Dynamical mass generation for the gravitino in N = 1 supergravity

The Volkov-Akulov field is coupled to supergravity and it is gauged away through a field redefinition, remaining with a negative cosmological constant plus N = 1 supergravity lagrangian. Then the gravitino sector is quantized and a positive cosmological constant is obtained along with a mass-like term for the gravitino. Imposing the effective cosmological constant to be zero, consequently a genuine mass term for the gravitino is obtained. The corresponding energy-gap equation shows that this mass turns out to be of the order of the Planck mass.     

Gauss-Bonnet as Effective Cosmological Constant

It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant.We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions.Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter.One branch(the "-" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero,in which case the effective cosmological constant becomes identical with the bare value,while the other(i.e.the "+") branch is singular in the same limit,and beyond this singular limit,the effective cosmological constant is inversely proportional to the Gauss-Bonnet parameter with a negative constant of proportionality when the bare value vanishes.     

Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity

Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism are derived, and variations of a generic set of higher-order curvature terms appearing in string effective actions are studied. It is shown that there often exists a particular set of solutions to the field equations of pure gravity theories, consisting of different combinations of curvature tensors, which satisfies the vacuum equations with cosmological constant. Implications of generalized symmetries of the field equations derived from the superstring effective action for the cosmological constant problem are discussed.     

Evolution of the cosmological constant in effective gravity

In contrast to the phenomenon of nullification of the cosmological constant in equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological constant to evolve in a nonequilibrium vacuum. An attempt is made to extend the Einstein equation in the direction suggested by the condensed matter analogy of the quantum vacuum. Different scenarios are found depending on the behavior of and the relation between the relaxation parameters involved, some of these scenarios having been discussed in the literature. One of them reproduces the scenario in which the effective cosmological constant emerges as a constant of integration. The second one describes the situation when, after the cosmological phase transition, the cosmological constant drops from zero to a negative value; this scenario describes the relaxation from this big negative value back to zero and then to a small positive value. In the third example, the relaxation time is not a constant but depends on matter; this scenario demonstrates that vacuum energy (or its fraction) can play the role of cold dark matter.     

Cosmological constant: a lesson from Bose-Einstein condensates

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.     

A mechanism for reducing the value of the cosmological constant

A mechanism is presented for relaxing an initially large, positive cosmological constant to a value near zero. This is done by introducing a scalar field whose vacuum energy compensates for the initial cosmological constant. The compensating sector involves small mass scales but no unnatural fine-tuning of parameters. It is not clear how to incorporate this mechanism into a realistic cosmology.     

Neutralization of the cosmological constant by membrane creation

The quantum creation of closed membranes by totally antisymmetric tensor and gravitational fields is considered in arbitrary space-time dimension. The creation event is described by instanton tunneling. As membranes are produced, the energy density associated with the antisymmetric tensor fielld decreases, reducing the effective value of the cosmological constant. For a wide range of parameters and initial conditions, this process will naturally stop as soon as the cosmological constant is near zero, even if the energy remaining in the antisymmetric tensor field is large. Among the instantons obtained, some are interpreted as representing a topology change, in which an open space spontaneously compactifies; however, the quantum probability for these processes vanishes.     

A feedback mechanism for the cosmological constant

We study the dynamics of the true vacuum in a cosmological phase transition governed by a Higgs field. When the mass of the field depends on the temperature there is a feedback mechanism for relaxing the cosmological constant near zero.This essay received the fifth award from the Gravity Research Foundation, 1990 — Ed.     

A new look at the accelerating universe

We show that the cosmological model having zero cosmological constant, but containing the vacuum energy of a simple quantized free scalar field of low mass (VCDM model), agrees with the cosmic microwave background radiation (CMBR) and supernova (SNe-Ia) data at least as well as the classical cosmological model with a small nonzero cosmological constant. We also show that in the VCDM model the ratio of vacuum pressure to vacuum energy density is less than -1. We display the VCDM results for a set of parameters that give a very good fit to the CMBR power spectrum, and show that the same parameters also give a good fit to the SNe-Ia data.     

Time evolution of <Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">μν</Emphasis></Subscript> and the cosmological constant problem

We study the cosmic time evolution of an effective quantum field theory energy-momentum tensor T _μν and show that, as a consequence of the effective nature of the theory, T _μν is such that the vacuum energy decreases with time. We find that the zero point energy at present time is washed out by the cosmological evolution. The implications of this finding for the cosmological constant problem are investigated.     

