Early universe: Gravitational waves and tensor metric fluctuations

In this work, we develop a model for the early universe in which preinflation is followed by a warming epoch and a subsequent sub-exponential quintessential expansion. We demonstrate that gravitational waves (GW) generated at the birth of the universe leave an imprint of that event, which is significantly suppressed a few Planckian times after that moment. We calculate the strengths of both, the total transverse GW and the b-polarization, for each mode. We use a nonlinear quantum algebra to calculate the expectation value of the quantum metric tensor perturbations: δgˆαβ, which are induced by the geometric quantum field with which we extend the Riemann manifold. A measure for the temperature fluctuations at the Hubble horizon is proposed: δT/Th=−bgαβδgˆαβ(k∗,t).