We study the naturalness of electroweak symmetry breaking and baryogenesis in the next-to-minimal supersymmetric standard model (NMSSM). Our study is motivated by the recent LEP bounds on the Higgs boson mass which severely constrains the low \tan\beta region of the minimal supersymmetric standard model (MSSM). We show that the low \tan \beta region of the NMSSM is clearly favoured over the MSSM with regard to the physical Higgs boson mass, fine-tuning, and electroweak baryogenesis.

M. Bastero-Gil C. Hugonie S. F. King D. P. Roy S. Vempati

In this talk we address the issue of how the observables in our present Universe are affected by processes that may have occured at superplanckian energies (referred to as the {\it transplanckian regime}). For example, the origin of the cosmological perturbation spectrum. We model the transplanckian regime by introducing a 1-parameter family of smooth non-linear dispersion relations which modify the frequencies at very short distances. For this family of dispersions, we present the exact solutions and show that the CMBR spectrum is that of a (nearly) black body, and that the adiabatic vacuum is the only choice for the initial conditions. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta $k$ (for $k>M_P$). Modes with ultralow frequencies equal or less than the current Hubble rate are still frozen today. Therefore, their energy today provides a strong candidate for the dark energy of the Universe.

M. Bastero-Gil

As yet, there is no underlying fundamental theory for the transplanckian regime. There is a need to address the issue of how the observables in our present Universe are affected by processes that may have occurred at superplanckian energies (referred to as the transplanckian regime. Specifically, we focus on the impact the transplanckian regime has on the dark energy. We model the transplanckian regime by introducing a 1-parameter family of smooth non-linear dispersion relations which modify the frequencies at very short distances. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta $k$ (for $k>M_P$). We show that the range of modes with frequencies equal or less than the current Hubble rate $H_0$ which are still frozen today provides a strong candidate for the dark energy of the Universe.

L. Mersini

We discuss the potentially important role played by preheating in certain variants of the curvaton mechanism in which isocurvature perturbations of a D-flat (and F-flat) direction become converted to curvature perturbations during reheating. We analyse the transition from inflation to reheating in some detail, including the dynamics of the coupled curvaton and inflation fields during this transition. We discover that preheating could be an important source of adiabaticity where parametric resonance of the isocurvature components amplifies the super-horizon fluctuations by a significant amount. As an example of these effects we develop a particle physics motivated model which we recently introduced in which the D-flat direction is identified with the usual Higgs field. Our new results show that it is possible to achieve the correct curvature perturbations for initial values of the curvaton fields of order the weak scale. In this model we show that the prediction for the spectral index of the final curvature perturbation only depends on the mass of the curvaton during inflation, where consistency with current observational data requires the ratio of this mass to the Hubble constant to be < 0.3.

M. Bastero-Gil V. Di Clemente S. F. King

We propose a model of cosmology and particle physics in which all relevant scales arise in a natural way from an intermediate string scale. We are led to assign the string scale to the intermediate scale M_* \sim 10^{13} GeV by four independent pieces of physics: electroweak symmetry breaking; the \mu parameter; the axion scale; and the neutrino mass scale. The model involves hybrid inflation with the waterfall field N being responsible for generating the \mu term, the right-handed neutrino mass scale, and the Peccei-Quinn symmetry breaking scale. The large scale structure of the Universe is generated by the lightest right-handed sneutrino playing the role of a coupled curvaton. We show that the correct curvature perturbations may be successfully generated providing the lightest right-handed neutrino is weakly coupled in the see-saw mechanism, consistent with sequential dominance.

M. Bastero-Gil V. Di Clemente S. F. King

Minimal supersymmetric hybrid inflation based on a minimal Kahler potential predicts a spectral index n_s\gsim 0.98. On the other hand, WMAP three year data prefers a central value n_s \approx 0.95. We propose a class of supersymmetric hybrid inflation models based on the same minimal superpotential but with a non-minimal Kahler potential. Including radiative corrections using the one-loop effective potential, we show that the prediction for the spectral index is sensitive to the small non-minimal corrections, and can lead to a significantly red-tilted spectrum, in agreement with WMAP.

M. Bastero-Gil S. F. King Q. Shafi

Observational evidence suggests that our universe is presently dominated by a dark energy component and undergoing accelerated expansion. We recently introduced a model, motivated by string theory for short-distance physics, for explaining dark energy without appealing to any fine-tuning. The idea of the transplanckian dark energy (TDE) was based on the freeze-out mechanism of the ultralow frequency modes, $\omega(k)$ of very short distances, by the expansion of the background universe, $\omega(k) \leq H$. In this paper we address the issue of the stress-energy tensor for the nonlinear short-distance physics and explain the need to modify Einstein equations in this regime. From the modified Einstein equations we then derive the equation of state for the TDE model, which has the distinctive feature of being continually time-dependent. The explanation of the coincidence puzzle relies entirely on the intrinsic time-evolution of the TDE equation of state.

M. Bastero-Gil L. Mersini

The problem of dark energy arises due to its self-gravitating properties. Therefore explaining vacuum energy may become a question for the realm of quantum gravity, that can be addressed within string theory context. In this talk I concentrate on a recent, string-inspired model, that relies on nonlinear physics of short-distance perturbation modes, for explaining dark energy without any fine-tuning. Dark energy can be observationally probed by its equation of state, w. Different models predict different types of equations of state and string-inspired ones have a time dependent w(z) as their unique signature. Exploring the link between dark energy and string theory may provide indirect evidence for the latter, by means of precision cosmology data.

L. Mersini M. Bastero-Gil

We have studied preheating of field perturbations in a 3-dimensional lattice including the effect of scalar metric perturbations, in two generic models of inflation: chaotic inflation with a quartic potential, and standard hybrid inflation. We have prepared the initial state for the classical evolution of the system with vanishing vector and tensor metric perturbations, consistent with the constraint equations, the energy and momentum constraints. The non-linear evolution inevitably generates vector and tensor modes, and this reflects on how well the constraint equations are fulfilled during the evolution. The induced preheating of the scalar metric perturbations is not large enough to backreact onto the fields, but it could affect the evolution of vector and tensor modes. This is the case in hybrid inflation for some values of the coupling $g$ and the height of potential $V_0^{1/4}$. For example with $V_0^{1/4} \simeq 10^{15}$ GeV, preheating of scalar perturbations is such that their source term in the evolution equation of tensor and vector becomes comparable to that of the field anisotropic stress.

M. Bastero-Gil M. Tristram J. Macias-Perez D. Santos

We present the evolution of the full set of Einstein equations during preheating after inflation. We study a generic supersymmetric model of hybrid inflation, integrating fields and metric fluctuations in a 3-dimensional lattice. We take initial conditions consistent with Eintein's constraint equations. The induced preheating of the metric fluctuations is not large enough to backreact onto the fields, but preheating of the scalar modes does affect the evolution of vector and tensor modes. In particular, they do enhance the induced stochastic background of gravitational waves during preheating, giving an energy density in general an order of magnitude larger than that obtained by evolving the tensors fluctuations in an homogeneous background metric. This enhancement can improve the expectations for detection by planned gravitational waves observatories.

M. Bastero-Gil J. Macias-Perez D. Santos