Supersymmetric inflation with constraints on superheavy neutrino masses

G. Lazarides; R. K. Schaefer; Q. Shafi

doi:10.1103/PhysRevD.56.1324

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Supersymmetric inflation with constraints on superheavy neutrino masses

G. Lazarides

R. K. Schaefer and Q. Shafi

Physics Division, School of Technology, University of Thessaloniki, Thessaloniki, Greece

Bartol Research Institute, University of Delaware, Newark, Delaware 19716

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Phys. Rev. D 56, 1324 – Published 15 July, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.1324

Abstract

We consider a supersymmetric model of inflation in which the primordial density fluctuations are nearly scale invariant (spectral index $n \approx 0.98)$ with an amplitude proportional to ${(M / M}_{Planck})^{2}$ , where $M \sim 10^{16}$ GeV denotes the scale of the gauge symmetry breaking associated with inflation. The 60 or so $e$ foldings take place when all relevant scales are close to $M$ , which helps suppress supergravity corrections. The gravitino and baryogenesis (via leptogenesis) constraints help determine the two heaviest right-handed neutrino masses to be $\approx 2 \times 10^{13}$ GeV and $6 \times 10^{9}$ GeV.

References (14)

G. Dvali, Q. Shafi, and R. K. Schaefer, Phys. Rev. Lett. 73, 1886 (1994).
A. D. Linde, Phys. Lett. B 259, 38 (1991); Phys. Rev. D 49, 748 (1994).
For an earlier attempt at inflation with this superpotential, see E. J. Copeland, A. R. Liddle, D. H. Lyth, E. D. Stewart, and D. Wands, Phys. Rev. D 49, 6410 (1994). Supersymmetric inflation has a long history and there are several reviews available, see, e.g., A. D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Switzerland, 1990).
The soft supersymmetry-breaking scalar masses can be safely ignored.
A. R. Liddle and D. H. Lyth, Phys. Rep. 231, 1 (1993).
The supergravity-induced inflaton mass remains exactly zero even if we include in $W$ all possible nonrenormalizable terms involving $S$ , $φ$ , $\bar{φ}$ allowed by the gauge and $R$ symmetries, and with a minimal Kähler potential [see first reference in [[3]] and E. D. Stewart, Phys. Rev. D 51, 6847 (1995).] The fact that $S ≪ M_{P}$ plays a crucial role if higher order terms are included in the Kähler potential. The inflaton mass can then be kept $≪ H$ with only a mild tuning of just one parameter [G. Dvali (private communication)]. In many other inflationary scenarios one needs to adjust an infinite number of parameters.
W. Buchmüller and D. Wyler, Phys. Lett. B 249, 458 (1990); W. Buchmüller and T. Yanagida, 302, 240 (1993).
K. S. Babu (private communication).
M. Fugugita and T. Yanagida, Phys. Lett. B 174, 45 (1986); G. Lazarides and Q. Shafi, 258, 305 (1991); G. Lazarides, C. Panagiotakopoulos, and Q. Shafi, 315, 325 (1993); L. Covi, E. Roulet, and F. Vissani, 384, 169 (1996).
J. A. Harvey and M. S. Turner, Phys. Rev. D 42, 3344 (1990).
L. E. Ibáñez and F. Quevedo, Phys. Lett. B 283, 261 (1992).
Q. Shafi and F. W. Stecker, Phys. Rev. Lett. 53, 1292 (1984). For a recent review, see A. R. Liddle, D. H. Lyth, R. K. Schaefer, Q. Shafi, and P. T. Viana, Mon. Not. R. Astron. Soc. 281, 531 (1996).
R. K. Schaefer, Q. Shafi, and F. W. Stecker, Astrophys. J. 347, 575 (1989); J. Holtzman, Astrophys. J. Suppl. Ser. 74, 1 (1989).
C. L. Bennett, et al., Astrophys. J. Lett. 464, 1 (1996).

[c1] G. Dvali, Q. Shafi, and R. K. Schaefer, Phys. Rev. Lett. 73, 1886 (1994).

[c2] A. D. Linde, Phys. Lett. B 259, 38 (1991); Phys. Rev. D 49, 748 (1994).

[c3] For an earlier attempt at inflation with this superpotential, see E. J. Copeland, A. R. Liddle, D. H. Lyth, E. D. Stewart, and D. Wands, Phys. Rev. D 49, 6410 (1994). Supersymmetric inflation has a long history and there are several reviews available, see, e.g., A. D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Switzerland, 1990).

[c4] The soft supersymmetry-breaking scalar masses can be safely ignored.

[c5] A. R. Liddle and D. H. Lyth, Phys. Rep. 231, 1 (1993).

[c6] The supergravity-induced inflaton mass remains exactly zero even if we include in $W$ all possible nonrenormalizable terms involving $S$ , $φ$ , $\bar{φ}$ allowed by the gauge and $R$ symmetries, and with a minimal Kähler potential [see first reference in [[3]] and E. D. Stewart, Phys. Rev. D 51, 6847 (1995).] The fact that $S ≪ M_{P}$ plays a crucial role if higher order terms are included in the Kähler potential. The inflaton mass can then be kept $≪ H$ with only a mild tuning of just one parameter [G. Dvali (private communication)]. In many other inflationary scenarios one needs to adjust an infinite number of parameters.

[c7] W. Buchmüller and D. Wyler, Phys. Lett. B 249, 458 (1990); W. Buchmüller and T. Yanagida, 302, 240 (1993).

[c8] K. S. Babu (private communication).

[c9] M. Fugugita and T. Yanagida, Phys. Lett. B 174, 45 (1986); G. Lazarides and Q. Shafi, 258, 305 (1991); G. Lazarides, C. Panagiotakopoulos, and Q. Shafi, 315, 325 (1993); L. Covi, E. Roulet, and F. Vissani, 384, 169 (1996).

[c10] J. A. Harvey and M. S. Turner, Phys. Rev. D 42, 3344 (1990).

[c11] L. E. Ibáñez and F. Quevedo, Phys. Lett. B 283, 261 (1992).

[c12] Q. Shafi and F. W. Stecker, Phys. Rev. Lett. 53, 1292 (1984). For a recent review, see A. R. Liddle, D. H. Lyth, R. K. Schaefer, Q. Shafi, and P. T. Viana, Mon. Not. R. Astron. Soc. 281, 531 (1996).

[c13] R. K. Schaefer, Q. Shafi, and F. W. Stecker, Astrophys. J. 347, 575 (1989); J. Holtzman, Astrophys. J. Suppl. Ser. 74, 1 (1989).

[c14] C. L. Bennett, et al., Astrophys. J. Lett. 464, 1 (1996).

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Supersymmetric inflation with constraints on superheavy neutrino masses

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