D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. We discuss possible implications of this result for the question of singularity resolution in quantum cosmology and comment on the differences with other approaches.
We study the quantum fermionic billiard defined by the dynamics of a quantized supersymmetric squashed three-sphere (Bianchi IX cosmological model within D=4 simple supergravity). The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. We focus on the 15- and 20-dimensional subspaces (with fermion numbers N_F=2 and N_F=3) where there exist propagating solutions of the supersymmetry constraints that carry (in the small-wavelength limit) a chaotic spinorial dynamics generalizing the Belinskii-Khalatnikov-Lifshitz classical "oscillatory" dynamics. By…
A short overview of the billiard approach for cosmological-type models with n Einstein factor-spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider cosmological model with multicomponent "perfect-fluid" and cosmological-type model with composite branes. The second one describes cosmological and spherically-symmetric configurations in a theory with scalar fields and fields of forms. The conditions for appearance of asymptotical Kasner-like and oscillating behaviors in the limit τ\to +0 and τ\to + \infty (wh…
Belinski, Khalatnikov and Lifshitz (BKL) pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a space-like singularity. We show how the use of a "cosmological billiard" description allows one to refine and deepen the understanding of these statistical properties. Contrary to previous treatments, we do not quotient the dynamics by its discrete symmetry group (of order 6), thereby uncovering new phenomena, such as correlations between the successive billiard corners in which the oscillations take place. S…
We present a systematic study of the cosmological billiard structures of Einstein-p-form systems in which all spatial directions are compactified on a manifold of nontrivial topology. This is achieved for all maximally oxidised theories associated with split real forms, for all possible compactifications as defined by the de Rham cohomology of the internal manifold. In each case, we study the Coxeter group that controls the dynamics for energy scales below the Planck scale as well as the relevant billiard region. We compare and contrast them with the Weyl group and fundamental domain that emer…
Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possib…
The mini-superspace quantization of D=11 supergravity is equivalent to the quantization of a E10/K(E10) coset space sigma model, when the latter is restricted to the E10 Cartan subalgebra. As a consequence, the wavefunctions solving the relevant mini-superspace Wheeler-DeWitt equation involve automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O). Using Dirichlet boundary conditions on the billiard domain a general inequality for the Laplace eigenvalues of these automorphic forms is derived, entailing a wave function of the universe that is generically complex and always tend…
Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scalar fields and multiple exponential potential is considered. The dynamics of the model near the singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky space H^{N-1}, N = n+l. It is shown that for n > 1 the oscillating behaviour near the singularity is absent and solutions have an asymptotical Kasner-like behavior. For the case of one scale factor (n =1) billiards with finite volumes (e.g. coinciding with that of the Bianchi-IX model) are described and oscillating behaviour of scala…
The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the (n-1)-dimensional Lobachevsky space H^{n-1}. The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of (n-2)-dimensional sphere S^{n-2} by point-like sources. Some examples are considered.
This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike singularities we derive in a step-by-step manner the cosmological billiard conjecture: we show that the generic asymptotic dynamics of solutions is represented by (randomized) sequences of heteroclinic orbits on the `billiard attractor'. Our analysis rests on two pillars: (i) a dynamical systems formulation based on the conformal Hubble-normalized orthonormal frame …
We construct a large class of vacuum solutions of the Einstein equations without any symmetries and with controlled asymptotics near a timelike singularity. The solutions are obtained by a Fuchs analysis of the equations which evolve the metric in a spacelike direction. We further observe that the changes of signs of some of the terms (walls) in the associated Hamiltonian invalidate the "cosmological billards" heuristic arguments for existence of singularities of mixmaster type in the current context.
