Semiclassical Theory Of Gravity Research Articles

PARTICLE PRODUCTION OF COHERENTLY OSCILLATING NONCLASSICAL INFLATON IN FRW UNIVERSE

We study particle production of coherently oscillating inflaton in semiclassical theory of gravity by representing inflaton in coherent and squeezed state formalisms. A comparative study of the inflaton in classical gravity with coherent state inflaton in semiclassical gravity is also presented.

Particle Creation in the Oscillatory Phase of Inflaton

A thermal squeezed state representation of inflaton is constructed for a flat Friedmann-Robertson-Walker background metric and the phenomenon of particle creation is examined during the oscillatory phase of inflaton, in the semiclassical theory of gravity. An approximate solution to the semiclassical Einstein equation is obtained in thermal squeezed state formalism by perturbatively and is found obey the same power-law expansion as that of classical Einstein equation. In addition to that the solution shows oscillatory in nature except on a particular condition. It is also noted that, the coherently oscillating nonclassical inflaton, in thermal squeezed vacuum state, thermal squeezed state and thermal coherent state, suffer particle production and the created particles exhibit oscillatory behavior. The present study can account for the post inflation particle creation due to thermal and quantum effects of inflaton in a flat FRW universe.

Oscillatory Phase of Inflaton and Power-Law Expansion in Bianchi Type-I Universe

A homogeneous massive scalar field, minimally coupled to the spatially homogeneous and anisotropic background metric, in the semiclassical theory of gravity is examined. In the oscillatory phase of inflaton, the approximate leading solution to the semiclassical Einstein equation for the Bianchi type-I universe shows, each scale factor in each direction obeys t2/3 power-law expansion. Further noted that the evolution of scale factors are mutually correlated.

NONCLASSICAL STATE REPRESENTATION OF INFLATON AND POWER-LAW EXPANSION IN FRW UNIVERSE

We have examined a homogeneous massive scalar field minimally coupled to the spatially flat Friedmann–Robertson–Walker metric, in squeezed and coherent state formalisms, in semiclassical theory of gravity. In the oscillatory phase of inflaton, the approximate leading solution to the semiclassical Einstein equation has the same power-law expansion as that of the classical Einstein equation for both coherent and squeezed state formalisms. Quantum fluctuations of the inflaton in coherent and squeezed vacuum states are studied, by using dispersion relations. The uncertainty relation for coherent state does not depend on the coherent state parameter while the uncertainty relation for squeezed vacuum state depends on the associated squeezing parameter and squeezing angle.

THERMAL SQUEEZING AND DENSITY FLUCTUATIONS IN SEMICLASSICAL THEORY OF GRAVITY

A thermal squeezed state representation is constructed for each mode of a quantized scalar field in a spatially homogeneous and flat Robertson–Walker metric and the validity of semiclassical Einstein equation by analyzing the density fluctuation is examined. The density fluctuation in thermal squeezed state is very large and therefore the semiclassical theory may not be valid for squeezing parameter more than unity, however the theory holds when the associated squeezing parameter is much less than the unity. Further noted that the semiclassical theory is consistent in thermal coherent state formalism. The present study can account for the density fluctuations due to the thermal and quantum effects in semiclassical theory of gravity.

EXTREMAL BLACK HOLES AND THE LIMITS OF THE THIRD LAW

Recent results of quantum field theory on a curved spacetime suggest that extremal black holes are not thermal objects and that the notion of zero temperature is ill-defined for them. If this is correct, one may have to go to a full semiclassical theory of gravity, including backreaction, in order to make sense of the third law of black hole thermodynamics. Alternatively it is possible that we shall have to drastically revise the status of extremality in black hole thermodynamics.

Thermal Squeezed State Representation of Scalar Field and Energy Density in Semiclassical Theory of Gravity

The semiclassical theory of gravity is studied in terms of representation of scalar field in thermal coherent state and thermal squeezed state formalisms. For the FRW cosmological model with a minimal scalar field, the semiclassical Einstein equation reduces to zero-point energy term plus a finite temperature term and classical term in thermal coherent state. In thermal squeezed vacuum state it reduces to quantum term in addition to the finite temperature term and zero-point energy term. The present study can account for nonclassical state and finite temperature effect contributions to energy density in semiclassical theory of gravity.

Fluctuations of the Hawking flux

The fluctuations of the flux radiated by an evaporating black hole will be discussed. Two approaches to this problem will be adopted. In the first, the squared flux operator is defined by normal ordering. In this case, both the mean flux and the mean-squared flux are well-defined local quantites. It is shown that the flux undergoes large fluctuations on a time scale of the order of the black hole's mass. Thus the semiclassical theory of gravity, in which a classical gravitational field is coupled to the expectation value of the stress tensor, breaks down below this time scale. In the second approach, one does not attempt to give meaning to the squared flux as a local quantity, but only as a time-averaged quantity. In both approaches, the mean-squared mass minus the square of the mean mass grows linearly in time, but 4 times as fast in the second approach as in the first.

