Abstract
In conformally flat background geometries the long wavelength gravitons can be described in the fluid approximation and they induce scalar fluctuations both during inflation and in the subsequent radiation-dominated epoch. While this effect is minute and suppressed for a de Sitter stage of expansion, the fluctuations of the energy-momentum pseudo-tensor of the graviton fluid lead to curvature perturbations that increase with time all along the post-inflationary evolution. An explicit calculation of these effects is presented for a standard thermal history and it is shown that the growth of the curvature perturbations caused by the long wavelength modes is approximately compensated by the slope of the power spectra of the energy density, pressure and anisotropic stress of the relic gravitons.
Highlights
The tensor modes of the geometry can be efficiently amplified in conformally flat space-times thanks to the pumping action of the curvature [1]
Relic gravitons are often regarded as a direct signature of any scenario positing an early variation of the background gravitational field: typical examples are the conventional inflationary paradigm [2–4] and various completions of the concordance lore [5,6]
Since there is no unique expression for the energymomentum tensor of the relic gravitons, we must instead deal with a variety of pseudotensors whose definitions are mathematically different but physically equivalent
Summary
The tensor modes of the geometry can be efficiently amplified in conformally flat space-times thanks to the pumping action of the (extrinsic) curvature [1]. The classic Landau and Lifshitz approach [9] stipulates that a valid energy-momentum pseudotensor can be obtained (in Minkowski space) from the second-order fluctuations of the Einstein tensor In a complementary perspective Ford and Parker [13] suggested that the second-order action for the tensor modes of the geometry in a conformally flat space-time of Friedmann-Robertson-Walker type coincides with the action of two minimally coupled scalar fields (one for each tensor polarization): it is plausible to argue that the energy-momentum tensor of each polarization of the. In the present investigation it is observed that the fluctuations of the energy density, of the pressure and of the anisotropic stress of the relic gravitons produce secondary scalar modes of the geometry. Some technical results of the analysis have been collected in the Appendices
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