Letter: State of Matter for Effective Yang-Mills Fields and Energy Conditions

It has been known that the Penrose-Hawking energy conditions are satisfied by conventional matter. The scalar fields employed in inflationary models can violate the strong energy condition, but not the weak energy condition. Recent observational data of the cosmic microwave background radiation seem to favor a perturbation spectrum index n > 1, which implies that the weak energy condition should be violated by the dominant matter during the inflation. In this paper the state of matter for the effective Yang-Mills fields is examined, and it is found that the quantum Yang-Mills fields in some particular states can violate the weak energy condition naturally.     

Operator product expansion of inflationary correlators and conformal symmetry of de Sitter

We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special conformally invariant. We exploit the operator product expansion technique of conformal field theories to study the inflationary correlators enjoying the symmetries present during the de Sitter epoch. The operator product expansion is particularly powerful in characterizing inflationary correlation functions in two observationally interesting limits, the squeezed limit of the three-point correlator and the collapsed limit of the four-point correlator. Despite the fact that the shape of the four-point correlators is not fixed by the symmetries of de Sitter, its exact shape can be found in the collapsed limit making use of the operator product expansion. By employing the fact that conformal invariance imposes the two-point cross-correlations of the light fields to vanish unless the fields have the same conformal weights, we are able to show that the Suyama–Yamaguchi inequality relating the coefficients _fNL$f_{\mathrm{NL}}$ of the bispectrum in the squeezed limit and _τNL${\tau }_{\mathrm{NL}}$ of the trispectrum in the collapsed limit also holds when the light fields are intrinsically non-Gaussian. In fact, we show that the inequality is valid irrespectively of the conformal symmetry, being just a consequence of fundamental physical principles, such as the short-distance expansion of operator products. The observation of a strong violation of the inequality will then have profound implications for inflationary models as it will imply either that multifield inflation cannot be responsible for generating the observed fluctuations independently of the details of the model or that some new non-trivial degrees of freedom play a role during inflation.     

Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.     

The quasi-steady state cosmology: Theory and observations

This is a review of an alternative cosmology, recently proposed by Fred Hoyle, Geoffrey Burbidge and this author. It begins with a brief discussion of why one needs an alternative cosmology, when the standard hot big bang cosmology is claimed to be doing well. It is argued that the observational and theoretical constraints on the standard big bang cosmology, from various directions, leave a very narrow window, if any, in the parameter space of plausible models. There is thus a strong case for alternative cosmologies. The rest of the review concentrates on one alternative, the quasi steady state cosmology (QSSC) and summarises the recent work on this model. This includes, the theoretical formulation and simple exact solutions of the basic equations, their relationship to various observations, the stability of solutions and the toy model for understanding the growth of structures in the Universe.     

Extra Force from an Extra Dimension: Comparison Between Brane Theory, Space-Time-Matter Theory, and Other Approaches

We investigate the question of how an observer in 4D perceives the five-dimensional geodesic motion. We consider the interpretation of null and non-null bulk geodesics in the context of brane theory, space-time-matter theory (STM) and other non-compact approaches. We develop a frame-invariant formalism that allows the computation of the rest mass and its variation as observed in 4D. We find the appropriate expression for the four-acceleration and thus obtain the extra force observed in 4D. Our formulae extend and generalize all previous results in the literature. An important result here is that the extra force in brane-world models with Z ₂-symmetry is continuous and well defined across the brane. This is because the momentum component along the extra dimension is discontinuous across the brane, which effectively compensates the discontinuity of the extrinsic curvature. We show that brane theory and STM produce identical interpretation of the bulk geodesic motion. This holds for null and non-null bulk geodesics. Thus, experiments with test particles are unable to distinguish whether our universe is described by the brane world scenario or by STM. However, they do discriminate between the brane/STM scenario and other non-compact approaches. Among them the canonical and embedding approaches, which we examine in detail here.     

Lessons from Quantum Field Theory: Hopf Algebras and Spacetime Geometries

We discuss the prominence of Hopf algebras in recent progress in Quantum Field Theory. In particular, we will consider the Hopf algebra of renormalization, whose antipode turned out to be the key to a conceptual understanding of the subtraction procedure. We shall then describe several occurrences of this, or closely related Hopf algebras, in other mathematical domains, such as foliations, Runge-Kutta methods, iterated integrals and multiple zeta values. We emphasize the unifying role which the Butcher group, discovered in the study of numerical integration of ordinary differential equations, plays in QFT.     

New Concepts from the Evans Unified Field Theory. Part One: The Evolution of Curvature,Oscillatory Universe Without Singularity,Causal Quantum Mechanics,and General Force and Field Equations

No Heading The Evans field equation is solved to give the equations governing the evolution of scalar curvature R and contracted energy-momentum T. These equations show that R and T are always analytical, oscillatory, functions without singularity and apply to all radiated and matter fields from the sub-atomic to the cosmological level. One of the implications is that all radiated and matter fields are both causal and quantized, contrary to the Heisenberg uncertainty principle. The wave equations governing this quantization are deduced from the Evans field equation. Another is that the universe is oscillatory without singularity, contrary to contemporary opinion based on singularity theorems. The Evans field equation is more fundamental than, and leads to, the Einstein field equation as a particular example, and so modifies and generalizes the contemporary Big Bang model. The general force and conservation equations of radiated and matter fields are deduced systematically from the Evans field equation. These include the field equations of electrodynamics, dark matter, and the unified or hybrid field.