The propagating speed of relic gravitational waves and their refractive index during inflation

Abstract

If the refractive index of the tensor modes increases during a conventional inflationary stage of expansion the relic graviton spectrum is tilted towards high frequencies. Two apparently diverse parametrizations of this effect are shown to be related by a rescaling of the four-dimensional metric through a conformal factor that involves the refractive index itself. Non-monotonic spectra with a maximum in the MHz region correspond to a limited variation of the refractive index terminating well before the end of inflation. After exploring a general approach encompassing the ones proposed so far, we estimate the required sensitivity for the direct detection of the predicted gravitational radiation and demonstrate that the allowed regions of the parameter space are within reach for some of the planned detectors operating either in the audio band (like Ligo/Virgo and Kagra) or in the mHz band (like Lisa, Bbo and Decigo).

32 pages, 12 figures; corrected typos and comments added

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• Cosmological constraints on slow-roll inflation: an update
• Intermittent null energy condition violations during inflation and primordial gravitational waves
• Inflation, the Hubble Tension and Early Dark Energy: an alternative overview
• Inflationary Potential as seen from Different Angles: Model Compatibility from Multiple CMB Missions
• Primordial tensor non-Gaussianities from general single-field inflation with non-Bunch-Davies initial states
• Generating enhanced primordial GWs during inflation with intermittent violation of NEC and diminishment of GW propagating speed
• Tracking the Multifield Dynamics with Cosmological Data: A Monte Carlo approach
• The refractive index of the relic gravitons and the nHz band
• Relic gravitons and pulsar timing arrays: a theoretical viewpoint
• Relic gravitons at intermediate frequencies and the expansion history of the Universe