Case for an EeV Gravitino

Abstract

We consider the possibility that supersymmetry is broken above the inflationary mass scale and that the only "low" energy remnant of supersymmetry is the gravitino with mass of order the EeV scale. The gravitino in this class of models becomes a candidate for the dark matter of the Universe. To avoid the over-production of gravitinos from the decays of the next-to-lightest supersymmetric particle we argue that the supersymmetric spectrum must lie above the inflationary mass scale (MSUSY > 10 −5 MP ∼ 10 13 GeV). [5,6]. This may indicate one of the following: 1) low energy supersymmetry is still around the corner waiting to be discovered at a slightly higher energy scale [6,7]; 2) part of the supersymmetric spectrum lies at very high energy as in split supersymmetry [8]; 3) essentially the entire supersymmetric spectrum lies at very high energy as in supersplit supersymmetry [9] (aka the Standard Model). Here, we consider the possibility that the only remnant of supersymmetry surviving down to energies significantly below the Planck scale 1 is the gravitino.

Gravitino decay in high scale supersymmetry with R -parity violation

“…It is difficult to obtain neutralinos with masses in excess of a few TeV, with relic densities still compatible with cosmic microwave background observations [14]. By combining the limit on the relic density with limits from big bang nucleosynthesis, one can derive an upper limit of roughly 4 TeVon the gravitino mass [7]. This limit is evaded in high-scale supersymmetry models, when no superpartners other than the gravitino are produced during reheating and a new window of gravitino masses opens up above Oð0.1Þ EeV [7].…”

“…If that scale is above the inflationary scale, ∼3 × 10 13 GeV, supersymmetric particles, with one exception, may not have participated in the reheating process and were never part of the thermal background in the early Universe. The exception may be the gravitino with an approximately EeV mass [7]. In this case, we still have a viable supersymmetric dark matter candidate, namely the gravitino which is produced from the thermal bath during reheating [7][8][9].…”

“…In high-scale supersymmetry models with the gravitino as the only superpartner lighter than the inflaton, gravitinos can be pair produced during reheating [7,8]. The gravitino production rate density was derived in Ref.…”

“…Indeed, the only way to produce the gravitino in the early Universe if the supersymmetrybreaking scale lies above the reheating temperature, 7 T RH , is through the exchange of highly virtual sparticles with Planck-suppressed couplings, such as t-channel processes of the type GG →G → ψ μ ψ μ , with G,G representing the gluon and gluino, respectively [8]. Because the production FIG.…”

“…The exception may be the gravitino with an approximately EeV mass [7]. In this case, we still have a viable supersymmetric dark matter candidate, namely the gravitino which is produced from the thermal bath during reheating [7][8][9]. Interestingly, in the context of an SO(10) GUT, such highscale supersymmetric models are still able to account for gauge coupling unification, radiative electroweak symmetry breaking and the stability of the Higgs vacuum [10].…”