Effect of interacting particles on primordial nucleosynthesis

Edward W. Kolb; Michael S. Turner; Terrence P. Walker

doi:10.1103/PhysRevD.34.2197

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Effect of interacting particles on primordial nucleosynthesis

Edward W. Kolb and Michael S. Turner

Terrence P. Walker

NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 and Astronomy and Astrophysics Center, The University of Chicago, Chicago, Illinois 60637

NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 and Department of Astronomy, Indiana University, Bloomington, Indiana 47405

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Phys. Rev. D 34, 2197 – Published 15 October, 1986

DOI: https://doi.org/10.1103/PhysRevD.34.2197

Abstract

We modify the standard model for big-bang nucleosynthesis to allow for the presence of a generic particle species, i.e., one which maintains good thermal contact with either the photons or the light-neutrino species throughout the epoch of primordial nucleosynthesis. The production of D, ${}^{3}{He}$ , ${}^{4}{He}$ , and ${}^{7}{Li}$ is calculated as a function of the mass, degrees of freedom, and spin statistics of the generic particle. We show that in general, the effect of an additional generic species cannot simply be parametrized as the equivalent number of additional light-neutrino species. The presence of generic particles also affects the predicted value for the neutrino-to-photon temperature ratio.

References (22)

For recent reviews of the standard model of primordial nucleosynthesis and its use as a probe of particle physics, see J. Yang, M. S. Turner, G. Steigman, N. D. Schramm and K. A. Olive, Astrophys. J. 281, 493 (1984); G. Steigman and A. M. Boesgaard, Annu. Rev. Astron. Astrophys. 23, 319 (1985), and references therein.
The effect of additional relativistic degrees of freedom on primordial nucleosynthesis has been frequently discussed. See, for example, V. F. Shvartsman, Pis'ma Zh. Eksp. Teor. Fiz. 9, 315 (1969) [JETP Lett. 9, 184 (1969)]; G. Steigman, D. N. Schramm and J. E. Gunn, Phys. Lett. 66 B, 202 (1977); J. Yang, D. N. Schramm and R. T. Rood, Astrophys. J. 227, 697 (1979); K. A. Olive, D. N. Schramm and G. Steigman, Nucl. Phys. B180, 497 (1981); K. A. Olive, D. N. Schramm, G. Steigman, M. S. Turner and J. Yang, Astrophys. J. 246, 557 (1981); A. S. Szalay, Phys. Lett. 101 B, 453 (1981); Yang et al. (Ref. 1).
E. W. Kolb and R. J. Scherrer, Phys. Rev. D 25, 1481 (1982).
G. Steigman, K. A. Olive and D. N. Schramm, Phys. Rev. Lett. 43, 239 (1979).
Y. Chikashige, R. N. Mohapatra and R. D. Peccei, Phys. Lett. 98 B, 265 (1981); G. B. Gelmini and M. Roncadelli, ibid. 99 B, 411 (1981); H. M. Georgi, S. L. Glashow and S. Nussinov, Nucl. Phys. B193, 297 (1981).
See, for example, R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977); S. Weinberg, ibid. 40, 223 (1978); F. Wilczek, ibid. 40, 279 (1978); J. Kim, ibid. 43, 103 (1979); M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104 B, 199 (1981).
F. Hoyle and R. J. Taylor, Nature (London) 203, 1108 (1964); P. J. E. Peebles, Astrophys. J. 146, 542 (1966); R. V. Wagoner, W. A. Fowler and F. Hoyle, ibid. 148, 3 (1967).
R. V. Wagoner, Astrophys. J. 179, 343 (1973).
The actual neutrino decoupling temperature is slightly different for each species. See D. A. Dicus, E. W. Kolb, A. M. Gleeson, E. C. G. Sudarshan, V. L. Teplitz and M. S. Turner, Phys. Rev. D 26, 2694 (1982).
D. A. Dicus, E. W. Kolb, V. L. Teplitz and R. V. Wagoner, Phys. Rev. D 17, 1529 (1978).
See Ref. 5.
See Ref. 9.
As mentioned in Sec. III, particles of m <wig 100 eV which couple to photons transfer their entropy to photons too late for thermalization to occur by the present epoch, and thus eta would be unaltered. Therefore, the effect of m < 100 eV generic particles coupled to photons throughout nucleosynthesis is due to their energy density, and thus they produce the effect of an equivalent number of neutrino species. The curves of Figs. 2–5 should coincide with the analogous curves for generic particles coupled to neutrinos below m/ $m_{e}$ $10^{- 3}$ . Of course, the decays of such particles will distort the microwave background and therefore are cosmologically unacceptable (see Ref. 10).
In order to determine whether or not a generic species maintains thermal equilibrium with photons or light neutrinos we should solve the rate equation n dot = -3Hn + < σ v > ( $n_{eq}$ ${}^{2}$ - $n^{2}$ ) where n is the number density of the species and $n_{eq}$ is the equilibrium number density, see, e.g., S. Wolfram, Nucl. Phys. B82, 65 (1979); G. Steigman, Annu. Rev. Nucl. Part. Sci. 29, 313 (1979); J. Brenstein, L. Brown and G. Feinberg, Phys. Rev. D 32, 3261 (1985); R. Scherrer and M. Turner, ibid. 33, 1585 (1986). Our approximate method will suffice to illustrate the point.
The evolution of heavy neutrinos in the Majoron model of Gelmini and Roncadelli has been discussed in detail by H. Georgi, S. Glashow and S. Nussinov, Nucl. Phys. E. Kolb and M. S. TurnerB193, 297 (1981) and , Phys. Lett. 159 B, 102 (1985).
We would like to G. Gelmini for emphasizing this point.
M. Fukugita, S. Watamura and M. Yoshimura, Phys. Rev. Lett. 48, 1522 (1982); D. Dearborn, D. Schramm and G. Steigman, ibid. 56, 26 (1986).
E. Kolb, M. Turner, and T. Walker (unpublished).
W. Bardeen and S. Tye, Phys. Lett. 74 B, 229 (1978).
D. Dicus, E. Kolb, V. Teplitz and R. Wagoner, Phys. Rev. D 18, 1829 (1978); ibid. 22, 839 (1980); M. Fukugita, S. Watamura and M. Yoshimura, ibid. 26, 1840 (1982); see also Ref. 17.
J. Schweppe et al., Phys. Rev. Lett. 51, 2261 (1983); T. Cowan et al., ibid. 54, 1761 (1985); , ibid. 56, 444 (1986).
A. Balantekin, C. Bottcher and M. Strayer, Phys. Rev. Lett. 55, 461 (1985); A. Schäfer, , J. Phys. G 11, (1985); A. Chodos and L. Wijewardhana, Phys. Rev. Lett. 56, 302 (1986); D. Carrier, A. Chodos and L. Wijewarhana, Phys. Rev. D 34, 1332 (1986); L. M. Krauss and F. Wilczek, Phys. Lett. 173 B, 189 (1986).

