Invisible gravitons and large-scale magnetism

The large-scale limits on the relic signals of gravitational radiation complement the bounds coming from the interferometric detectors (in the audio band) and from the pulsar timing arrays (in the nHz range). Within this inclusive perspective the spectral energy density of the gravitons is sharply suppressed in the aHz region even though the high frequency signal can be comparatively much larger both in the kHz and GHz domains. For there are no direct tests on the expansion rate prior to the formation of the light nuclei, a modified postinflationary timeline affects the total number of e-folds and additionally suppresses the tensor to scalar ratio by making the relic signals effectively invisible in the aHz range. The expansion rate prior to nucleosynthesis is further bounded by the evolution of the hypercharge field and the large-scale magnetism also constrains the decelerated expansion rate. The magnetogenesis requirements are compatible with a potentially detectable spectral energy density of the relic gravitons between the MHz and the THz while the tensor to scalar ratio remains suppressed in the aHz region. A maximum of the spectral energy density of the gravitons in the audio domain leads instead to a larger magnetic field when the scale of the gravitational collapse of the protogalaxy (of the order of the Mpc) gets comparable with the Hubble radius before equality. Along a converse viewpoint the results obtained here imply that a long decelerated stage expanding faster than radiation does not affect the high frequency range but reduces the effective number of e-folds by so enhancing the tensor to scalar ratio, possibly beyond its observational limit.