Cylindrical self-consistent solutions of semiclassical gravity

The possibility of the creation of curved spacetimes or spacetimes with a nontrivial topological structure by the vacuum fluctuations of quantum fields is discussed. This problem is considered in the framework of the self-consistent semiclassical theory of gravity. The approximate method for obtaining the vacuum expectation value of the renormalized stress-energy tensor of conformally invariant quantum fields in static spacetimes is used. The particular solutions of Einstein equations for the different boundary conditions at the cylinder symmetry axis are obtained.

Semiclassical gravitation and quantization for the Bianchi type-I universe with large anisotropy

We use a perturbative method to evaluate the effective action of a free scalar field propagating in the Bianchi type I spacetime with large space anisotropy. The zeta- function regularization method is used to evaluate the action to the second order in the Schwinger perturbative formula. As the quantum corrections contain fourth derivative in the metric we apply the method of iterative reduction to reduce it to the second-order form to obtain the self-consistent solution of the semiclassical gravity theory, The reduced Einstein equation shows that the space anisotropy, which will be smoothed out during the evolution of universe, may play an important role in the dynamics of early universe. We quantize the corresponding minisuperspace model to investigate the behavior of the space anisotropy in the initial epoch. From the wavefunction of the Wheeler-DeWitt equation we see that the probability for the Bianchi type I spacetime with large anisotropy is less then that with a small anisotropy.

Expansion of effective action in curved spacetime with large anisotropy

A simple perturbative method is used to evaluate the renormalized effective action of a free scalar field in the Bianchi type I spacetime with large anisotropy. With the help of the zeta function regularization method the action is expanded to the second order in the Schwinger perturbative formula. We apply the method of iterative reduction to reduce the generalized Einstein equation to a second-order equation to obtain the self-consistent solution of the semiclassical gravity theory. The reduced equation shows that the space anisotropy, which will be smoothed out during the evolution of Universe, may play an important role in the dynamics of early Universe. We thus quantize the corresponding minisuperspace model to investigate the behavior of space anisotropy in the early Universe. From the wavefunction of the Wheeler–De Witt equation we see that the state probability of the Bianchi type I spacetime with large anisotropy is less than that with a small anisotropy.

Quantum fluctuations of scalar field in conical space

We consider vacuum polarization effect of a conformally coupled massless scalar field in the background produced by an idealized straight cosmic string. Using previous criterion we show the calculation of back reaction of the field to the metric in the context of semiclassical gravity theory is not valid , in some regions due to large quantum fluctuations in the conical space.

Quantization of semiclassical gravitation theory in anisotropic spacetime

The renormalized effective action of a free scalar field propagating in the Bianchi type I spacetime is examined. As it contains higher-order derivatives of the metric the Hamiltonian structure of the theory will be changed. Thus, to obtain the self-consistent solution of the semiclassical gravity theory the method of iterative reduction is used to reduce it to a second-order equation. We solve the reduced equation and see that the space anisotropy, which will be smoothed out during the evolution of Universe, may play important role in the dynamics of early Universe. To investigate the behavior of space anisotropy in the early Universe we then quantize the corresponding minisuperspace. The associated Wheeler-DeWitt equation is solved in the WKB approximation and, from the solution, it is seen that the most probable state of the Bianchi type I spacetime is that with a small anisotropy.

An interpretation of the non-tidal acceleration in Earth's rotation in terms of post-glacial rebound : Yang Zhi-gen Shanghai Observatory, Chinese Academy of Sciences, Shanghai 200030

The renormalized effective action of a free scalar field propagating in the Bianchi type I spacetime is examined. As it contains higher-order derivatives of the metric the Hamiltonian structure of the theory will be changed. Thus, to obtain the self-consistent solution of the semiclassical gravity theory the method of iterative reduction is used to reduce it to a second-order equation. We solve the reduced equation and see that the space anisotropy, which will be smoothed out during the evolution of Universe, may play important role in the dynamics of early Universe. To investigate the behavior of space anisotropy in the early Universe we then quantize the corresponding minisuperspace. The associated Wheeler-DeWitt equation is solved in the WKB approximation and, from the solution, it is seen that the most probable state of the Bianchi type I spacetime is that with a small anisotropy.

Back reaction in semiclassical gravity: The Einstein-Langevin equation.

Using the influence functional formalism we show how to derive a generalized Einstein equation in the form of a Langevin equation for the description of the back reaction of quantum fields and their fluctuations on the dynamics of curved spacetimes. We show how a functional expansion on the influence functional gives the cumulants of the stochastic source, and how these cumulants enter in the equations of motion as noise sources. We derive an expression for the influence functional in terms of the Bogolubov coefficients governing the creation and annihilation operators of the Fock spaces at different times, thus relating it to the difference in particle creation in different histories. We then apply this to the case of a free quantum scalar field in a spatially flat Friedmann-Robertson-Walker universe and derive the Einstein-Langevin equations for the scale factor for these semiclassical cosmologies. This approach based on statistical field theory extends the conventional theory of semiclassical gravity based on a semiclassical Einstein equation with a source given by the average value of the energy-momentum tensor, thus making it possible to probe into the statistical properties of quantum fields such as noise, fluctuations, entropy, decoherence, and dissipation. Recognition of the stochastic nature of semiclassical gravity is an essential step towards the investigation of the behavior of fluctuations, instability, and phase transition processes associated with the crossover to quantum gravity.