Dynamical approach to the cosmological constant

We consider a dynamical approach to the cosmological constant. There is a scalar field with a potential whose minimum occurs at a generic, but negative, value for the vacuum energy, and it has a nonstandard kinetic term whose coefficient diverges at zero curvature as well as the standard kinetic term. Because of the divergent coefficient of the kinetic term, the lowest energy state is never achieved. Instead, the cosmological constant automatically stalls at or near zero. The merit of this model is that it is stable under radiative corrections and leads to stable dynamics, despite the singular kinetic term. The model is not complete, however, in that some reheating is required. Nonetheless, our approach can at the very least reduce fine-tuning by 60 orders of magnitude or provide a new mechanism for sampling possible cosmological constants and implementing the anthropic principle.     

Chaplygin gas quantum universe in the presence of the cosmological constant

We present a Chaplygin gas Friedmann-Robertson-Walker quantum cosmological model in the presence of the cosmological constant. We apply the Schutz’s variational formalism to recover the notion of time, and this gives rise to Wheeler-DeWitt equation for the scale factor. We study the early and late time universes and show that the presence of the Chaplygin gas leads to an effective positive cosmological constant for the late times. This suggests the possibility of changing the sign of the effective cosmological constant during the transition from the early times to the late times. For the case of an effective negative cosmological constant for both epoches, we solve the resulting Wheeler-DeWitt equation using the Spectral Method and find the eigenvalues and eigenfunctions for positive, zero, and negative constant spatial curvatures. Then, we use the eigenfunctions in order to construct wave packets for each case and obtain the time-dependent expectation value of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation value of the scale factors never tend to the singular point, we have an initial indication that this model may not have singularities at the quantum level.     

Randall-Sundrum model for self-tuning the cosmological constant

The vanishing cosmological constant in the four-dimensional space-time is obtained in a 5D Randall-Sundrum model with a brane (B1) located at y = 0. The matter fields can be located at the brane. For settling any vacuum energy generated at the brane to zero, we need a three-index antisymmetric tensor field A(MNP) with a specific form for the Lagrangian. For the self-tuning mechanism, the bulk cosmological constant should be negative.     

Positive cosmological constant,non-local gravity and horizon entropy

We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant Λ>0$\Lambda >0$ and with zero Λ. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive Λ, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.     

Comprehensive solution to the cosmological constant,zero-point energy,and quantum gravity problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.     

Conformally coupled scalar field solutions and the cosmological constant

Solutions are presented for a scalar field coupled conformally to Einstein gravity with a nonvanishing cosmological constant, in the case that the spacetime metric is spatially homogeneous and isotropic. Since the cosmological constant destroys the conformal invariance of the action, these solutions cannot be obtained by solving the flat space wave equation for the scalar field. It turns out that the metric is determined entirely by the cosmological constant, while the scalar field acquires an apparent mass squared which is proportional to the cosmological constant. It is conjectured that the cosmological constant in the universe at present may thus be disguised as the mass of some scalar field.     

Probable values of the cosmological constant in a holographic theory

We point out that for a large class of universes, holography implies that the most probable value for the cosmological constant is zero. In four space-time dimensions, the probability distribution takes the Baum-Hawking form, dP approximately exp(cM(2)(p)/Lambda)dLambda.     

A Cosmological Model with Static Extra Dimensions and Varying Cosmological Constant

A five dimensional cosmological model with FLRW type Kaluza-Klien metric has been investigated with static extra dimensions and varying cosmological constant. The field equations with static extra dimension are solved by considering the cosmological constant as a function of time for different cases. The effective pressure is considered as the difference of pressure corresponding to the extra dimension and the usual four dimensions. The conditions for acceleration of the universe are then discussed.     

Dimensionality and the cosmological constant

In the Kaluza-Klein model with a cosmological constant Λ and a flux, the external spacetime of the created universe from aS ^s × S ^n−s seed instanton can be identified in quantum cosmology. One can also show that in the internal space theeffective cosmological constant is most probably zero.     

The Cosmological constant problem

Observational evidence seems to indicate that the expansion of the universe is currently accelerating. Such an acceleration strongly suggests that the content of the universe is dominated by a non-clustered form of matter, the so-called dark energy. The cosmological constant, introduced by Einstein to reconcile General Relativity with a closed and static Universe, is the most likely candidate for dark energy although other options such as a weakly interacting field, also known as quintessence, have been proposed. The fact that the dark energy density is some one hundred and twenty orders of magnitude lower than the energy scales present in the early universe constitutes the cosmological constant problem. We review various aspects of the cosmological constant problem and some interesting scenarios using supersymmetry or extra-dimensions attempting to solve one of the most puzzling issues in physics.