It is shown in detail that the dynamics of the Einstein-dilaton-p-form system in the vicinity of a spacelike singularity can be asymptotically described, at a generic spatial point, as a billiard motion in a region of Lobachevskii space (realized as an hyperboloid in the space of logarithmic scale factors). This is done within the Hamiltonian formalism, and for an arbitrary number of spacetime dimensions $D \geq 4$. A key role in the derivation is played by the Iwasawa decomposition of the spatial metric, and by the fact that the off-diagonal degrees of freedom, as well as the p-form degrees o…
The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically simplified by the use of the Arnowitt-Deser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solution is describable, at each (generic) spatial point, as a billiard motion in an auxiliary Lorentzian space. For certain Einstein-matter systems, notably for pure Einstein gravity in any spacetime dimensi…
The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically simplified by the use of the Arnowitt-Deser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solution is describable, at each (generic) spatial point, as a billiard motion in an auxiliary Lorentzian space. For certain Einstein-matter systems, notably for pure Einstein gravity in any spacetime dimensi…
Spatially homogeneous cosmological models reduce to Hamiltonian systems in a low dimensional Minkowskian space moving on the total energy shell $H=0$. Close to the initial singularity some models (those of Bianchi type VIII and IX) can be reduced further, in a certain approximation, to a non-compact triangular billiard on a 2-dimensional space of constant negative curvature with a separately conserved positive kinetic energy. This type of billiard has long been known as a prototype chaotic dynamical system. These facts are reviewed here together with some recent results on the energy level sta…
Bianchi type I cosmological model in (n+1)-dimensional gravity with several forms is considered. When the electric non-composite brane ansatz is adopted, the Wheeler-DeWitt (WDW) equation for the model, written in a conformally covariant form, is analyzed. Under certain restrictions, asymptotic solutions to the WDW equation near the singularity are found, which reduce the problem to the so-called quantum billiard on the (n-1)-dimensional Lobachevsky space H^{n-1}. Two examples of quantum billiards are considered: a 2-dimensional quantum billiard for a 4D model with three 2-forms and a 9D quant…
The Selberg trace formula is specified for cosmological billiards in $4=3+1$ spacetime dimensions. The spectral formula is rewritten as an exact sum over the initial conditions for the Einstein field equations for which periodic orbits are implied. For this, a suitable density of measure invariant under the billiard maps has been defined, within the statistics implied by the BKL paradigm. The trace formula has also been specified for the stochastic limit of the dynamics, where the sum over initial conditions has been demonstrated to be equivalent to a sum over suitable symmetry operations on t…
Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky space, N = n+l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of (N-2)-dimensional sphere by point-like …
The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested.
Gravitational D-dimensional model with l scalar fields and several forms is considered. When cosmological type diagonal metric is chosen, an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed the conformally covariant Wheeler-DeWitt (WDW) equation for the model is studied. Under certain restrictions asymptotic solutions to WDW equation are found in the limit of the formation of the billiard walls which reduce the problem to the so-called quantum billiard on the (D+ l -2)-dimensional Lobachevsky space. Two examples of quantum billiards are consi…
It is shown that the never ending oscillatory behaviour of the generic solution, near a cosmological singularity, of the massless bosonic sector of superstring theory can be described as a billiard motion within a simplex in 9-dimensional hyperbolic space. The Coxeter group of reflections of this billiard is discrete and is the Weyl group of the hyperbolic Kac-Moody algebra E$_{10}$ (for type II) or BE$_{10}$ (for type I or heterotic), which are both arithmetic. These results lead to a proof of the chaotic (``Anosov'') nature of the classical cosmological oscillations, and suggest a ``chaotic …
An alternative way of introducing the supersymmetric cosmological term in a supergravity theory is presented. We show that the $AdS$-Lorentz superalgebra allows to construct a geometrical formulation of supergravity containing a generalized supersymmetric cosmological constant. The $N=1$, $D=4$ supergravity action is built only from the curvatures of the $AdS$-Lorentz superalgebra and corresponds to a MacDowell-Mansouri like action. The extension to a generalized $AdS$-Lorentz superalgebra is also analyzed.
The existence of a singularity by definition implies a preferred scale--the affine parameter distance from/to the singularity of a causal geodesic that is used to define it. However, this variable scale is also captured by the expansion along the geodesic, and this can be used to obtain a regularized state space picture by means of a conformal transformation that factors out the expansion. This leads to the conformal `Hubble-normalized' orthonormal frame approach which allows one to translate methods and results concerning spatially homogeneous models into the generic inhomogeneous context, wh…
The multidimensional cosmological model describing the evolution of $n$ Einstein spaces in the presence of multicomponent perfect fluid is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the $(n-1)$-dimensional Lobachevsky space $H^{n-1}$. The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of $(n-2)$-dimensional sphere $S^{n-2}$ by point-like sources. Some generalization …
Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the ${\cal N}=(1,1)$ Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the ${\cal N}=1$ model but we find new solutions with a time-like Killing vector that are absent in the ${\cal N}=1$ case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an $…
Using technique of supersymmetric quantum mechanics we present new cosmological quantum solution, in the regime for FRW cosmological model using a barotropic perfect fluid as matter field.