[c1] For recent reviews of the standard model of primordial nucleosynthesis and its use as a probe of particle physics, see J. Yang, M. S. Turner, G. Steigman, N. D. Schramm and K. A. Olive, Astrophys. J. 281, 493 (1984); G. Steigman and A. M. Boesgaard, Annu. Rev. Astron. Astrophys. 23, 319 (1985), and references therein.

[c2] The effect of additional relativistic degrees of freedom on primordial nucleosynthesis has been frequently discussed. See, for example, V. F. Shvartsman, Pis'ma Zh. Eksp. Teor. Fiz. 9, 315 (1969) [JETP Lett. 9, 184 (1969)]; G. Steigman, D. N. Schramm and J. E. Gunn, Phys. Lett. 66 B, 202 (1977); J. Yang, D. N. Schramm and R. T. Rood, Astrophys. J. 227, 697 (1979); K. A. Olive, D. N. Schramm and G. Steigman, Nucl. Phys. B180, 497 (1981); K. A. Olive, D. N. Schramm, G. Steigman, M. S. Turner and J. Yang, Astrophys. J. 246, 557 (1981); A. S. Szalay, Phys. Lett. 101 B, 453 (1981); Yang et al. (Ref. 1).

[c3] E. W. Kolb and R. J. Scherrer, Phys. Rev. D 25, 1481 (1982).

[c4] G. Steigman, K. A. Olive and D. N. Schramm, Phys. Rev. Lett. 43, 239 (1979).

[c5] Y. Chikashige, R. N. Mohapatra and R. D. Peccei, Phys. Lett. 98 B, 265 (1981); G. B. Gelmini and M. Roncadelli, ibid. 99 B, 411 (1981); H. M. Georgi, S. L. Glashow and S. Nussinov, Nucl. Phys. B193, 297 (1981).

