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The abundance of moduli, modulini and gravitinos produced by the vacuum fluctuation
High Energy Physics - Phenomenology · Submitted 15 Sep 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Existing estimates are confirmed; the abundance of modulini and (probably) of moduli created from the vacuum is less than from thermal collisions, but the abundance of gravitinos may be much bigger, leading to a tighter bound on $T\sub R$ if supersymmetry breaking is gravity-mediated.
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The abstract, sentence by sentence
Moduli, modulini and the gravitino have gravitational-strength interactions, and thermal collisions after reheating create all of them with roughly the same abundance. With their mass of order $100\GeV$, corresponding to gravity-mediated supersymmetry breaking, this leads to the well-known bound $\gamma T\sub R\lsim 10^9\GeV$ on the reheat temperature, where $\gamma\leq 1$ is the entropy dilution factor. The vacuum fluctuation also creates these particles, with abundance determined by the solution of the equation for the mode function. Taking the equation in each case to be the one corresponding to a free field, we consider carefully the behaviour of the effective mass during the crucial era after inflation. It may have a rapid oscillation, which does not however affect the particle abundance. Existing estimates are confirmed; the abundance of modulini and (probably) of moduli created from the vacuum is less than from thermal collisions, but the abundance of gravitinos may be much bigger, leading to a tighter bound on $T\sub R$ if supersymmetry breaking is gravity-mediated. It is noted that in the case of gauge-mediated supersymmetry breaking, the abundance of the gravitino may be sufficient to make it a dark matter candidate.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Moduli, modulini and the gravitino have gravitational-strength interactions, and thermal collisions after reheating create all of them with roughly the same abundance. | background 1.00 | 0.08 | 0.07 | asserted 1.00 |
| s1 | With their mass of order $100\GeV$, corresponding to gravity-mediated supersymmetry breaking, this leads to the well-known bound $\gamma T\sub R\lsim 10^9\GeV$ on the reheat temperature, where $\gamma\leq 1$ is the entropy dilution factor. | background 0.98 | 0.09 | 0.07 | asserted 1.00 |
| s2 | The vacuum fluctuation also creates these particles, with abundance determined by the solution of the equation for the mode function. | contribution 0.70 | 0.42 | 0.06 | asserted 1.00 |
| s3 | Taking the equation in each case to be the one corresponding to a free field, we consider carefully the behaviour of the effective mass during the crucial era after inflation. | method 0.92 | 0.79 | 0.03 | asserted 0.71 |
| s4 | It may have a rapid oscillation, which does not however affect the particle abundance. | result 0.84 | 0.65 | 0.03 | hedged possibility 0.83 |
| s5 | Existing estimates are confirmed; the abundance of modulini and (probably) of moduli created from the vacuum is less than from thermal collisions, but the abundance of gravitinos may be much bigger, leading to a tighter bound on $T\sub R$ if supersymmetry breaking is gravity-mediated. | result 0.95 | 0.82 | 0.88 | hedged possibility 0.79 |
| s6 | It is noted that in the case of gauge-mediated supersymmetry breaking, the abundance of the gravitino may be sufficient to make it a dark matter candidate. | result 0.54 | 0.37 | 0.06 | hedged possibility 1.00 |
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Original abstract
Moduli, modulini and the gravitino have gravitational-strength interactions, and thermal collisions after reheating create all of them with roughly the same abundance. With their mass of order $100\GeV$, corresponding to gravity-mediated supersymmetry breaking, this leads to the well-known bound $\gamma T\sub R\lsim 10^9\GeV$ on the reheat temperature, where $\gamma\leq 1$ is the entropy dilution factor. The vacuum fluctuation also creates these particles, with abundance determined by the solution of the equation for the mode function. Taking the equation in each case to be the one corresponding to a free field, we consider carefully the behaviour of the effective mass during the crucial era after inflation. It may have a rapid oscillation, which does not however affect the particle abundance. Existing estimates are confirmed; the abundance of modulini and (probably) of moduli created from the vacuum is less than from thermal collisions, but the abundance of gravitinos may be much bigger, leading to a tighter bound on $T\sub R$ if supersymmetry breaking is gravity-mediated. It is noted that in the case of gauge-mediated supersymmetry breaking, the abundance of the gravitino may be sufficient to make it a dark matter candidate.
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