It has been argued that the quantum (conformal) trace anomaly could potentially provide us with a dynamical explanation of the cosmological constant problem. In this paper, however, we show by means of a semiclassical analysis that the trace anomaly does not affect the cosmological constant. We construct the effective action of the conformal anomaly for flat FLRW spacetimes consisting of local quadratic geometric curvature invariants. Counterterms are thus expected to influence the numerical value of the coefficients in the trace anomaly and we must therefore allow these parameters to vary. We calculate the evolution of the Hubble parameter in quasi de Sitter spacetime, where we restrict our Hubble parameter to vary slowly in time, and in FLRW spacetimes. We show dynamically that a Universe consisting of matter with a constant equation of state, a cosmological constant and the quantum trace anomaly evolves either to the classical de Sitter attractor or to a quantum trace anomaly driven one. When considering the trace anomaly truncated to quasi de Sitter spacetime, we find a region in parameter space where the quantum attractor destabilises. When considering the exact expression of the trace anomaly, a stability analysis shows that whenever the trace anomaly driven attractor is stable, the classical de Sitter attractor is unstable, and vice versa. Semiclassically, the trace anomaly does not affect the classical late time de Sitter attractor and hence it does not solve the cosmological constant problem.
The trace anomaly in six-dimensional space is given by the local terms which have six derivatives of the metric. We find the effective action which is responsible for the anomaly. The result is presented in non-local covariant form and also in the local covariant form which employs two auxiliary scalar fields.
A model is proposed to describe a transition from a Schwarzschild black hole of mass $M_{0}$ to a Schwarzschild black hole of mass $M_{1}$ $\leq M_{0}$. The basic equations are derived from the non-vacuum Einstein field equations taking a source representing a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace anomaly of the scalar field prevents a complete evaporation.
We study the infrared effective theory of gravity that stems from the quantum trace anomaly. Quantum fluctuations of the metric induce running of the cosmological constant and the Newton constant at cosmological scales. By imposing the generalized Bianchi identity we obtain a prediction for the scale dependence of the dark matter and dark energy densities in terms of the parameters of the underlying conformal theory. For certain values of the model parameters the dark energy equation of state and the observed spectral index of the primordial density fluctuations can be simultaneously reproduce…
The trace anomaly and the cosmological constant problem are two typical breakdowns when applying the quantum principle to a general covariant or gravitational system. A quantum theory of spacetime reference frame is proposed and reviewed. We study the theory by functional method, and show that the trace anomaly of the theory is closely related to some of the Perelman's functionals. The functionals may provide us possible links between the trace anomaly and the cosmological constant. We find that to cancel the trace anomaly at the lab's scale up to very high energy, a cosmological constant is r…
Conformal scalar fields coupled to the dilaton appear naturally in two-dimensional models of black hole evaporation. We calculate their trace anomaly. It follows that an RST-type counterterm appears naturally in the one-loop effective action.
The trace anomaly for nonminimally coupled scalars in spherically reduced gravity obtained by Bousso and Hawking (hep-th/9705236) is incorrect. We explain the reasons for the deviations from our correct (published) result which is supported by several other recent papers.
Trace anomaly for conformally invariant higher derivative 4D scalar-dilaton theory is obtained by means of calculating divergent part of one-loop effective action for such system. Its applications are briefly mentioned
We discuss stationary supersymmetric bosonic configurations of the Einstein-Maxwell theory embedded in $N=2$ supergravity. Some of these configurations, including the Kerr-Newman solutions with $m = |q|$ and arbitrary angular momentum per unit mass $a$, exhibit naked singularities. However, $N=2$ supergravity has trace anomaly. The nonvanishing anomalous energy-momentum tensor of these Kerr-Newman solutions violates a consistency condition for a configuration to admit unbroken supersymmetry. Thus, the trace anomaly of this theory prevents the supersymmetric solutions from exhibiting naked sing…
We calculate the trace (conformal) anomaly for chiral fermions in a general curved background using Hadamard subtraction. While in intermediate steps of the calculation imaginary terms proportional to the Pontryagin density appear, imposing a vanishing divergence of the stress tensor these terms completely cancel, and we recover the well-known result equal to half the trace anomaly of a Dirac fermion. We elaborate in detail on the advantages of the Hadamard method for the general definition of composite operators in general curved spacetimes, and speculate on possible causes for the appearance…
In this note we address the discrepancy found by Hung, Myers and Smolkin between the holographic calculation of entanglement entropy (using the Jacobson-Myers functional for the holographic minimal surface) and the CFT trace anomaly calculation if one uses the Wald prescription to compute the entropy in six dimensions. As anticipated in our previous work [1] the discrepancy originates entirely from a total derivative term present in the trace anomaly in six dimensions.
