Conference

If inflation is to be considered in an unbiased way, as possibly originating from one of a wide range of underlying theories,then observations need not be simply applied to reconstructing the inflaton potential, V(phi), or a specific kinetic term, as in DBI inflation, but rather to reconstruct the inflationary action in its entirety. I will discuss the constraints that can be placed on a generalsingle field action from measurements of the primordial scalar and tensor fluctuation power spectra and non-Gaussianities. I will also briefly present the flow equation formalism for reconstructing a general inflationary Lagrangian, in a general gauge, that reduces to canonical and DBI inflation in a specific gauge.

Many string theorists and cosmologists have recently turned their attention to building and testing string theory models of inflation. One of the main goals is to find novel features that could distinguish stringy models from their field theoretic counterparts. This is difficult because, in most examples, string theory is used to derived an effective theory operating at energies well below the string scale. However, since string theory provides a complete description of dynamics also at higher energies, it may be interesting to construct inflationary models which take advantage of this distinctive feature. I will discuss recent progress in this direction using p-adic string theory - a toy model of the bosonic string for which the full series of higher dimensional operators is known explicitly - as a playground for studying string cosmology to all order in $alpha\'$. The p-adic string is a nonlocal theory containing derivatives of all orders and this structure is also ubiquitous in string field theory. After discussing the difficulties (such as ghosts and classical instabilities) that arise in working with higher derivative theories I will show how to construct generic inflationary models with infinitely many derivatives. Novel features include the possibility of realizing slow roll inflation with a steep potential and large nongaussian signatures in the CMB.

We study the effects of boundary terms in models with a flat \'Universal\'\' Extra Dimension in which all Standard Model fields propagate in the bulk. We show how non-minimal boundary terms change the mass spectrum and interactions of Kaluza-Klein modes, allow for new dark matter candidates from UED, and how they alter collider phenomenology.

I will present extensions of hybrid inflationary models in the context of supersymmetric D-term in- flation. I will show that there exists a large domain of parameters in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular I will explicitly present the expected bi- and trispectrum for such models and compared the results to the current and expected observational constraints. It is to be noticed that it is necessary to use both the bi- and tri-spectra of CMB anisotropies to efficiently reduce the parameter space of such models.

\'BPS preons were conjectured (PRL 86, 4451 (2001), hep-th/0101113) as the basic constituents of M-theory; they are states preserving 31/32 supersymmetries. We discuss the absence of preonic solutions in D=10,11 supergravities and its possible implications. The AdS generalization of the BPS preons, the AdS preons defined over an AdS vacuum, will also be discussed. This leads to the {it AdS-M-algebra}, a deformation of the M-algebra which is identifed as $osp(1|32)$.\'

In supersymmetric (SUSY) models with the gravitino being the lightest SUSY particle (LSP), the SUSY breaking scale (i.e., the gravitino mass) could be determined by measuring the lifetime of the next-to-lightest SUSY particle (NLSP). However, for an ultralight gravitino of mass of O(1) eV, which is favored cosmologically, the determination of the SUSY breaking scale, or the gravitino mass, is difficult because the NLSP decay length is too short to be measured directly. We propose a new determination of the gravitino mass by measuring a branching fraction of two decay modes of sleptons, and demonstrate that the gravitino mass may indeed be determined at the LHC with an accuracy of a few 10% for an integrated luminosity 10-100 fb^{-1}. I will also mention dark matter candidates for such a light gravitino LSP.

We first discuss the possibility of getting a non-supersymmetric dS minimum with the inclusion of perturbative and non-perturbative alpha\' corrections and instanton contributions in the large volume limit of certain Swiss Cheese Calabi Yau orientifold type IIB compactifications. We then discuss axionic slow roll inflation with the NS-NS axions providing a flat direction for slow-roll inflation to proceed from a saddle point to the nearest dS minimum.

In the last years, the NA48/2 experiment at the CERN SPS has recorded an unprecedented sample of charged kaon decays. From this, we report very precise measurements of fundamental parameters of Chiral Perturbation Theory (ChPT) and the study of low energy pi-pi scattering. Several rare and very rare decays have been studied. From more than 10^6 K+- -> pi+ pi0 gamma decays, a first measurement of the interference between Bremsstrahlung and Direct Emission amplitudes and a stringent limit on direct CP violation in this channel is presented. For K+- -> pi+ gamma gamma, about 1000 events have been selected, more than 30 times the existing statistics. Also, the first observation of K+- -> pi+ gamma e+ e- is reported with 120 events. For both decays, the branching fraction and the free parameter of O(p4) ChPT has been measured with high accuracy. Finally, we report on a new precise measurement of the branching fraction and form factors of K+- -> pi+- e+ e-, which is highly suppressed by the GIM mechanism. The measurement of the e+ e- spectrum is an important input for ChPT and probes the weak static interaction. The analyses of K+- -> pi+- pi0 pi0 (K3pi) and K+- -> pi+ pi- e+- nu (Ke4) decays give complementary approaches to the study of low energy pi-pi scattering. From data samples of ~90 Millions 3pi and ~1 Million Ke4 decays, precise values of a0 and a2, the Isospin 0 and 2 S-wave PI-PI scattering lengths, can be extracted with an unprecedented experimental precision, allowing accurate tests of Chiral Perturbation Theory predictions. The form factors of the Ke4 decays and their energy dependence are also measured with an improved precision, while the Dalitz plot parameters of the K3PI decays are determined including a new quadratic term.

We study observables in a conformal field theory which are very closely related to the ones used to describe hadronic events at colliders. We focus on the correlation functions of the energies deposited on calorimeters placed at a large distance from the collision. We consider initial states produced by an operator insertion and we study some general properties of the energy correlation functions for conformal field theories. We argue that the small angle singularities of energy correlation functions are controlled by the twist of non-local light-ray operators with a definite spin. We relate the charge two point function to a particular moment of the parton distribution functions appearing in deep inelastic scattering. The one point energy correlation functions are characterized by a few numbers. For ${cal N}=1$ superconformal theories the one point function for states created by the R-current or the stress tensor are determined by the two parameters $a$ and $c$ charac terizing the conformal anomaly. Demanding that the measured energies are positive we get bounds on $a/c$. We also give a prescription for computing the energy and charge correlation functions in theories that have a gravity dual. The prescription amounts to probing the falling string state as it crosses the $AdS$ horizon with gravitational shock waves. In the leading, two derivative, gravity approximation the energy is uniformly distributed on the sphere at infinity, with no fluctuations. We compute the stringy corrections and we show that they lead to small, non-gaussian, fluctuations in the energy distribution. Corrections to the one point functions or antenna patterns are related to higher derivative corrections in the bulk.