In this work we consider a flat cosmological model with a set of fluids in the framework of supersymmetric cosmology. The obtained supersymmetric algebra allowed us to take quantum solutions. It is shown that only in the case of a cosmological constant we have a condition between the density of dark energy $ρ_Λ$ and density energy of matter $ρ_M$, $ρ_Λ> 2ρ_M$.
In recent work Kachru, Kumar and Silverstein introduced a special class of non-supersymmetric type II string theories in which the cosmological constant vanishes at the first two orders of perturbation theory. Heuristic arguments suggest the cosmological constant may vanish in these theories to all orders in perturbation theory leading to a flat potential for the dilaton. A slight variant of their model can be described in terms of a dual heterotic theory. The dual theory has a non-zero cosmological constant which is non-perturbative in the coupling of the original type II theory. The dual the…
Cosmological billiards arise as a map of the solution to the Einstein equations, when the most general symmetry of the metric tensor is implemented, under the BKL (named after Belinskii, Khalatnikov and Lifshitz) paradigm, for which points are spatially decoupled in the asymptotical limit close to the cosmological singularity. Cosmological billiards in $4=3+1$ dimensions for the case of pure gravity are analyzed for those features, for which the content of Weyl reflections in the BKL maps requires definition of a 3-dimensional restricted phase space. The role of Poincaré sections in these proc…
This work summarises recent progress obtained by the mini-superpspace quantization of $\mathcal N=1$, $d=4$ supergravity, formulated in the framework of the Bianchi IX cosmological model. The emphasis is put on three main results : the completeness of the solution space obtained, the elements suggesting a hidden Kac-Moody structure of the theory and those leading to conjecture an avoidance of the cosmological singularity by some branches of the wave function of the Universe.
We investigate the question whether there are cosmological models in 2+1 space-time dimensions which exhibit dynamics similar to BKL oscillations, as the cosmological singularity is approached. Based on intuition, we conceive a toy model which displays such oscillatory dynamics. We show that in the phase space of this model, the cosmological singularity is represented by a separatrix curve and discuss the model's dynamics within the cosmological billiards picture. Finally, we offer a physical interpretation for a family of similar cosmological models in terms of the topological degrees of free…
A string motivated, N=1 global supersymmetric, general Lagrangian is obtained that represents an inflaton interacting with the modes of a string. Focus is placed on the Lagrangian's relevance to warm inflation, which is a cosmology based on dissipative dynamics. Several interaction schemes are identified from the general Lagrangian that may have interesting consequences for dissipative dynamics. Distributed-mass-models, which have been shown to solve the horizon problem within a warm inflation regime, are identified in the general Lagrangian.
Spatially homogeneous models in quantum supergravity with a nonvanishing cosmological constant are studied. A class of exact nontrivial solutions of the supersymmetry and Lorentz constraints is obtained in terms of the Chern-Simons action on the spatially homogeneous 3-manifold, both in Ashketar variables where the solution is explicit up to reality conditions, and, more concretely, in the tetrad-representation, where the solutions are given as integral representations differing only by the contours of integration. In the limit of a vanishing cosmological constant earlier exact solutions for B…
In this paper, we present novel non-relativistic superalgebras which correspond to supersymmetric extensions of the enlarged extended Bargmann algebra. The three-dimensional non-relativistic Chern-Simons supergravity actions invariant under the aforementioned superalgebras are constructed. The new non-relativistic superalgebras allow to accommodate a cosmological constant in a non-relativistic supergravity theory. Interestingly, we show that one of the non-relativistic supergravity theories presented here leads to the recently introduced Maxwellian exotic Bargmann supergravity when the flat li…
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in arXiv:0804.0009, hep-th/0406238 . The second class is constructed…
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D=4 simple supergravity for an SO(3)-homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact sub-algebra of the rank-3 h…
We discuss cosmological implications of nonlinear supersymmetric(NLSUSY) general relativity(GR) of the form of Einstein-Hilbert(EH) action for empty spacetime, where NLSUSY GR is obtained by the geomtrical arguments on new spacetime just inspired by NLSUSY. The new action of NLSUSY GR is unstable and breaks down spontaneously to EH action with Nambu-Goldstone(NG) fermion matter. We show that NLSUSY GR elucidates the physical meanings of the cosmologically important quantities, e.g., the spontaneous SUSY breaking scale, the cosmological constant, the dark energy and the neutrino mass and descri…
A Chern--Simons system in $2+1$ dimensions invariant under local Lorentz rotations, $SU(2)$ gauge transformations, and local $\mathcal{N}=2$ supersymmetry transformations is proposed. The field content is that of $(2+1)$-gravity plus an $SU(2)$ gauge field, a spin-1/2 fermion charged with respect to $SU(2)$ and a trivial free abelian gauge field. A peculiarity of the model is the absence of gravitini, although it includes gravity and supersymmetry. Likewise, no gauginos are present. All the parameters involved in the system are either protected by gauge invariance or emerge as integration cons…
We describe in superspace a classical theory of two dimensional $(1,1)$ dilaton supergravity with a cosmological constant, both with and without coupling to a massive superparticle. We give general exact non-trivial superspace solutions for the compensator superfield that describes the supergravity in both cases. We then use these compensator solutions to construct models of two-dimensional supersymmetric cosmological black holes.
