimopoulos and Dvali, the inverse size of the extra dimensions is expressed as R−1 = 2π M∗(M∗/MPl)2/n where M∗ is the fundamental Planck scale, MPl is the four dimensional or observed Planck scale ∼ O(1018) GeV, and n is the number of the extra dimensions [6,7]
As we will indicate in the present work, this new hierarchy problem can be resolved with a fiber fabric of five dimensional spacetime where the inverse size of the fifth dimension and the fundamental Planck scale would all be of the order of the TeV scale
Summary
The problems of GR motivate alternative theories of gravity or the extensions of four dimensional spacetime. As we will indicate in the present work, this new hierarchy problem can be resolved with a fiber fabric of five dimensional spacetime where the inverse size of the fifth dimension and the fundamental Planck scale would all be of the order of the TeV scale. It is worth investigating alternatives which are more elegant and nature There is another important problem of the higher dimensional theories based on the generalization of GR to the higher dimensions: what is the mechanism to fix the size of the extra dimensions or the mass of the radion field?
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