Abstract
We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during the early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the spectrum of the tensor metric fluctuations of an effective 4D Schwarzschild–de Sitter metric on cosmological scales. This metric is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution, in the context of a non-compact Kaluza–Klein theory of gravity. We found that the spectrum is nearly scale invariant under certain conditions. One interesting aspect of this model is that it is possible to derive the dynamical field equations for the tensor metric fluctuations, valid not just at cosmological scales, but also at astrophysical scales, from the same theoretical model. The astrophysical and cosmological scales are determined by the gravity–antigravity radius, which is a natural length scale of the model, that indicates when gravity becomes repulsive in nature.
Highlights
One of the greatest challenges of the modern cosmology is to explain the origin of the present day accelerated expansion
In this letter we study the generation of relic background of cosmological gravitational waves during inflation, derived from a non-compact KK theory of gravity in the context of a repulsive gravity theory
III we study the propagation of the 5D tensor metric fluctuations along the extra coordinate, on cosmological scales
Summary
One of the greatest challenges of the modern cosmology is to explain the origin of the present day accelerated expansion. The theory considers a 5D geometrical vacuum defined by (5)Rab = 0, a, b = 0, 1, 2, 3, 4., which are the field equations of the theory This idea has generated a new kind of cosmological models on which accelerating expansion periods are included. The scenarios there described can explain the generation of gravitational waves on cosmological, but not on astrophysical scales It is useful and very instructive to study the relic background of gravitational waves generated during inflation on the framework of a large scale repulsive gravity model, since gravitons under such conditions must live imprints on the power spectrum and polarization of the cosmic microwave background radiation (CMBR).
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