We consider 2+1 dimensional off-shell N = 1 pure supergravity that is constructed from graviton, gravitino and auxiliary field. We show that the $R^2$ supersymmetric invariant and $R^2_{μν}$ supersymmetric invariant are expressed as local supersymmetric exact terms up to mass terms for gravitino. In both cases, the mass parameter is proportional to the off-shell supersymmetric cosmological constant.
We analyze the quantum supersymmetric cosmological FRW model with a scalar field, with a conditional probability density and the scalar field identified as time. The Hilbert space has a spinorial structure and there is only one consistent solution, with a conserved probability density. The dynamics of the scale factor is obtained from its mean value. The uncertainty relations are fulfilled and the corresponding fluctuations are consistent with a semiclassical Universe. We give two examples which turn out to have negative potential.
Recent data point in the direction of a cosmological constant dominated universe. We investigate the role of supersymmetric QCD with N_f < N_c as a possible candidate for dynamical cosmological constant (``quintessence''). We take in full consideration the multi-scalar nature of the model, allowing for different initial conditions for the N_f independent scalar VEVs and studying the coupled system of N_f equations of motion. The issues related to the coupling of the scalars with other cosmological fields are also addressed.
We describe in superspace a classical theory of two dimensional $(1,1)$ cosmological dilaton supergravity coupled to a massive superparticle. We give an exact non-trivial superspace solution for the compensator superfield that describes the supergravity, and then use this solution to construct a model of a two-dimensional supersymmetric black hole.
In this work we present cosmological quantum solutions for all Bianchi Class A cosmological models obtained by means of supersymmetric quantum mechanics . We are able to write one general expression for all bosonic components occuring in the Grassmann expansion of the wave function of the Universe for this class of models. These solutions are obtained by means of a more general ansatz for the so-called master equations.
The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gravity models. The cases of cubic (bosonic) and quartic (supersymmetric) tachyon potential in general relativity are automatically included. We comment the validity of the slow-roll approximation, the sta…
The problem of construction of a general ihomogeneous solution of $D$-dimensional Einstein equations in the vicinity of a cosmological singularity is considered. It is shown that near the singularity a local behavior of metric functions is described by a billiard on a space of a constant negative curvature. The billiard is shown to have a finite volume and consequently to be a mixing one. Dynamics of inhomogeneities of metric is studied and it is shown that its statistical properties admit a complete description. An invariant measure describing statistics of inhomogeneities is obtained and a r…
We derive a special scalar field potential using the anisotropic Bianchi type I cosmological model from canonical quantum cosmology under determined conditions in the evolution to anisotropic variables $β_\pm$. In the process, we obtain a family of potentials that has been introduced by hand in the literature to explain cosmological data. Considering supersymmetric quantum cosmology, this family is scanned, fixing the exponential potential as more viable in the inflation scenario $\rm V (ϕ) = V_0 \,e^{-\sqrt{3}ϕ}$.
