London-Like Tensor Modes of Gravitational Waves in Cosmic String Cosmology

From a classical analysis, we show that gravitational waves in a cosmological medium with the equation of state parameter \(w=-1/3\) can follow a London-like equation, implying that some gravitational wave solutions present a decay for certain wavelengths. This scenario, corresponding to a cosmic string cosmology, induces an attenuation temporal scale on the gravitational wave propagation. We discuss on how these solutions impose a limit on the wavelength of the waves that can propagate, which depends on the type of spatial curvature and the energy density content of this type of cosmology.