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We critically review the role of cosmological moduli in determining the post-inflationary history of the universe. Moduli are ubiquitous in string and M-theory constructions of beyond the Standard Model physics, where they parametrize the geometry of the compactification manifold. For those with masses determined by supersymmetry breaking this leads to their eventual decay slightly before Big Bang Nucleosynthesis (without spoiling its predictions). This results in a matter dominated phase shortly after inflation ends, which can influence baryon and dark matter genesis, as well as observations of the Cosmic Microwave Background and the growth of large-scale structure. Given progress within fundamental theory, and guidance from dark matter and collider experiments, nonthermal histories have emerged as a robust and theoretically well-motivated alternative to a strictly thermal one. We review this approach to the early universe and discuss both the theoretical challenges and the observational implications. * 5 The case of non-thermal histories with multiple moduli was considered in [12]. Generically, string / M-theory theories have many moduli with various masses, and the lightest is typically the relevant one. 6 One can argue rather generally for the positivity of cn based on causality, unitarity, and demanding that the model have a UV completion (although a few known counter-examples exist in gravitational systems). We refer the reader to [14] for details. On the other hand, the choice of c 1 positive (leading to a tachyonic mass) is chosen to realize the general expectation that the high energy and low energy minima of the field would not generically be expected to coincide in a gravitational and/or time dependent background [15]. Ideally one would like to calculate this in an explicit, UV complete model. 7 This is a generic expectation in string theories where new thresholds before the Planck scale are common place. Examples include both the compactification (Kaluza-Klein) scale M kk and string scale Ms where M M pl is required for consistency of the effective theory [16]. 9 The relation between moduli and gravitino mass in this case was first noted in [23]. 10 It is noteworthy that even defining the level of fine-tuning can be an issue, see e.g. [28]. 11 We note that already in 2006 this mass range for the lightest scalars and gravitino was noted in [29] long before the Higgs discovery and LHC bounds favoring heavy scalar superpartners.

It is commonly assumed that the energy density of the Universe was dominated by radiation between reheating after inflation and the onset of matter domination 54,000 years later. While the abundance of light elements indicates that the Universe was radiation dominated during Big Bang Nucleosynthesis (BBN), there is scant evidence that the Universe was radiation dominated prior to BBN. It is therefore possible that the cosmological history was more complicated, with deviations from the standard radiation domination during the earliest epochs. Indeed, several interesting proposals regarding various topics such as the generation of dark matter, matter-antimatter asymmetry, gravitational waves, primordial black holes, or microhalos during a nonstandard expansion phase have been recently made. In this paper, we review various possible causes and consequences of deviations from radiation domination in the early Universe -taking place either before or after BBN -and the constraints on them, as they have been discussed in the literature during the recent years.

We undertake a careful analysis of stochastic gravitational wave production from cosmological phase transitions in an expanding universe, studying both a standard radiation as well as a matter dominated history. We analyze in detail the dynamics of the phase transition, including the false vacuum fraction, bubble lifetime distribution, bubble number density, mean bubble separation, etc., for an expanding universe. We also study the full set of differential equations governing the evolution of plasma and the scalar field during the phase transition and generalize results obtained in Minkowski spacetime. In particular, we generalize the sound shell model to the expanding universe and determine the velocity field power spectrum. This ultimately provides an accurate calculation of the gravitational wave spectrum seen today for the dominant source of sound waves. For the amplitude of the gravitational wave spectrum visible today, we find a suppression factor arising from the finite lifetime of the sound waves and compare with the commonly used result in the literature, which corresponds to the asymptotic value of our suppression factor. We point out that the asymptotic value is only applicable for a very long lifetime of the sound waves, which is highly unlikely due to the onset of shocks, turbulence and other damping processes. We also point out that features of the gravitational wave spectral form may hold the tantalizing possibility of distinguishing between different expansion histories using phase transitions.

Metastable vacua in supersymmetric QCD in the presence of single and multitrace deformations of the superpotential are explored, with the aim of obtaining an acceptable phenomenology. The metastable vacua appear at one loop, have a broken R-symmetry, and a magnetic gauge group that is completely Higgsed. With only a single trace deformation, the adjoint fermions from the meson superfield are approximately massless at one loop, even though they are massive at tree level and R-symmetry is broken. Consequently, if charged under the standard model, they are unacceptably light. A multitrace quadratic deformation generates fermion masses proportional to the deformation parameter. Phenomenologically viable models of direct gauge mediation can then be obtained, and some of their features are discussed.