We explain that supersymmetric attractors in general have several critical points due to the algebraic nature of the stabilization equations. We show that the critical values of the cosmological constant of the adS_5 vacua are given by the topological (moduli independent) formulae analogous to the entropy of the d=5 supersymmetric black holes. We present conditions under which more than one critical point is available (for black hole entropy as well as to the cosmological constant) so that the system tends to its own locally stable attractor point. We have found several families of Z_2-symmetr…
The $N=1$ supersymmetric Born-Infeld theory coupled to $N=1$ supergravity in four spacetime dimensions is studied in the presence of a cosmological term with spontaneous supersymmetry breaking. The consistency is achieved by compensating a negative contribution to the cosmological term from the Born-Infeld theory by a positive contribution originating from the gravitino condensate. This leads to an identification of the Born-Infeld scale with the supersymmetry breaking scale. The dynamical formation of the gravitino condensate in supergravity is reconsidered and the induced one-loop effective …
We examine in a cosmological context the conditions for unbroken supersymmetry in N=1 supergravity in D=10 dimensions. We show that the cosmological solutions of the equations of motion obtained considering only the bosonic sector correspond to vacuum states with spontaneous supersymmetry breaking. With a non vanishing gravitino-dilatino condensate we find a solution of the equations of motion that satisfies necessary conditions for unbroken supersymmetry and that smoothly interpolates between Minkowski space and DeSitter space with a linearly growing dilaton, thus providing a possible example…
This article critically reviews the proposal for addressing the cosmological constant problem within the framework of supersymmetric large extra dimensions (SLED), as recently proposed in hep-th/0304256. After a brief restatement of the cosmological constant problem, a short summary of the proposed mechanism is given. The emphasis is on the perspective of the low-energy effective theory in order to see how it addresses the problem of why low-energy particles like the electron do not contribute too large a vacuum energy. This is followed by a discussion of the main objections, which are grouped…
In N=1 supergravity the scalar potential of the hidden sector may have degenerate supersymmetric (SUSY) and non-supersymmetric Minkowski vacua. In this case local SUSY in the second supersymmetric Minkowski phase can be broken dynamically. Assuming that such a second phase and the phase associated with the physical vacuum are exactly degenerate, we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced if in the second vacuum local SUSY breaking is induced by gaugino condensation at a scale which is just slightly lower tha…
We compute the 4--dimensional cosmological constant in string compactifications in which the Standard Model fields live on a non-supersymmetric brane inside a supersymmetric bulk. The cosmological constant receives contributions only from the vacuum energy of the bulk supergravity fields, but not from the vacuum energy of the brane fields. The latter is absorbed in a warp factor. Supersymmetry breaking on the brane at the TeV scale implies supersymmetry breaking in the bulk at the micrometer scale. This produces a tiny cosmological constant that agrees with experiment within a few orders of ma…
In this report we advance the current repertoire of quantum cosmological models to incorporate inhomogenous field modes in a supersymmetric manner. In particular, we introduce perturbations about a supersymmetric FRW model. A quantum state of our model has properties typical of the no-boundary (Hartle--Hawking) proposal. This solution may then lead to a scale--free spectrum of density perturbations.
In this note, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux and Nicolai in the study of the cosmological singularity. In particular we use the theory of Maass automorphic forms and recent mathematical results about arithmetical dynamical systems. The predictions of the billiard model give precise automorphic properties for the wave function (Maass-Hecke eigenform), the asymptotic number of quantum states (Selberg asymptotics for PSL(2,Z)), the distribution for the level spacing statistics (the Poissonian one) and the …
We provide an explicit example of a higher-dimensional model describing a non-supersymmetric spectrum of 4D particles of mass M, whose 4D geometry -- {\em including loop effects} -- has a curvature that is of order R ~ m_KK^4/M_p^2, where m_KK is the extra-dimensional Kaluza-Klein scale and M_p is the 4D Planck constant. m_KK is stabilized and can in particular satisfy m_KK << M. The system consists of a (5+1)-dimensional model with a flux-stabilized supersymmetric bulk coupled to non-supersymmetric matter localized on a (3+1)-dimensional positive-tension brane. We use recent techniques for ca…
In view of the imminent start of the LHC experimental programme, we use the available indirect experimental and cosmological information to estimate the likely range of parameters of the constrained minimal supersymmetric extension of the Standard Model (CMSSM), using a Markov-chain Monte Carlo (MCMC) technique to sample the parameter space. The 95% confidence-level area in the (m_0, m_1/2) plane of the CMSSM lies largely within the region that could be explored with 1/fb of integrated luminosity at 14 TeV, and much of the 68% confidence-level area lies within the region that could be explored…
We apply the strictly isospectral technique of standard supersymmetric quantum mechanics to the Q=0 factor ordered Wheeler-DeWitt equation for the Friedmann-Robertson-Walker (FRW) minisuperspace model. The resulting strictly isospectral one-parameter families of both FRW cosmological potentials and "wavefunctions of the universe" are exhibited with relevant plots