[c6] See, for example, R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977); S. Weinberg, ibid. 40, 223 (1978); F. Wilczek, ibid. 40, 279 (1978); J. Kim, ibid. 43, 103 (1979); M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104 B, 199 (1981).

[c7] F. Hoyle and R. J. Taylor, Nature (London) 203, 1108 (1964); P. J. E. Peebles, Astrophys. J. 146, 542 (1966); R. V. Wagoner, W. A. Fowler and F. Hoyle, ibid. 148, 3 (1967).

[c8] R. V. Wagoner, Astrophys. J. 179, 343 (1973).

[c9] The actual neutrino decoupling temperature is slightly different for each species. See D. A. Dicus, E. W. Kolb, A. M. Gleeson, E. C. G. Sudarshan, V. L. Teplitz and M. S. Turner, Phys. Rev. D 26, 2694 (1982).

[c10] D. A. Dicus, E. W. Kolb, V. L. Teplitz and R. V. Wagoner, Phys. Rev. D 17, 1529 (1978).

[c11] See Ref. 5.

[c12] See Ref. 9.

[c13] As mentioned in Sec. III, particles of m <wig 100 eV which couple to photons transfer their entropy to photons too late for thermalization to occur by the present epoch, and thus eta would be unaltered. Therefore, the effect of m < 100 eV generic particles coupled to photons throughout nucleosynthesis is due to their energy density, and thus they produce the effect of an equivalent number of neutrino species. The curves of Figs. 2–5 should coincide with the analogous curves for generic particles coupled to neutrinos below m/ $m_{e}$ $10^{- 3}$ . Of course, the decays of such particles will distort the microwave background and therefore are cosmologically unacceptable (see Ref. 10).

[c14] In order to determine whether or not a generic species maintains thermal equilibrium with photons or light neutrinos we should solve the rate equation n dot = -3Hn + < σ v > ( $n_{eq}$ ${}^{2}$ - $n^{2}$ ) where n is the number density of the species and $n_{eq}$ is the equilibrium number density, see, e.g., S. Wolfram, Nucl. Phys. B82, 65 (1979); G. Steigman, Annu. Rev. Nucl. Part. Sci. 29, 313 (1979); J. Brenstein, L. Brown and G. Feinberg, Phys. Rev. D 32, 3261 (1985); R. Scherrer and M. Turner, ibid. 33, 1585 (1986). Our approximate method will suffice to illustrate the point.

[c15] The evolution of heavy neutrinos in the Majoron model of Gelmini and Roncadelli has been discussed in detail by H. Georgi, S. Glashow and S. Nussinov, Nucl. Phys. E. Kolb and M. S. TurnerB193, 297 (1981) and , Phys. Lett. 159 B, 102 (1985).

[c16] We would like to G. Gelmini for emphasizing this point.

[c17] M. Fukugita, S. Watamura and M. Yoshimura, Phys. Rev. Lett. 48, 1522 (1982); D. Dearborn, D. Schramm and G. Steigman, ibid. 56, 26 (1986).

[c18] E. Kolb, M. Turner, and T. Walker (unpublished).

[c19] W. Bardeen and S. Tye, Phys. Lett. 74 B, 229 (1978).

[c20] D. Dicus, E. Kolb, V. Teplitz and R. Wagoner, Phys. Rev. D 18, 1829 (1978); ibid. 22, 839 (1980); M. Fukugita, S. Watamura and M. Yoshimura, ibid. 26, 1840 (1982); see also Ref. 17.

[c21] J. Schweppe et al., Phys. Rev. Lett. 51, 2261 (1983); T. Cowan et al., ibid. 54, 1761 (1985); , ibid. 56, 444 (1986).

[c22] A. Balantekin, C. Bottcher and M. Strayer, Phys. Rev. Lett. 55, 461 (1985); A. Schäfer, , J. Phys. G 11, (1985); A. Chodos and L. Wijewardhana, Phys. Rev. Lett. 56, 302 (1986); D. Carrier, A. Chodos and L. Wijewarhana, Phys. Rev. D 34, 1332 (1986); L. M. Krauss and F. Wilczek, Phys. Lett. 173 B, 189 (1986).

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Effect of interacting particles on primordial nucleosynthesis

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