Moduli-Induced Gravitino Problem

Abstract

We investigate the cosmological moduli problem by studying a modulus decay in detail and find that the branching ratio of the gravitino production is generically of O(0.01 − 1), which causes another cosmological disaster. Consequently, the cosmological moduli problem cannot be solved simply by making the modulus mass heavier than 100 TeV. We also illustrate our results by explicitly calculating the branching ratio into the gravitinos in the mixed modulus-anomaly/KKLT-and racetrack-type models.The cosmological moduli problem [1] is one of the most challenging puzzles in particle physics and cosmology. In this letter, we show that the problem is even more difficult than usually thought.In supergravity/superstring theories, generically there exist moduli fields which have flat potentials and obtain masses from supersymmetry (SUSY) breaking and nonperturbative effects. During an inflationary period, a modulus field X is likely to develop a large expectation value. After the end of the inflation, it starts a coherent oscillation and soon dominates the energy density of the universe. Due to the interaction suppressed by the Planck scale M P = 2.4 × 10 18 GeV, the decay rate of the modulus X is extremely small:which leads to an onset of a radiation-dominated universe with a very low temperature:Here, c is an order one coefficient and g * is the effective number of massless degrees of freedom. This is cosmologically unacceptable because a successful big-bang nucleosynthesis (BBN) requires that the (last) radiationdominated universe starts with temperature higher thanAs is clear from Eq. (2), a simple solution would be to assume that the modulus X is ultra heavy a :Actually, there have been proposed scenarios with such a large modulus mass (cf. [5,6,7,8,9]). However, there exists yet another serious cosmological obstacle even for heavy moduli scenarios. The new problem is caused by the gravitino which is produced by the modulus decay. Indeed, as we will show, the branching a See Refs. [3,4] for other solutions. ratio of the modulus decay into the gravitino is generically quite largewhich causes serious problems after the modulus decay. We call this problem the moduli-induced gravitino problem.The gravitino production via modulus decay and its cosmological implications have been previously discussed in Refs. [10,11], taking Br(X → gravitino) ≪ 1. The main purpose of this letter is to show that Eq. (4) holds in a generic setup, and to emphasize how disastrous its consequences are. We also exemplify explicit results in the mixed modulus-anomaly/KKLT mediation [6,7] and in the racetrack [8] setups.Let us first estimate the branching ratio of a modulus decay into gravitino(s). We consider a heavy modulus scenario, m X > ∼ 100 TeV [cf. Eq. (3)]. On the other hand, the gravitino is likely to be (much) lighter than 100 TeV, because too large gravitino mass requires a finetuning in the Higgs sector due to the anomaly-mediated effects. Thus, we assume m X ≫ m 3/2 hereafter. After choosing the unitary gauge in the Einstein frame, w...

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