Varying vacuum energy of a self-interacting scalar field

Understanding mechanisms capable of altering the vacuum energy is currently of interest in field theories and cosmology. We consider an interacting scalar field and show that the vacuum energy naturally takes any value between its maximum and zero because interaction affects the number of operating field modes, the assertion that involves no assumptions or postulates. The mechanism is similar to the recently discussed temperature evolution of collective modes in liquids. The cosmological implication concerns the evolution of scalar field ?$?$ during the inflation of the Universe. ?$?$ starts with all field modes operating and maximal vacuum energy in the early inflation-dominated epoch. As a result of inflation, ?$?$ undergoes a dynamical crossover and arrives in the state with one long-wavelength longitudinal mode and small positive vacuum energy predicted to be asymptotically decreasing to zero in the late epoch. Accordingly, we predict that the currently observed cosmological constant will decrease in the future, and comment on the possibility of a cyclic Universe.     

Gravity/CFT correspondence for three-dimensional Einstein gravity with a conformal scalar field

We study the three-dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an infinite Newton?s constant. There is a class of solutions with possible curvature singularities which asymptotic symmetries are given by two copies of the Virasoro algebra. We argue that the central charge of the corresponding CFT is infinite. Furthermore, we construct a family of Schwarzschild solutions which can be conformally mapped to the Martínez–Zanelli solution of Einstein?s equations with a negative cosmological constant coupled to conformal scalar field.     

Renormalization-group flow for the field strength in scalar self-interacting theories

We consider the renormalization-group coupled equations for the effective potential V(?)$V(?)$ and the field strength Z(?)$Z(?)$ in the spontaneously broken phase as a function of the infrared cutoff momentum k  . In the k→0$k\to 0$ limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(?)$V(?)$, indicates a sharp peaking of Z(?)$Z(?)$ close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.     

Constraining conformal field theory with higher spin symmetry in four dimensions

We analyze the constraints on the general form and the singularity structure of the correlation functions of the symmetric, traceless and conserved stress-energy tensor implied by conformal invariance and higher spin symmetry in four dimensions. In particular, we show that all these correlation functions will have at most double pole singularities. We then compute the 4-, 5- and 6-point functions of the stress-energy tensor and find that they are linear combinations of the three free field expressions (scalar, fermion and Maxwell field). This is a strong indication that all such theories are essentially free.     

Extended supersymmetry in massless conformal higher spin theory

We propose superfield equations in tensorial N-extended superspaces to describe the N=2,4,8 supersymmetric generalizations of free conformal higher spin theories. These can be obtained by quantizing a superparticle model in N-extended tensorial superspace. The N-extended higher spin supermultiplets just contain scalar and ‘spinor’ fields in tensorial space so that, in contrast with the standard (super)space approach, no nontrivial generalizations of the Maxwell or Einstein equations to tensorial space appear when N>2. For N=4,8, the higher spin-tensorial components of the extended tensorial superfields are expressed through additional scalar and spinor fields in tensorial space which obey the same free higher spin equations, but that are axion-like in the sense that they possess Peccei-Quinn-like symmetries.     

Nonstatic solutions for the repulsive massless scalar field Einstein equation

Presented in this paper are exact nonstatic solutions for the coupled repulsive sourceless massless scalar field and the gravitational field. The solutions have the same form as the spatially conformally flat static metricds ² =e ^2ψ dt ² +e ^?2ψ(dx ² +dy ² +dz ²).     

Exact scalar field cosmologies in a higher derivative theory

We obtain exact cosmological solutions of a higher derivative theory described by the Lagrangian L=R+2αR ² in the presence of interacting scalar field. The interacting scalar field potential required for a known evolution of the FRW universe in the framework of the theory is obtained using a technique different from the usual approach to solve the Einstein field equations. We follow here a technique to determine potential similar to that used by Ellis and Madsen in Einstein gravity. Some new and interesting potentials are noted in the presence of R ² term in the Einstein action for the known behaviours of the universe. These potentials in general do not obey the slow rollover approximation.     

On the evolution equations for a self-gravitating charged scalar field

We consider a complex scalar field minimally coupled to gravity and to a U(1) gauge symmetry and we construct of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Klein-Gordon system. Our analysis is based on a $1+3$ tetrad formalism which makes use of the components of the Weyl tensor as one of the unknowns. In order to ensure the symmetric hyperbolicity of the evolution equations, implied by the Bianchi identity, we introduce a tensor of rank 3 corresponding to the covariant derivative of the Faraday tensor, and two tensors of rank 2 for the covariant derivative of the vector potential and the scalar field.     

On a one-dimensional model for the three-dimensional vorticity equation

The one-dimensional model for the three-dimensional vorticity equation proposed by Constantin, Lax, and Majda is discussed. Some unsatisfactory points are examined, especially when the viscosity is introduced. A different model is suggested, which, while less solvable than the previous one, can be more strictly connected with the three-dimensional vorticity behavior. The study is of interest for the numerical treatment of the three-dimensional vorticity equation.     

Conformally Ricci-flat spacetimes admitting a Killing vector field parallel to the gradient of the conformal scalar field

It is shown that the stress-energy tensor of a conformally Ricci-flat spacetime in which there exists a Killing vector field parallel to the gradient of the conformal scalar field (a) cannot be of the perfect fluid type and (b) can only originate in an electromagnetic field when the latter is null and the solution belongs to a particular class of pp-waves.     

Renormalization group equation for the vacuum energy of a scalar field in curved space-time

The renormalization group equation is formulated for the vacuum energy of a scalar field. We calculate the two-loop functions and study the asymptotic behavior of the vacuum energy.     

On differential equation on four-point correlation function in the conformal Toda field theory

The properties of completely degenerate fields in the conformal Toda field theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy an ordinary differential equation, in contrast to the Liouville field theory. Some additional assumptions for other fields are required. Under these assumptions, we write such a differential equation and solve it explicitly. We use the fusion properties of the operator algebra to derive a special set of three-point correlation functions. The result agrees with the semiclassical calculations.