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In the present work we study in detail the primordial gravitational waves in cosmologies with a decaying vacuum. The cosmological framework is the FLRW Universe in General Relativity. The decaying vacuum models are an alternative to solve the cosmological constant problem attributing a dynamic to the vacuum energy of the type Lambda(H). The evolution equation of the linear tensor perturbations was derived and the time-dependent part decoupled from the spatial one. 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. The gravitational wave equation is established and its time-dependent part has analytically been solved for different cosmological eras. The main result is that unlike the standard cosmology, there is gravitational wave amplification during the radiation era. 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.

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Mexican physicist. Bachelor from the National Autonomous University of Mexico and PhD from the University of Sao Paulo, Brazil. His research interests are: theoretical cosmology, primordial gravitational waves, decaying vacuum models, dark energy models, inflation and gravitational wave physics; and philosophy of physics as parallel interest.

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