Chronology protection and quantized fields: Nonconformal and massive scalar fields in Misner space.

In the absence of an adequate theory of quantum gravity, the search for a mechanism of ``chronology protection'' is currently focused on the vacuum energy divergence of quantized matter fields at chronology horizons and its back reaction on the metric via the semiclassical theory of gravity. The divergence of the vacuum energy at the chronology horizon was first demonstrated by Hiscock and Konkowski for a conformal massless scalar field in the Misner space. In this paper, we extend this earlier work to calculate the vacuum stress-energy tensor of a massive nonconformally coupled scalar field in Misner space. We find that the asymptotic behavior of 〈${\mathit{T}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}$〉 as it diverges at the chronology horizon is, to leading order, independent of the curvature coupling and mass of the scalar field. Thus the vacuum energy of nonconformal and/or massive scalar fields diverges with the same strength as the massless conformal case. Since one important aspect of gravity is its nonconformal nature, this suggests that quantum gravity may be unable to act as the protector of chronology.

Semiclassical gravity theory and quantum fluctuations.

We discuss the limits of validity of the semiclassical theory of gravity in which a classical metric is coupled to the expectation value of the stress tensor. It is argued that this theory is a good approximation only when the fluctuations in the stress tensor are small. We calculate a dimensionless measure of these fluctuations for a scalar field on a flat background in particular cases, including squeezed states and the Casimir vacuum state. It is found that the fluctuations are small for states which are close to a coherent state, which describes classical behavior, but tend to be large otherwise. We find in all cases studied that the energy density fluctuations are large whenever the local energy density is negative. This is taken to mean that the gravitational field of a system with negative energy density, such as the Casimir vacuum, is not described by a fixed classical metric but is undergoing large metric fluctuations. We propose an operational scheme by which one can describe a fluctuating gravitational field in terms of the statistical behavior of test particles. For this purpose we obtain an equation of the form of the Langevin equation used to describe Brownian motion.

Adiabatic regularization of the quantum stress-energy tensor in curved spacetimes: Stochastic quantization method.

It is found that the adiabatic regularized quantum stress-energy tensor for matter in any background spacetime can be obtained in the framework of stochastic quantization. As an illustration, we investigate the modes of a massive scalar field with arbitrary curvature coupling to the inhomogeneous conformally flat spacetime. The difficulty of the mode-mixing behavior arising from the spacetime inhomogeneity is overcome and a simple algorithm is presented to evaluate the adiabatic regularized quantum stress-energy tensor. The expressions so obtained are useful in formulating the semiclassical theory of gravity and in the numerical study of the back-reaction effects of quantized fields in inhomogeneous spacetimes, such as the problems of homogenization in the early universe and the evaporation of a quantum black hole. It can be seen that our prescriptions may be extended to investigate more realistic models with fermions and gauge fields. This will be studied in future papers.

No Starobinsky inflation from self-consistent semiclassical gravity.

The same theory of semiclassical gravity that predicts Starobinsky inflation (de Sitter-like solutions driven only by higher-order curvature terms) also predicts flat space to be unstable to small perturbations. When semiclassical gravity is modified in a way suggested by and consistent with the perturbative nature of its derivation, flat space is predicted to be stable, in accord with observation, but Starobinsky inflation is no longer a solution. The modified semiclassical theory, constrained to only solutions perturbatively expandable in {h bar}, has the same dynamical degrees of freedom as the clasical gravitational field, despite the presence of fourth-order derivatives in the field equations. There are no de Sitter or de Sitter-like self-consistent solutions except in the presence of a cosmological constant, so inflation generated purely by curvature is not predicted. Furthermore, linearized gravitational perturbations in a de Sitter background (with a cosmological constant) show no signs of instability from quantum effects.

Renormalization of the quantum stress-energy tensor in inhomogeneous spacetimes: Adiabatic regularization method.

The adiabatic regularization method, known to be a particularly efficient method for numerical study of quantum field dynamics in curved spacetimes, is applicable to evaluate the renormalized stress-energy tensor for matter in any background metric which has sufficient symmetry to allow a decomposition of the quantized field into modes. In this paper we extend this method to more general spacetimes with a small inhomogeneity which is invariant under spatial reflection. We over-come the difficulty of the mode-mixing behavior arising from the inhomogeneity of spacetime and show a possible way of obtaining the WKB solution of the time-dependent mode function under the early-time approximation. As an illustration, we investigate the renormalization of the quantum stress-energy tensor for a massive scalar field with an arbitrary curvature coupling to the inhomogeneous conformally flat spacetime. Our expressions are useful in formulating the semiclassical theory of gravity and in the numerical study of the back reaction of quantized fields in the early Universe with a small inhomogeneity.