Effective energy density of relic gravitons

Abstract

The energy density, the pressure and the anisotropic stress of the relic gravitons do not have a unique gauge-invariant and frame-invariant expression since the equivalence principle ultimately forbids the localization of the energy-momentum of the gravitational field. All the strategies proposed so far suggest compatible descriptions inside the effective horizon but they lead to sharply different answers when the wavelengths of the gravitons exceed the Hubble radius by remaining shorter than the typical extension of causally connected patches. We present a coherent discussion of the energy-momentum pseudo-tensors of the relic gravitons in the different kinematical regimes with the aim of scrutinizing the mutual consistency of the competing suggestions. The various proposals are systematically compared by deducing and analyzing the explicit form of the observables in realistic physical situations. General lessons are drawn on the most plausible parametrization of the energy-momentum pseudo-tensor of the relic gravitons.

arXiv comment30 pages; minor typos corrected and slightly edited title to match the published version

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Cited by in corpus (8)

• Primordial backgrounds of relic gravitons
• Relic gravitons and high-frequency detectors
• Spurious gauge-invariance of higher-order contributions to the spectral energy density of the relic gravitons
• Relic gravitons and pulsar timing arrays: a theoretical viewpoint
• Effective anisotropic stresses of the relic gravitons
• Relic gravitons and non-stationary processes
• The Conserved Effective Stress Tensor of Gravitational Wave
• Relic gravitons at intermediate frequencies and the expansion history of the Universe