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In this paper, we represent a resolution for the hierarchy problem where theinverse size of the extra dimension and the fundamental Planck scale would allbe of the order of the TeV scale by proposing a fiber fabric of spacetime. Theorigin of the large hierarchy is essentially due to the $\cosh$ function whichhas a physical origin from the dynamics of the horizontal metric in the vacuumof non-zero energy. In addition, the fiber fabric of spacetime allows us toresolve elegantly and naturally the problems of the chirality fermions andstabilizing potential for the size of the extra dimension, which are usuallyencountered in the higher dimensional theories. Then, we explore the inflationwith the modulus of the extra dimension identified as the inflaton where ourslow-roll inflationary model belongs to the E-model class with $n=1$. Wecalculate the main inflationary observables which are consistent with thepresent experiments. Finally, we study how the geodesic motion of neutral testparticles gets modified from the extension of spacetime. We compute the radiusof the photon sphere, the innermost stable circular orbit, the perihelionshift, the light bending angle, and the observables of the strong gravitationallensing and the retrolensing phenomenon. By comparing the predicted values withthe experimental observations, we determine the constraints on the fiber fabricof spacetime.

Implications for the hierarchy problem, inflation and geodesic motion from fiber fabric of spacetime