Resurrecting no-scale supergravity phenomenology

In the context of phenomenological models in which the soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, M _in, above the GUT scale, M _GUT, it is possible that all the scalar mass parameters m ₀, the trilinear couplings A ₀ and the bilinear Higgs coupling B ₀ vanish simultaneously, as in no-scale supergravity. Using these no-scale inputs in a renormalisation-group analysis of the minimal supersymmetric SU(5) GUT model, we pay careful attention to the matching of parameters at the GUT scale. We delineate the region of M _in, m _1/2 and tan?β where the resurrection of no-scale supergravity is possible, taking due account of the relevant phenomenological constraints such as electroweak symmetry breaking, m _h ,b→s γ, the neutralino cold dark matter density Ω _χ h ² and g _μ ?2. No-scale supergravity survives in an L-shaped strip of parameter space, with one side having m _1/2?200 GeV, the second (orthogonal) side having M _in?5×10¹⁶ GeV. Depending on the relative signs and magnitudes of the GUT superpotential couplings, these may be connected to form a triangle whose third side is a hypotenuse at larger M _in, m _1/2 and tan?β, whose presence and location depend on the GUT superpotential parameters. We compare the prospects for detecting sparticles at the LHC in no-scale supergravity with those in the CMSSM and the NUHM.     

Non-singular anisotropic cosmologies of no-scale supergravity

The field equations of “no-scale” supergravity are shown to admit exact non-singular anisotropic cosmological solutions which are of Bianchi type I and type V. The isotropic FRW solutions are included as special cases.     

Vanishing scalar masses in no-scale supergravity

Radiative corrections to the effective scalar potential are studied in no-scale supergravity models with local supersymmetry spontaneously broken by a gravitino mass. A simple proof is given that gauge non-singlet scalar fields acquire no supersymmetry breaking masses at the one-loop level, and a general argument is given extending this result to all orders of perturbation theory in the effective low-energy theory, proving also that no trilinear soft supersymmetry breaking terms in the effective potential are generated. These results are applicable to the four-dimensional no-scale supergravity theory obtained from the superstring after compactification, and support suggestions that the dominant source of global supersymmetry breaking in this theory may be the gaugino mass.     

Invisible axion in the hidden sector of no-scale supergravity

We propose a new axion model which incorporates the U(1)_PQ symmetry into a hidden sector, as well as an observable sector, of no-scale supergravity models. The axion is a spin-zero field in the hidden sector. The U(1)_PQ symmetry is naturally embedded in the family symmetry of the no-scale models. Invisible axions live in the gravity hidden sector without conflict with the cosmological and astrophysical constraints.     

The neutralinos of theSU(N,1) minimal supergravity model and standard cosmology

We discuss the effect of the lightest supersymmetric particle (LSP), a Higgsino, and of the gravitino of theSU(N,1) minimal SUGRA model in the standard big bang theory. The freeze out of the LSP depends on the gravitino mass and on the top mass and leads to restrictive lower bounds for these parameters in the model. The decay of a gravitino with mass in the few TeV range leads to a delay in the cooling of the universe before nucleosynthesis. This constitutes the main bound on the gravitino mass of the model. The results are compared with the more standard “simultaneous decay approximation”.     

The reconciliation of physics with cosmology

Astronomical observations of redshifts and the cosmic background radiation show that there is a local frame of reference relative to which the solar system has a well-defined velocity. Also, in cosmology the cosmological principle implies the existence of cosmic time and unique local reference frames at all spacetime points. On the other hand, in a fundamental postulate, the theory of special relativity excludes the possibility of the velocity of the Earth from entering into theories of local physics.The theory put forward in this paper resolves this conflict between local physics and cosmology. The theory retains the essential ingredient of the mathematical structure of special relativity, namely covariance under the Lorentz symmetry group, but changes radically the interpretation of the physical significance of the Lorentz transformation. The theory is based on the postulate that in free space the fundamental interactions in physics are propagated with constant velocity with respect to the local rest frame. In Minkowski spacetime the local rest frame of reference defines a unique time axis and consequently a unique three-dimensional spatial hyperplane. One particularly important result of this is that the theory includes the classical notion of simultaneity. From the fundamental postulate it follows that the equations of local physics, when expressed in terms of the rest frame coordinate system, must be covariant under the Lorentz symmetry group. By the identification of the local rest frame with the (unique) cosmological local reference frame the two theories become mutually consistent.The effects of the motion of the Earth on laboratory experiments are discussed. It is pointed out that existing experimental data do not discriminate between the present theory and that of special relativity: a proposal for an experimental test is made.Address for the academic year 1990–1991: 415 Graduate Studies Research Center, University of Georgia, Athens, Georgia 30602.     

The component gauges in supergravity

We present N = 1 supergravity in superspace gauges where the relation to component supergravity is immediate. Among the new results are the inverse vielbein to all orders in φ, some important components of the connection, a Lorentz transformation between our two “component gauges”, the component transformations for a spinor multiplet and some results concerning the axial current for various matter systems coupled to supergravity.     

Friedmann cosmology with torsion

For the cosmological field equations of the Poincaré gauge theory a universal appearance of the Friedmann equations of general relativity is shown. Some exact solutions with torsion are presented.     

The cosmology of decaying gravitinos

We consider the cosmological constraints on unstable particles with masses O(m_W). Constraints from the energy density during primordial nucleosynthesis, from subsequent entropy generation, and from perturbations of the microwave background are not as restrictive as bounds from the dissociation of light elements. Most restrictive is the need to avoid over-production of D and ³He through the photo-dissociation of ⁴He. When applied to gravitinos, this bound imposes an upper limit of O(10⁸) GeV on the reheating temperature after inflation, which could create problems for baryosynthesis in supersymmetric theories. These problems can be avoided if the photino is heavier than the gravitino.     

The integrability of N=16 supergravity

For the maximally extended N=16 supergravity theory in two dimensions, we explicitly construct a linear system whose integrability conditions are equivalent to the full nonlinear field equations of this theory. All the (on-shell) information contained in it can thus be encoded into a single E₈ matrix and its dependence on a spectral parameter; the invariance of the equations of motion under E₉ is manifest. Possible consequences and further developments are briefly discussed.     

The failure of minimal coupling in supergravity

A systematic method of deriving a superfield covariant derivative is heuristically presented. The example chosen is two-dimensional, but the method generalises easily. Agreement with an earlier ansatz is obtained.     

The anomaly cancellation mechanism in N=1, D=4 supergravity and distorted supergravity algebra with Chern-Simon forms

A mechanism is exhibited which ensures that N=1, D=4 new minimal supergravity is free of Lorentz×U(1) anomalies, for any coupling to matter, although it contains an abelian chiral gauge field. This is achieved through the determination of a new supergravity algebra characterized by the presence of a U(1)×Lorentz Chern-Simon form in the field strength of a two-form gauge field. Our analysis provides therefore an example in which Chern-Simon type interactions do occur, while preserving local supersymmetry.