Graviton emission by a thermal bath of photons

Sergio del Campo; L. H. Ford

doi:10.1103/PhysRevD.38.3657

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Graviton emission by a thermal bath of photons

Sergio del Campo

L. H. Ford

Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155

Center for Theoretical Physics, Laboratory for Nuclear Science dge, Massachusetts 02139

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Phys. Rev. D 38, 3657 – Published 15 December, 1988

DOI: https://doi.org/10.1103/PhysRevD.38.3657

Abstract

The rate of emission of gravitons by a thermal bath of protons is calculated. Linearized quantum gravity is used to find the rate of graviton creation by thermal fluctuations of the photons. For the case of photons confined within a sphere of radius R and volume V at temperature T, the power radiated in gravitons is found to be P=(2.7× $10^{- 66}$ erg/s)(V/ ${cm}^{3}$ )(T/K $)^{7}$ ln(160RT/K/cm). If the thermal bath cools solely by emission of gravitons, the cooling time is of the order of τ=(3× $10^{51}$ s) (1 K/T $)^{3}$ ln(160RT/K cm). Any region which has been cooling by graviton emission since the early Universe has a maximum temperature of 10 MeV at the present.

References (7)

S. Wada, Prog. Theor. Phys. 75, 1365 (1986); J. J. Halliwell, Phys. Lett. B 196, 444 (1987); Phys. Rev. D 36, 3626 (1987) W. Boucher and J. Traschen, ibid. 37, 3522 (1988).
L. H. Ford, Ann. Phys. (N.Y.) 144, 238 (1982), hereafter referred to as I.
Note that for an operator such as $T_{α β}$ (x) $T^{α β}$ (x prime ) which is quartic in the fundamental fields, normal ordering is not simply subtracting the vacuum expectation value, as it is for quadratic operators.
Omitted end note.
S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), p. 266. Here an estimate is given of the power radiated in gravitons produced in electron-electron and electron-proton collisions in the Sun. The result is about 1 order of magnitude smaller than our estimate, Eq. (36). It is presumably a coincidence that the two effects are comparable for the Sun as the effect considered by Weinberg yields a power prop $T^{3 / 2}$ .
G. Schäfer and H. Dehner [Phys. Rev. D 27, 2684 (1983)] have discussed the radiation of gravitons due to particle collisions in a degenerate Fermi fluid.
See, e.g., T. D. Lee and G. C. Wick, Phys. Rev. D 8, 2291 (1974); E. Witten, ibid. 30, 272 (1984).

[c1] S. Wada, Prog. Theor. Phys. 75, 1365 (1986); J. J. Halliwell, Phys. Lett. B 196, 444 (1987); Phys. Rev. D 36, 3626 (1987) W. Boucher and J. Traschen, ibid. 37, 3522 (1988).

[c2] L. H. Ford, Ann. Phys. (N.Y.) 144, 238 (1982), hereafter referred to as I.

[c3] Note that for an operator such as $T_{α β}$ (x) $T^{α β}$ (x prime ) which is quartic in the fundamental fields, normal ordering is not simply subtracting the vacuum expectation value, as it is for quadratic operators.

[c4] Omitted end note.

[c5] S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972), p. 266. Here an estimate is given of the power radiated in gravitons produced in electron-electron and electron-proton collisions in the Sun. The result is about 1 order of magnitude smaller than our estimate, Eq. (36). It is presumably a coincidence that the two effects are comparable for the Sun as the effect considered by Weinberg yields a power prop $T^{3 / 2}$ .

[c6] G. Schäfer and H. Dehner [Phys. Rev. D 27, 2684 (1983)] have discussed the radiation of gravitons due to particle collisions in a degenerate Fermi fluid.

[c7] See, e.g., T. D. Lee and G. C. Wick, Phys. Rev. D 8, 2291 (1974); E. Witten, ibid. 30, 272 (1984).

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Graviton emission by a thermal bath of photons

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