The cosmological moduli problem and naturalness

Abstract

Nowadays, the cosmological moduli problem (CMP) comes in three parts: 1. potential violation of Big-Bang nucleosynthesis (BBN) constraints from late decaying moduli fields, 2. the moduli-induced gravitino problem wherein gravitinos are overproduced and their decays violate BBN or dark matter overproduction bounds and 3. the moduli-induced lightest SUSY particle (LSP) overproduction problem. Also, the CMP may be regarded as either a problem or else a solution to scenarios with dark matter over- or under-production. We examine the cosmological moduli problem and its connection to electroweak naturalness. We calculate the various two-body decay widths of a light modulus field into MSSM particles and gravitinos within general supersymmetric models. We include both phase space and mixing effects. We examine cases without and with helicity suppression of modulus decays to gravitinos (cases 1 & 2) and/or gauginos (cases A & B). For case B1, we evaluate regions of gravitino mass m3/2 vs. modulus mass mϕ parameter space constrained by BBN, by overproduction of gravitinos and by overproduction of neutralino dark matter, along with connections to naturalness. For this case, essentially all of parameter space is excluded unless mϕ ≳ 2.5 × 103 TeV with mϕ< 2m3/2. For a potentially most propitious case B2 with ϕ decay to Higgs and matter turned off, then modulus branching fractions to SUSY and to gravitinos become highly suppressed at large mϕ. But since the modulus number density increases faster than the branching fractions decrease, there is still gross overproduction of neutralino dark matter. We also show that in this scenario the thermally produced gravitino problem is fixed by huge entropy dilution, but non-thermal gravitino production from moduli decay remains a huge problem unless it is kinematically suppressed with mϕ< 2m3/2. In a pedagogical appendix, we present detailed calculations of modulus field two-body decay widths.

An anthropic solution to the cosmological moduli problem

“…We have computed all 2-body MSSM decay modes of the φ field using the Moroi-Randall [10] operators which are proportional to coupling parameters λ i , where i labels the various modulus couplings to gauge bosons/gauginos, Higgs superfields, and matter superfields. The results will be reported in a longer paper [11] but example results are shown in Fig. 1 which shows the modulus field partial widths as a function of m φ for all couplings λ i = 1 in case of helicity-suppressed decays to gauginos but unsuppressed decays to gravitinos [12][13][14].…”

“…1 which shows the modulus field partial widths as a function of m φ for all couplings λ i = 1 in case of helicity-suppressed decays to gauginos but unsuppressed decays to gravitinos [12][13][14]. This plot is shown assuming a natural SUSY benchmark point [11]. Once Γ φ is known, the modulus decay temperature T D and various branching fractions can be computed.…”

“…Further details will be reported in Ref. [11], but for the moment we will assume m φ ∼ m 3/2 so that the decay mode φ → ψ µ ψ µ is kinematically closed as suggested by Acharya et al Ref. [7].…”

On dark radiation from string moduli decay to ALPs

“…In this paper, we continue our earlier investigation [20] of the cosmological moduli problem (CMP) wherein we computed the various modulus decay rates into the MSSM particles including all phase space and mixing effects which are routinely ignored in the literature. Once these are known, then one may compute the modulus decay temperature T D Γ φ m P /(πg * /90) 1/4 and use these to implement BBN constraints (T D > T BBN ∼ 3 − 5 MeV).…”

“…Also, typically m φ < 2m 3/2 was needed to avoid the moduli-induced gravitino problem. For the well-motivated gravity-mediated SUSY breaking model, wherein the soft SUSY breaking scale m sof t ∼ m 3/2 , then the high mass modulus solution to the CMP would bring physics into conflict with naturalness of SUSY models which requires sparticles (save light higgsinos) typically in the several TeV range [20] 1 . An alternative solution which allows much lighter values of m φ ∼ 30 TeV is to find an anthropic selection on modulus field strength φ 0 ∼ 10 −7 m P which allows for a more comparable dark-matter-to-baryonic-matter ratio ∼ 1 − 10 [23].…”