Leonard Parker

Non-gaussianities and the Stimulated creation of quanta in the inflationary universe

Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator ρ describing an initial mixed state that includes probabilities for nonzero numbers of scalar perturbations to be present at early times during inflation. We analyze the primordial bispectrum for general configurations of the three different momentum vectors in its arguments. We find that the initial presence of quanta can significantly enhance non-gaussianities in the so-called squeezed limit. Our results show that an observation of non-gaussianities in the squeezed limit can occur for single-field inflation when the state in the very early inflationary universe is not the vacuum, but instead contains early-time perturbations. Valuable information about the initial state can then be obtained from observations of those non-gaussianities.

Sudden gravitational transition

We investigate the properties of a cosmological scenario which undergoes a gravitational phase transition at late times. In this scenario, the Universe evolves according to general relativity in the standard, hot big bang picture until a redshift z < or approx. 1. Nonperturbative phenomena associated with a minimally-coupled scalar field catalyzes a transition, whereby an order parameter consisting of curvature quantities such as R{sup 2}, R{sub ab}R{sup ab}, R{sub abcd}R{sup abcd} acquires a constant expectation value. The ensuing cosmic acceleration appears driven by a dark-energy component with an equation-of-state w<-1. We evaluate the constraints from type 1a supernovae, the cosmic microwave background, and other cosmological observations. We find that a range of models making a sharp transition to cosmic acceleration are consistent with observations.

Renormalization in the theory of a quantized scalar field interacting with a robertson-walker spacetime

Abstract We demonstrate the possibility of removing the divergences in the energy-momentum tensor by identifying divergent terms with renormalizations of the coupling constants in the gravitational field equation, modified to include a cosmological term and terms quadratic in the curvature. The model studied is that of a classical Robertson-Walker metric and a quantized minimally coupled neutral scalar field. The theory is constructed first with an ultraviolet cutoff as a phenomenological ansatz. The cutoff is then removed in an attempt to obtain a more fundamental theory, whereupon the question arises of the covariance and uniqueness of the resulting renormalized energy-momentum tensor. In the case of a massless field in a spatially flat universe, an apparent infrared divergence is discussed from the point of view of operational determination of the renormalized coupling constants. In the other cases, although the divergences are successfully accounted for by renormalization, we are left with finite leading terms which do not appear to be identifiable with geometrical tensors; the significance of this result is under investigation. If these anomalous terms are dropped, the renormalized energy-momentum tensor agrees with that defined by adiabatic regularization, provided that the limit of slow time variation taken in that method is generalized to a limit of “spacetime flatness.”

Einstein equation with quantum corrections reduced to second order

We consider the Einstein equation with first-order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth-order derivatives of the metric, the solutions which are physically relevant satisfy reduced equations which contain derivatives no higher than second order. We obtain the reduced equations for a range of stress-energy tensors. These reduced equations are suitable for a numerical solution, are expected to contain fewer numerical instabilities than the original fourth-order equations, and yield only physically relevant solutions. We give analytic and numerical solutions or reduced equations for particular examples, including Friedmann-Lema\^{\i}tre universes with a cosmological constant, a spherical body of constant density, and more general conformally flat metrics.

Aspects of Quantum Field Theory in Curved Space-Time: Effective Action and Energy-Momentum Tensor

The theory of quantized fields in curved spacetime has reached a high level of development, and a number of important physical consequences have been predicted. By treating the metric of the gravitational field classically, one avoids the nonrenormalizability problems of quantized gravity, but nevertheless retains a wide domain of applicability. I have already given a recent review of quantized fields in curved spacetime [L. Parker, 1977], in which the creation of elementary particles by strong gravitational fields (as in cosmology and near black holes) was emphasized. The present lectures will emphasize material which was not covered in the previous review.

The Production of Elementary Particles by Strong Gravitational Fields

The creation of particles by gravitational fields is a natural consequence of quantum field theory in curved space-time. It occurs in particle-antiparticle pairs in the models considered, and does not violate the local conservation laws. This process has important consequences in cosmological and black hole metrics.

Stimulated creation of quanta during inflation and the observable universe

Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding stimulated creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave background and galaxy distribution can then tell us about the state of the universe that existed at the time when quantum field theory in curved spacetime first emerged as a plausible effective theory.

Semi-infinite throat as the end-state geometry of two-dimensional black hole evaporation

We study a modified two-dimensional dilaton gravity theory which is exactly solvable in the semiclassical approximation including back reaction. Infalling matter in an initially static radiationless spacetime forms a black hole if its energy is above a certain threshold. The black hole singularity is initially hidden behind a timelike apparent horizon. As the black hole evaporates by emitting Hawking radiation, the singularity meets the shrinking horizon in finite retarded time to become naked. A boundary condition exists at the naked singularity which preserves energy conservation, stability, and continuity of the metric and results in a unique end state for all evaporating black holes. The end-state geometry is static and asymptotically flat at its right spatial infinity, while its left spatial infinity is a semi-infinite throat extending into the strong coupling region. This end-state geometry is the ground state in our model.

Hawking radiation and unitary evolution.

We find a family of exact solutions to the semi-classical equations (including back-reaction) of two-dimensional dilaton gravity, describing infalling null matter that becomes outgoing and returns to infinity without forming a black hole. When a black hole almost forms, the radiation reaching infinity in advance of the original outgoing null matter has the properties of Hawking radiation. The radiation reaching infinity after the null matter consists of a brief burst of negative energy that preserves unitarity and transfers information faster than the theoretical bound for positive energy.

Revising the predictions of inflation for the cosmic microwave background anisotropies

We point out that, if quantum field renormalization is taken into account and the counterterms are evaluated at the Hubble-radius crossing time or few e-foldings after it, the predictions of slow-roll inflation for both the scalar and the tensorial power spectrum change significantly. This leads to a change in the consistency condition that relates the tensor-to-scalar amplitude ratio with spectral indices. A reexamination of the potentials varphi;{2} and varphi;{4} shows that both are compatible with five-year WMAP data. Only when the counterterms are evaluated at much larger times beyond the end of inflation does one recover the standard predictions. The alternative predictions presented here may soon come within the range of measurement of near-future experiments.