Supergravitational Conformal Galileons

The worldvolume actions of 3+1 dimensional bosonic branes embedded in a five-dimensional bulk space can lead to important effective field theories, such as the DBI conformal Galileons, and may, when the Null Energy Condition is violated, play an essential role in cosmological theories of the early universe. These include Galileon Genesis and "bouncing" cosmology, where a pre-Big Bang contracting phase bounces smoothly to the presently observed expanding universe. Perhaps the most natural arena for such branes to arise is within the context of superstring and $M$-theory vacua. Here, not only are branes required for the consistency of the theory, but, in many cases, the exact spectrum of particle physics occurs at low energy. However, such theories have the additional constraint that they must be $N=1$ supersymmetric. This motivates us to compute the worldvolume actions of $N=1$ supersymmetric three-branes, first in flat superspace and then to generalize them to $N=1$ supergravitation. In this paper, for simplicity, we begin the process, not within the context of a superstring vacuum but, rather, for the conformal Galileons arising on a co-dimension one brane embedded in a maximally symmetric $AdS_{5}$ bulk space. We proceed to $N=1$ supersymmetrize the associated worldvolume theory and then generalize the results to $N=1$ supergravity, opening the door to possible new cosmological scenarios.Comment: 39 pages, 1 figure. Version 4: Typos corrected, minor points on notation clarifie

Aspects Of Phenomenology And Cosmology In Heterotic M-Theory

We present an exploration of models of particle phenomenology and cosmology which arise from the E_8 x E_8 heterotic string theory and its strong-coupled limit, known as heterotic M-theory. We first re-examine the B-L MSSM, a realistic supersymmetric extension of the Standard Model, in a more generic region of moduli space. We modify our previous analysis by demanding that the mass scales of the two Wilson lines be simultaneous, and we show that the resulting absence of gauge unification is consistent with string threshold corrections. Using these results, we build a realistic model of inflation where a scalar constructed from the fields of the B-L MSSM is taken to be the inflaton. The subsequent period of reheating is then investigated in detail. Finally, it is known that M-theory admits five-branes, which wrap holomorphic curves upon dimensional compactification. We construct an effective N=1 supersymmetric action to describe the world-volume theory of the resulting three-branes, which live in the bulk space of heterotic M-theory

Perturbative Reheating in Sneutrino-Higgs Cosmology

The theory of perturbative reheating in the Sneutrino-Higgs cosmology of the $B-L$ MSSM is presented. It is shown that following an epoch of inflation consistent with all Planck2015 data, the inflaton begins to oscillate around its minimum at zero and to reheat to various species of standard model and supersymmetric matter. The perturbative decay rates to this matter are computed, both analytically and numerically. Using these results, the Hubble parameter and the relative energy densities for each matter species, including that of the inflaton, are calculated numerically. The inflaton energy density is demonstrated to vanish at an energy scale of ${\cal{O}}(10^{13})~{\rm GeV}$, signaling the end of the period of reheating. The newly created matter background is shown to be in thermal equilibrium, with a reheating temperature of $\simeq 1.13 \times 10^{13}~{\rm GeV}$. To allow for a $B-L$ breaking scale sufficiently smaller than the reheating scale, we extend the statistical method of determining the soft supersymmetry breaking parameters developed in previous work. The result is that one can determine a large number of phenomenologically realistic initial conditions for which the $B-L$ breaking scale is an order of magnitude or more smaller than the reheating scale.Comment: 77 pages, 25 figures. Version 2: Updated to match version published in JHEP, includes new references and a brief discussion of preheatin

Index Formulae for Line Bundle Cohomology on Complex Surfaces

We conjecture and prove closed-form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. Further, for all compact toric surfaces we provide a simple algorithm which allows expression of any line bundle cohomology in terms of an index. These formulae follow from general theorems we prove for a wider class of surfaces. In particular, we construct a map that takes any effective line bundle to a nef line bundle while preserving the zeroth cohomology dimension. For complex surfaces, these results explain the appearance of piecewise polynomial equations for cohomology and they are a first step towards understanding similar formulae recently obtained for Calabi-Yau three-folds.Comment: 30 page