Abstract
We revisit gravitino production following inflation. As a first step, we review the standard calculation of gravitino production in the thermal plasma formed at the end of post-inflationary reheating when the inflaton has completely decayed. Next we consider gravitino production prior to the completion of reheating, assuming that the inflaton decay products thermalize instantaneously while they are still dilute. We then argue that instantaneous thermalization is in general a good approximation, and also show that the contribution of non-thermal gravitino production via the collisions of inflaton decay products prior to thermalization is relatively small. Our final estimate of the gravitino-to-entropy ratio is approximated well by a standard calculation of gravitino production in the post-inflationary thermal plasma assuming total instantaneous decay and thermalization at a time t ≃ 1.2/Γϕ. Finally, in light of our calculations, we consider potential implications of upper limits on the gravitino abundance for models of inflation, with particular attention to scenarios for inflaton decays in supersymmetric Starobinsky-like models.
Highlights
Measurements by the Planck satellite [1] and ground-based experiments such as BICEP2/Keck Array [2, 3] are probing the cosmic microwave background (CMB) ever more precisely, a new round of experiments is on the way, and far more accurate experiments are being proposed for the future
We provide an analytic solution to the late time gravitino yield when the instantaneous decay approximation is dropped
−1 2.9 × 10−9 1.5 × 10−6 for for m3/2 = 3 TeV, m3/2 = 6 TeV. These bounds would be weakened for larger values of m3/2, disappearing altogether if the gravitino is sufficiently heavy to decay before Big-Bang nucleosynthesis (BBN)
Summary
Measurements by the Planck satellite [1] and ground-based experiments such as BICEP2/Keck Array [2, 3] are probing the cosmic microwave background (CMB) ever more precisely, a new round of experiments is on the way, and far more accurate experiments are being proposed for the future. Cosmological and astrophysical constraints on the abundance of gravitinos produced after inflation yield complementary restrictions on the amount of reheating, and y [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25] These constraints may arise from considerations of the relic dark matter density due to gravitinos or their decay products and/or from limits on late-decaying gravitinos imposed, e..g., by the success of Big-Bang nucleosynthesis calculations [26, 27, 16, 22].
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