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

Abstract In this paper, we represent a resolution for the hierarchy problem where inverse size of extra dimension and fundamental Planck scale would all be order TeV by proposing fiber fabric spacetime. The origin large is essentially due to $$\cosh $$ cosh function which physically originated from dynamics horizontal metric in vacuum non-zero energy. addition, spacetime allows us resolve elegantly naturally problems chirality fermions stabilizing potential dimension, are usually encountered higher dimensional theories. Then, explore inflation with modulus identified as inflaton our slow-roll inflationary model belongs E-model class $$n=1$$ n = 1 . We calculate main observables consistent present experiments. Finally, study how geodesic motion neutral test particles gets modified extension compute radius photon sphere, innermost stable circular orbit, perihelion shift, light bending angle, strong gravitational lensing retrolensing phenomenon. By comparing predicted values experimental observations, determine constraints on