Gravitational Waves in Decaying Vacuum Cosmologies - Ramirez, David Alejandro Tamayo (2015)
In the present monograph we study in detail the primordial gravitational waves in cosmologies with a decaying vacuum. The decaying vacuum models are an alternative to solve the cosmological constant problem attributing a dynamic to the vacuum energy. The problem of primordial gravitational waves is discussed in the framework of an expanding, flat, spatially homogeneous and isotropic FLRW Universe described by General Relativity theory with decaying vacuum energy density of the type $\\Lambda \\equiv \\Lambda(H)$. Two particular interesting limits of a class of decaying vacuum models were investigated. A first-order tensor perturbation term was introduced to the FLRW metric, the evolution equation of the perturbations was derived and then expressed in terms of a Fourier expansion, the time-dependent part decouples from the spatial part. The resulting equation has the form of a damped harmonic oscillator which depends on the scale factor, which carries all the cosmological and decaying vacuum characteristics. In the first model studied, the decaying vacuum has the form $\\Lambda \\propto H^2$. The gravitational wave equation is established and its time-dependent part has analytically been solved for different epochs in the case of a flat geometry. The main result is unlike the standard $\\Lambda$CDM cosmology (no interacting vacuum): in this model there is gravitational wave amplification during the radiation era, which in quantum field theory means graviton production. This difference is a clear signature of the decaying vacuum models which a eventual observation could give empirical clues about it. However, high frequency modes are damped out even faster than in the standard cosmology, both in the radiation and matter-vacuum dominated epoch. The physical gravitational wave quantities like the modulus of the mode function, power and gravitational wave energy density spectra generated at different cosmological eras are also explicitly evaluated. The second model studied is a decaying vacuum of the form $\\Lambda \\propto H^3$. This model drives a nonsingular flat cosmology which is termed complete in the sense that the cosmic evolution occurs between two extreme de Sitter stages. The particularity which makes interesting this model is that the transition from the early de Sitter era to the radiation phase is smooth avoiding the graceful exit problem. The gravitational wave equation is derived and its time-dependent part numerically integrated in a relevant period previously delimited. The gravitational wave solutions for the other eras were calculates analytically. Today\'s gravitational wave spectra were calculated and compared with the standard result where an abrupt transition is assumed. It is found that the stochastic background of gravitational waves is very similar to the one predicted by the cosmic concordance model plus inflation except for the higher frequencies.