Primordial Inflation and Present-Day Cosmological Constant from Extra Dimensions

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as rho_LAMBDA ~ M^8/M_P^4, where M_P is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D = 2 extra dimensions with radius b(t) curled up at the ADD length scale b_0 = M_P/M^2 ~ 0.1 mm. Vacuum fluctuations in the compactified space perturb b_0 very slightly, generating a small present-day cosmological constant. The radius of the compactified dimensions is predicted to be b_0 = k^{1/4} 0.09 mm (or equivalently M = 2.4 TeV/k^{1/8}), where the Casimir energy density is k/b^4. Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M ~ 10^{-17} cm, rolls down its potential to b_0.Comment: 10 pages; Version 2: added discussion of brane tension and zero of the stabilization potential; expanded abstrac

Holography in an Early Universe with Asymmetric Inflation

We discuss the validity of the holographic principle in a $(4+n)$ dimensional universe in an asymmetric inflationary phase.Comment: The correct discussion of the holography problem in the Einstein frame has replaced a previous on

Dynamically Warped Theory Space and Collective Supersymmetry Breaking

We study deconstructed gauge theories in which a warp factor emerges dynamically and naturally. We present nonsupersymmetric models in which the potential for the link fields has translational invariance, broken only by boundary effects that trigger an exponential profile of vacuum expectation values. The spectrum of physical states deviates exponentially from that of the continuum for large masses; we discuss the effects of such exponential towers on gauge coupling unification. We also present a supersymmetric example in which a warp factor is driven by Fayet-Iliopoulos terms. The model is peculiar in that it possesses a global supersymmetry that remains unbroken despite nonvanishing D-terms. Inclusion of gravity and/or additional messenger fields leads to the collective breaking of supersymmetry and to unusual phenomenology.Comment: 28 pages LaTeX, JHEP format, 7 eps figures (v2: reference added

Single production of new gauge bosons from the littlest Higgs model at the TeVTeV energy e−γe^{-}\gamma colliders

In the context of the littlest Higgs(LH) model, we study single production of the new gauge bosons $B_{H}$, $Z_{H}$ and $W_{H}^{\pm}$ via $e^{-}\gamma$ collisions and discuss the possibility of detecting these new particles in the $TeV$ energy $e^{+}e^{-}$ collider($LC$). We find that these new particles can not be detected via the $e^{-}\nu\nu$ signal in all of the parameter space preferred by the electroweak precision data. However, the heavy gauge bosons $B_{H}$ and $Z_{H}$ may be observed via the decay channel $B_{H}(Z_{H})\to l^{+}l^{-}$ in wide range of the parameter space.Comment: references added, typos corrected. To be published in Phys. Rev.

The Momentum Amplituhedron

In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in N = 4 super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron M n,k is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.Peer reviewedFinal Published versio

Towards the Amplituhedron Volume

21 pages; v2: version published in JHEPIt has been recently conjectured that scattering amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. In this paper we show some interesting connections between the tree-level amplituhedron and a special class of differential equations. In particular we demonstrate how the amplituhedron volume for NMHV amplitudes is determined by these differential equations. The new formulation allows for a straightforward geometric description, without any reference to triangulations. Finally we discuss possible implications for volumes related to generic N^kMHV amplitudes.Peer reviewe

Flavor at the TeV Scale with Extra Dimensions

Theories where the Standard Model fields reside on a 3-brane, with a low fundamental cut-off and extra dimensions, provide alternative solutions to the gauge hierarchy problem. However, generating flavor at the TeV scale while avoiding flavor-changing difficulties appears prohibitively difficult at first sight. We argue to the contrary that this picture allows us to lower flavor physics close to the TeV scale. Small Yukawa couplings are generated by ``shining'' badly broken flavor symmetries from distant branes, and flavor and CP-violating processes are adequately suppressed by these symmetries. We further show how the extra dimensions avoid four dimensional disasters associated with light fields charged under flavor. We construct elegant and realistic theories of flavor based on the maximal U(3)^5 flavor symmetry which naturally generate the simultaneous hierarchy of masses and mixing angles. Finally, we introduce a new framework for predictive theories of flavor, where our 3-brane is embedded within highly symmetrical configurations of higher-dimensional branes.Comment: 40 pages, 8 figure

Gravity in Dynamically Generated Dimensions

A theory of gravity in $d+1$ dimensions is dynamically generated from a theory in $d$ dimensions. As an application we show how $N$ dynamically coupled gravity theories can reduce the effective Planck mass.Comment: 7 pages, LaTeX (Revtex

Solving the Hierarchy Problem with Exponentially Large Dimensions

In theories with (sets of) two large extra dimensions and supersymmetry in the bulk, the presence of non-supersymmetric brane defects naturally induces a logarithmic potential for the volume of the transverse dimensions. Since the logarithm of the volume rather than the volume itself is the natural variable, parameters of O(10) in the potential can generate an exponentially large size for the extra dimensions. This provides a true solution to the hierarchy problem, on the same footing as technicolor or dynamical supersymmetry breaking. The area moduli have a Compton wavelength of about a millimeter and mediate Yukawa interactions with gravitational strength. We present a simple explicit example of this idea which generates two exponentially large dimensions. In this model, the area modulus mass is in the millimeter range even for six dimensional Planck scales as high as 100 TeV.Comment: 13 pages, 7 figures, corrected typo

The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and particle content. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlators are controlled by an approximate conformal symmetry on the boundary of the spacetime. After classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities completely fixes this correlator. A spin-raising operator relates it to the correlators associated with the exchange of particles with spin, while weight-shifting operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. We reproduce many classic results in the literature and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. The inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta.Comment: 110 pages, 13 figures, 1 table; V3: minor corrections and references adde