We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.
The holographic principle relates (classical) gravitational waves in the bulk to quantum fluctuations and the Weyl anomaly of a conformal field theory on the boundary (the brane). One can thus argue that linear perturbations in the bulk of static black holes located on the brane be related to the Hawking flux and that (brane-world) black holes are therefore unstable. We try to gain some information on such instability from established knowledge of the Hawking radiation on the brane. In this context, the well-known trace anomaly is used as a measure of both the validity of the holographic pictu…
By means of a semiclassical analysis we show that the trace anomaly does not affect the cosmological constant. We calculate the evolution of the Hubble parameter in quasi de Sitter spacetime, where the Hubble parameter varies slowly in time, and in FLRW spacetimes. We show dynamically that a Universe consisting of matter with a constant equation of state, a cosmological constant and the quantum trace anomaly evolves either to the classical de Sitter attractor or to a quantum trace anomaly driven one. There is no dynamical effect that influences the effective value of the cosmological constant.
We revisit the computation of the trace anomaly for Weyl fermions using dimensional regularization. For a consistent treatment of the chiral gamma matrix $γ_*$ in dimensional regularization, we work in $n$ dimensions from the very beginning and use the Breitenlohner-Maison scheme to define $γ_*$. We show that the parity-odd contribution to the trace anomaly vanishes (for which the use of dimension-dependent identities is crucial), and that the parity-even contribution is half the one of a Dirac fermion. To arrive at this result, we compute the full renormalized expectation value of the fermion…
We adapt a calculation due to Massacand and Schmid to the coordinate independent definition of time and vacuum given by Capri and Roy in order to compute the trace anomaly for a massless scalar field in a curved spacetime in 1+1 dimensions. The computation which requires only a simple regulator and normal ordering yields the well-known result $\frac{R}{24π}$ in a straightforward manner.
In the present letter we find that Starobinsky's inflationary solution is also valid in the Dvali-Gabadadze-Porrati (DGP) model where a 3-brane is embedded in 5-dimensional Minkowski bulk. We show that such a solution is typically not supported by the Self-Accelerated branch of the model, giving therefore a natural selection of the conventional branch of solutions. In the absence of brane induced Einstein-Hilbert term the SA branch is always selected out. We then study the linearized modes around all such de Sitter brane solutions finding perturbative stability for a range of parameters of the…
We compute the corrections, using the tunneling formalisim based on a quantum WKB approach, to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are shown to be equivalent to findings inferred from Hawking's original calculation based on path integrals using zeta function regularization. Finally, exploiting the corrected temperature and periodicity arguments we also find the modification to the original Schwarzschild metric which captures the effect of quantum corrections.
We construct a new example of the high derivative four-dimensional conformal operator. This operator acts on fermions, and its contribution to the trace anomaly has opposite sign, as compared to conventional scalars, spinors and vectors. Possible generalizations and applications are discussed.
We explore trace-anomaly driven inflation in modified gravity. It is explicitly shown that in $T^2$ teleparallel gravity, the de Sitter inflation can occur, although quasi de Sitter inflation happens in $R^2$ gravity. Furthermore, we investigate the influence of the trace anomaly on inflation. It is found that in $f(T)$ gravity, the de Sitter inflation can end because it becomes unstable due to the trace anomaly, whereas also in higher derivative gravity, the de Sitter inflation can be realized and it will be over thanks to the trace anomaly for smaller parameter regions in comparison with tho…
We have used the results of renormalization of a two-dimensional quantum stress tensor to develop a conformally invariant dynamical model. The model requires the consideration of those conformal frames in which there exists a correspondence between the trace anomaly and a cosmological constant. We apply this model to a two dimensional-Schwarzschild (-de Sitter) spacetime to show that in these conformal frames one may achieve Hawking radiation without recourse to the trace anomaly .
