Recently it was demonstrated that free fermionic heterotic strings can produce models with solely the minimal supersymmetric standard model states in the low energy spectrum. This unprecedented result provides further strong evidence for the possibility that the true string vacuum shares some of the properties of the free fermionic models. Past free fermionic models have focused on several possible unbroken observable SO(10) subgroups at the string scale, which include the flipped SU(5) ͑FSU5͒, the Pati-Salam ͑PS͒ string models, and the string standard-like models ͑SLM͒. We extend this study to include the case in which the SO(10) symmetry is broken to the left-right symmetric ͑LRS͒ gauge group, SO(10)→SU(3) C ϫU(1) BϪL ϫSU(2) L ϫSU(2) R . We present several models of this type and discuss their phenomenological features. The most striking new outcome of the LRS string models, in contrast with the case of the FSU5, the PS, and the SLM string models, is that they can produce effective field theories that are free of Abelian anomalies. We discuss the distinction between the two types of free fermionic models which result in the presence, or absence, of an anomalous U(1). As a counterexample we also present a LRS model that does contain an anomalous U(1). Additionally, we discuss how in string models the standard model spectrum may arise from the three 16 representations of SO(10), while the weak hypercharge does not have the canonical SO(10) embedding.

We address intermediate scales within a class of string models. The intermediate scales occur due to the SM singlets S i acquiring non-zero VEVs due to radiative breaking; the mass-square m 2 i of S i is driven negative at µ RAD due to O(1) Yukawa couplings of S i to exotic particles (calculable in a class of string models). The actual VEV of S i depends on the relative magnitude of the non-renormalizable terms of the typeŜWe mainly consider the case in which the S i are charged under an additional non-anomalous U (1) ′ gauge symmetry and the VEVs occur along F -and Dflat directions. We explore various scenarios in detail, depending on the type of Yukawa couplings to the exotic particles and on the initial boundary values of the soft SUSY breaking parameters. We then address the implications of these scenarios for the µ parameter and the fermionic masses of the standard model.

The evolutions of the flat FLRW universe and its linear perturbations are studied systematically in the dressed metric approach of LQC. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating, {\em bouncing, transition and slow-roll inflation}. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolutions of the background and its linear perturbations are found explicitly, and then matched to the ones given in the other two phases. Hence, once the initial conditions are imposed, the linear scalar and tensor perturbations will be uniquely determined. Considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the pre-inflationary dynamics, the scalar and tensor power spectra become scale-dependent. Comparing with the Planck 2015 data, we find constraints on the total e-folds that the universe must have expanded since the bounce, in order to be consistent with current observations.Comment: revtex4, 23 figures, and 5 tables. Some typos were corrected. Phys. Rev. D 96, 083520 (2017

The recent conjecture of possible equivalence between the string scale M S and the minimal supersymmetric standard model unification scale M U ≈ 2.5 × 10 16 GeV is considered in the context of string models. This conjecture suggests that the observable gauge group just below the string scale should bespectrum of the observable sector should consist solely of the MSSM spectrum. We demonstrate that string models can actually be constructed that possess these observable features. Two aspects generic to many classes of three family SU (3) C × SU (2) L × U (1) Y string models are both an extra local anomalous U (1) A and numerous (often fractionally charged) exotic particles beyond the MSSM. Thus, for these classes, the key to obtaining an M S = M U ≈ 2.5 × 10 16 GeV string model is the existence of F -and D-flat directions that near the string scale can simultaneously break the anomalous U (1) and give mass to all exotic SM-charged observable particles, decoupling them from the low energy spectrum. In this letter we show, in the context of free fermionic strings, that string models with flat directions possessing these features do exist. We present one such string derived model in which all such exotic observable states beyond the MSSM receive mass at the scale generated by the Fayet-Iliopoulos term. The associated F -and D-flat direction is proven flat to all orders of the superpotential.