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We discuss the conformal symmetry between Jordan and Einstein frames considering their relations with the metric and Palatini formalisms for modified gravity. Appropriate conformal transformations are taken into account leading to the evident connection between the gravitational actions in the two mentioned frames and the Hilbert-Einstein action with a cosmological constant. We show that the apparent differences between Palatini and metric formalisms strictly depend on the representation while the number of degrees of freedom is preserved. This means that the dynamical content of both formalism is identical. [ABSTRACT FROM AUTHOR]

After a brief review of the linearized gravity in de Sitter (dS) four-dimensional space and ambient flat five-dimensional notations, the linearized field equation is written in terms of the Casimir operators of dS group. It is shown that the field equation is gauge invariant under some special gauge transformations. Because of this gauge freedom, a gauge-fixing parameter c is inserted in the field equation. It is shown that the solution to the field equation can be written as the multiplication of a generalized symmetric rank-2 polarization tensor and a massless minimally coupled scalar field in ambient space notations. The graviton two-point function has been thoroughly calculated, which is dS-invariant and free of any divergences. This two-point function has been expressed in terms of the intrinsic dS coordinates, from its ambient space counterpart, which is clearly dS-invariant and free of any divergences again. [ABSTRACT FROM AUTHOR]

The cosmological dynamics of a minimally coupled scalar field that couples to the background matter with thermal interactions is investigated using statefinder diagnostics. The time evolution of the statefinder pairs {r, s} and {r, q} are obtained under the circumstance that different values of model parameters are chosen. We show that the thermal coupling term does not affect the location of the late-time attractor, but exerts an influence on the evolution of the statefinder parameters. The most notable feature of the r–s plane for the thermal coupling model, which is distinguished from the other dark energy models, is that some part of the curve with thermal coupling can form a closed loop in the second quadrant (r > 1, s < 0). [ABSTRACT FROM AUTHOR]

This paper studies the cosmological equations for a scalar field φ in the framework of a quantum gravity modified Einstein–Hilbert Lagrangian where G and Λ are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Λ = Λ(G) and the potential V = V(φ) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, the additional variable being the running Newton coupling. [ABSTRACT FROM AUTHOR]

The cosmological implications of an evolutionary quantum gravity are analyzed in the context of a generic inhomogeneous model. The Schrödinger problem is formulated and solved in the presence of a scalar field, an ultrarelativistic matter and a perfect gas regarded as the dust-clock. Considering the actual phenomenology, it is shown how the evolutionary approach overlaps the Wheeler-DeWitt one. [ABSTRACT FROM AUTHOR]

We offer a critical assessment of some generic features of various current approaches to the construction of a theory of quantum gravity. We argue that there is a need for further conceptual clarifications before such an enterprise can be launched in a truly well-grounded setting, and that one of the guiding principles that can be viewed as part of the reasons for successes of the past theoretical developments is the identification of unspeakables — concepts that should not only play no role in the formulation of the theories, but ones that the formalism of the theory itself should prevent from ever being spoken about. [ABSTRACT FROM AUTHOR]

We investigate the Dynamical Casimir Effect (DCE) in the case of a scalar field enclosed in a box which undergoes a phase of strong acceleration (a kick) during its motion. Following a general-relativistic approach, we describe the acceleration field as a time-dependent space–time metric in the frame of a comoving, noninertial observer. Assuming a nonrelativistic motion of the box, we perturbatively solve the Klein–Gordon equation for the matter field, evaluating the β-Bogolubov coefficients, related to the particle creation. We show that, after the kick, a (small) number of created quanta is found inside the box. The resulting spectrum carries, in principle, information about the details of the box acceleration phase. The present approach can serve to shed light on the close relationship between DCE and Unruh–Hawking effect. [ABSTRACT FROM AUTHOR]

In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space–time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space–time and review the relevant results for unitary implementability. [ABSTRACT FROM AUTHOR]

A dynamical fuzzy space might be described by a three-index variable $C_{ab}^c$, which determines the algebraic relations $f_af_b=C_{ab}^cf_c$ among the functions fa on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on fa. We study equations for the three-index variable invariant under the general linear transformation and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, we study SO(3) symmetric solutions and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework. [ABSTRACT FROM AUTHOR]

It has been shown that the negative norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter space.1,2 In this process, ultraviolet and infrared divergences have been automatically eliminated.3 A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λϕ4 theory) has been achieved through the consideration of the negative norm states.4 The one-loop effective action for scalar field in a general curved space-time has been calculated by this method, and a natural renormalization procedure in the one-loop approximation has been established. [ABSTRACT FROM AUTHOR]

Recently Gambini and Pullin proposed a new consistent discrete approach to quantum gravity and applied it to cosmological models. One remarkable result of this approach is that the cosmological singularity can be avoided in a general fashion. However, whether the continuum limit of such discretized theories exists is model dependent. In the case of massless scalar field coupled to gravity with Λ=0, the continuum limit can only be achieved by fine tuning the recurrence constant. We regard this failure as the implication that cosmological constant should vary with time. For this reason we replace the massless scalar field by Chaplygin gas which may contribute an effective cosmological constant term with the evolution of the universe. It turns out that the continuum limit can indeed be reached in this case. [ABSTRACT FROM AUTHOR]

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born–Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of noninteracting (incoherent), nonrotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following an earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late "time" we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler–de Witt equation of quantum gravity. [ABSTRACT FROM AUTHOR]

A non-perturbative canonical quantization of the Gowdy T³ polarized models is considered here. This approach profits from the equivalence between the symmetry reduced model and 2 + 1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is made, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a two-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert space of quantum states. The implications of this result for both the quantization of fields on curved manifolds and other physically relevant questions regarding the initial singularity are discussed. [ABSTRACT FROM AUTHOR]