B-mode of gravitational waves in preinflation with negative spatial curvature

Abstract

I study primordial gravitational waves in a preinflationary scenario with negative spatial curvature K = −H 2 0 and an initially null energy density. In this scenario the expansion is driven by a scalar (phantom) field with negative kinetic energy density and the cosmological parameter is given by the expectation value of the flow the field σˆ µ , σˆ -being the geometric response to the quantum fluctuations of the phantom field. In this framework, the dynamics of gravitational waves components δΨˆ ij is studied and the b-polarization mode for gravitational waves is calculated. Finally, it is obtained the gravitational energy by unit time and transversal area, transported by each k-mode of the GW: I(k, t) = IIS(k, t)II, related to the vector field: S(k, t) = c √ g00 [ u(k, t) × v(k, t) ] .