We study the conformal symmetry and the energy-momentum conservation of scalar field interacting with a curved background at D=2. We avoid to incorporate the metric determinant into the measure of the scalar field to explain the conformal anomaly and the consequent energy-momentum conservation. Contrarily, we split the scalar field in two other fields, in such a way that just one of them can be quantized. We show that the same usual geometric quantities of the anomaly are obtained, which are accompanied by terms containing the new field of the theory.
Despite the finiteness of stress tensor for a scalar field on the four-dimensional Schwarzschild black hole in the Israel-Hartle-Hawking vacuum, the Tolman temperature in thermal equilibrium is certainly divergent on the horizon due to the infinite blueshift of the Hawking temperature. The origin of this conflict is due to the fact that the conventional Tolman temperature was based on the assumption of a traceless stress tensor, which is, however, incompatible with the presence of the trace anomaly responsible for the Hawking radiation. Here, we present an effective Tolman temperature which is…
Black hole solutions in the context of a generic matter-coupled two-dimensional dilaton gravity theory are discussed both at the classical and semiclassical level. Starting from general assumptions, a criterion for the existence of black holes is given. The relationship between conformal anomaly and Hawking radiation is extended to a broad class of two-dimensional dilaton gravity models. A general and simple formula relating the magnitude of the Hawking effect to the dilaton potential evaluated on the horizon is derived.
There are evidences that the cosmic microwave background (CMB) large-angle anomalies imply a departure from statistical isotropy and hence from the standard cosmological model. We propose a LCDM model extension whose dark energy component preserves its nondynamical character but wield anisotropic vacuum pressure. Exact solutions for the cosmological scale factors are presented, upper bounds for the deformation parameter are evaluated and its value is estimated considering the elliptical universe proposal to solve the quadrupole anomaly. This model can be constructed from a Bianchi I cosmology …
The evaporation of four-dimensional spherically symmetric black holes is presented in the framework of quantum field theory in curved spacetimes and semiclassical gravity. It is discussed how the evaporation process can be sourced by the presence of the trace anomaly of a massless, conformally coupled scalar field outside the apparent horizon of the black hole.
We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of non-local actions, including displaying the action for the full non-local energy-momentum tensor. As an application, we show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light.
We investigate the classical and semiclassical features of generic 2D, matter-coupled, dilaton gravity theories. In particular, we show that the mass, the temperature and the flux of Hawking radiation associated with 2D black holes are invariant under dilaton-dependent Weyl rescalings of the metric. The relationship between quantum anomalies and Hawking radiation is discussed.
A model is proposed to describe a transition from a charged black hole of mass $M$ and charge $Q$ to one of mass $\bar{M}$ and charge $\bar{Q}$. The basic equations are derived from the non-vacuum Einstein field equations sourced by the Coulomb field and by a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace of the energy-momentum tensor prevents the formation of a naked singularity.
We construct concrete counterterms of the Balasubramanian-Kraus type for Einstein-scalar theories with designer gravity boundary conditions in AdS$_{4}$, so that the total action is finite on-shell and satisfy a well defined variational principle for an arbitrary scalar field potential. We focus on scalar fields with the conformal mass, $m^{2}=-2l^{-2}$, and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual field theory in the generic case, as well as when there exist logarithmic branches of non-linear origin. As e…
The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscop…
The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED as an example, we compute the full one-loop triangle amplitude of the fermionic stress tensor with two current vertices, <T^{mn} J^a J^b>, and exhibit the scalar pole in this amplitude associated with the trace anomaly, in the limit of zero electron mass m -> 0. To emphasize the infrared aspect of the anomaly, we use a dispersive approach and show that this …
We analyze the semiclassical Einstein equations for quantum scalar fields satisfying modified dispersion relations. We first discuss in detail the renormalization procedure based on adiabatic subtraction and dimensional regularization. We show that, contrary to what expected from power counting arguments, in 3+1 dimensions the subtraction involves up to the fourth adiabatic order even for dispersion relations containing higher powers of the momentum. Then we analyze the dependence of the trace of the renormalized energy momentum tensor with the scale of new physics, and we recover the usual tr…
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.
