Magnetic Knots as the origin of Spikes in the Gravitational Wave Backgrounds

The dynamical symmetries of hot and electrically neutral plasmas in a highly conducting medium suggest that, after the epoch of the electron-positron annihilation, magnetohydrodynamical configurations carrying a net magnetic helicity can be present. The simultaneous conservation of the magnetic flux and helicity implies that the (divergence free) field lines will possess inhomogeneous knot structures acting as source seeds in the evolution equations of the scalar, vector and tensor fluctuations of the background geometry. We give explicit examples of magnetic knot configurations with finite energy and we compute the induced metric fluctuations. Since magnetic knots are (conformally) coupled to gravity via the vertex dictated by the equivalence principle, they can imprint spikes in the gravitational wave spectrum for frequencies compatible with the typical scale of the knot corresponding, in our examples, to a present frequency range of $10^{-11}$--$10^{-12}$ Hertz. At lower frequencies the spectrum is power-suppressed and well below the COBE limit. For smaller length scales (i.e. for larger frequencies) the spectrum is exponentially suppressed and then irrelevant for the pulsar bounds. Depending upon the number of knots of the configuration, the typical amplitude of the gravitational wave logarithmic energy spectrum (in critical units) can be even four orders of magnitude larger than the usual flat (inflationary) energy spectrum generated thanks to the parametric amplification of the vacuum fluctuations