We reconsider the strength of the electroweak phase transition in the singlet Majoron extension of the Standard Model, with a low ( < ∼ TeV) scale of the singlet VEV. A strongly first order phase transition, of interest for electroweak baryogenesis, is found in sizeable regions of the parameter space, especially when the cross-coupling λ hs |S| 2 |H| 2 between the singlet and the doublet Higgs is significant. Large Majorana Yukawa couplings of the singlet neutrinos, y i Sν c i ν i , are also important for strengthening the transition. We incorporate the LEP and Tevatron constraints on the Higgs masses, and electroweak precision constraints, in our search for allowed parameters; successful examples include singlet masses ranging from 5 GeV to several TeV. Models with a strong phase transition typically predict a nonstandard Higgs with mass in the range 113 GeV < ∼ m H < ∼ 200 GeV and production cross sections reduced by mixing with the singlet, with cos 2 θ significantly less than 1. We also find examples where the singlet is light and the decay H → SS can modify the Higgs branching ratios relative to Standard Model expectations. * current address: Barclays Capital Japan Limited

We provide an analytical study of the coupling of short and long wavelength fluctuation modes during the initial phase of reheating in two field models like hybrid inflation. In these models, there is -at linear order in perturbation theory -an instability in the entropy modes of cosmological perturbations which, if not cut off, could lead to curvature fluctuations which exceed the current observational values. Here, we demonstrate that the back-reaction of short wavelength fluctuations is too weak to lead to a truncation of the instability for the long wavelength modes on time scales comparable to the typical instability time scale of the long wavelength entropy modes. Hence, unless there are other mechanisms which truncate the instability, then in models such as hybrid inflation the curvature perturbations produced during reheating on scales of current observational interest may be very important.PACS numbers: 98.80.Cq

Abstract. The global behaviour of the normal function associated with van Geemen's family of lines on the mirror quintic is studied. Based on the associated inhomogeneous Picard-Fuchs equation, the series expansions around large complex structure, conifold, and around the open string discriminant are obtained. The monodromies are explicitly calculated from this data and checked to be integral. The limiting value of the normal function at large complex structure is an irrational number expressible in terms of the di-logarithm.