Trace anomaly contributions to semi-classical wormhole geometries
Shahid Bahonar University（沙希德·巴孔加尔大学）；Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), University of Maragheh（马拉盖天文与天体物理研究所（RIAAM），马拉盖大学）；Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa（里斯本大学科学学院空间科学与天体物理研究所）；Departamento de Física, Faculdade de Ciências da Universidade de Lisboa（里斯本大学科学学院物理系）
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic background, and then verify the stability of such background with respect to metric perturbations. The problem under consideration has several interesting applications. Our first purpose is to explore the stability of the classical cosmological solutions in the theory with quantum effects taken into account. There is an interesting literature about stability of…
According to recent astrophysical observations the large scale mean pressure of our present universe is negative suggesting a positive cosmological constant like term. This article addresses the question of whether non-perturbative effects of self-interacting quantum fields in curved space-times may yield a significant contribution. Focusing on the trace anomaly of quantum chromo-dynamics (QCD), a preliminary estimate of the expected order of magnitude yields a remarkable coincidence with the empirical data, indicating the potential relevance of this effect. PACS: 04.62.+v, 12.38.Aw, 12.38.Lg,…
The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this effective action in four dimensions requires two additional scalar fields, not contained in classical general relativity, which remain relevant at macroscopic distance scales. The auxiliary scalar fields depend upon boundary conditions for their complete specification, and therefore carry global information about the geometry and macroscopic quantum state of …
The existence of trace anomalies for conformally coupled quantum fields in curved spacetimes, despite the vanishing of the trace of the conformally invariant classical stress-energy tensor, was firmly established in the 1970's, and expressions for the anomalous trace of the semi-classical quantum stress-energy tensor constructed from the curvature tensors of the background spacetime were proven to hold independent of the quantum state of the field. Subsequently, effective actions were devised whose variation with respect to the metric gives a conserved "anomalous stress-energy tensor" or ASET.…
This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of space-time, the classical perturbative treatment must be rethought carefully. The present discussion provides a unified picture of several previous works, together with new treatments of higher-order perturbations and the specification of initial states.
Quantum effects due to conformal matter in a black hole background result in universal logarithmic corrections to black-hole entropy. The universality resides in the connection of the log term coefficient with those of type-A and type-B Weyl anomalies, regularization-scheme independent quantities. We presently study the case of extremal black holes within Wald's Noether charge formalism. In the conformal class of flat metrics, we are again able to unveil the log term in the entropy from the horizon value of the solution to the Q-curvature uniformization problem. Beyond conformally flat backgro…
We consider dark energy cosmology in a de Sitter universe filled with quantum conformal matter. Our model represents a Gauss-Bonnet model of gravity with contributions from quantum effects. To the General Relativity action an arbitrary function of the GB invariant, f(G), is added, and taking into account quantum effects from matter the cosmological constant is studied. For the considered model the conditions for a vanishing cosmological constant are considered. Creation of a de Sitter universe by quantum effects in a GB modified gravity is discussed.
We analyze decay processes of the inflaton field, phi, during the coherent oscillation phase after inflation in f(phi)R gravity. It is inevitable that the inflaton decays gravitationally into gauge fields in the presence of f(phi)R coupling. We show a concrete calculation of the rate that the inflaton field decays into a pair of gauge fields via the trace anomaly. Comparing this new decay channel via the anomaly with the channels from the tree-level analysis, we find that the branching ratio crucially depends on masses and the internal multiplicities (flavor quantum number) of decay product pa…
Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of mass, length and time arbitrarily at each point. To be able to have this view, it is necessary that the background on which the quantum field is based be conformal invariant as well. Consequently, defining the unambiguous expectation value of the energy-momentum tensor of such a quantum field through the Wald renormalizing prescription necessitates breaking…
In the spatially flat case of loop quantum cosmology, the connection $\bar{k}$ is usually replaced by the holonomy $\frac{\sin(\barμk)}{\barμ}$ in the effective theory. In this paper, instead of the $\barμ$ scheme, we use a generalised, undertermined function $g(\bar{k},\bar{p})$ to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction on the form of $g(\bar{k},\bar{p})$, then we derive the gauge invariant equations of motion of the scalar, tensor and vector perturbations and study the inflat…
An almost brief, though lengthy, review introduction about the long history of higher order gravities and their applications, as employed in the literature, is provided. We review the analogous procedure between higher order gravities and GR, as described in our previous works, in order to highlight its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a \emph{criteria} in order to distinguish correct metric theories of gravity. For example, it does not permit the inclusion of only one of the second order Lagrangi…
