Igor V. Mishakov

Quantum origin of the early inflationary universe

Abstract We give a detailed presentation of a recently proposed mechanism of generating the energy scale of inflation by loop effects in quantum cosmology. We discuss the quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states and present a universal effective action algorithm for the distribution function of chaotic inflationary cosmologies in both of these states. The energy scale of inflation is calculated by finding a sharp probability peak in this distribution function for a tunnelling mode] driven by the inflaton field with large negative constant ξ of non-minimal interaction. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant H ≃ 10−5mp, its quantum width ΔH H ≃ 10 −5 and the number of inflationary e-foldings N ⩾ 60) are found to be in good correspondence with the observational status of inflation theory, provided the coupling constants of the theory are constrained by a condition which is likely to be enforced by the (quasi) supersymmetric nature of the sub-Planckian particle physics model.

One-Loop Amplitudes in Euclidean Quantum Gravity

This paper studies the linearized gravitational field in the presence of boundaries. For this purpose,

Euclidean Maxwell theory in the presence of boundaries. II

\zeta

Decoherence in quantum cosmology at the onset of inflation

-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of flat Euclidean four-space bounded by a three-sphere. On choosing the de Donder gauge-averaging term, the resulting

ζ-FUNCTION TECHNIQUE FOR QUANTUM COSMOLOGY: THE CONTRIBUTIONS OF MATTER FIELDS TO THE HARTLE-HAWKING WAVE FUNCTION OF THE UNIVERSE

\zeta(0)

Gravitons in one-loop quantum cosmology: Correspondence between covariant and noncovariant formalisms.

value is found to agree with the space-time covariant calculation of the same amplitudes, which relies on the recently corrected geometric formulas for the asymptotic heat kernel in the case of mixed boundary conditions. Two sets of mixed boundary conditions for Euclidean quantum gravity are then compared in detail. The analysis proves that one cannot restrict the path-integral measure to transverse-traceless perturbations. By contrast, gauge-invariant amplitudes are only obtained on considering from the beginning all perturbative modes of the gravitational field, jointly with ghost modes.

1-loop quantum cosmology: the contributions of matter fields to the wavefunction of the universe

-function regularization is applied to complete a recent analysis of the quantized electromagnetic field in the presence of boundaries. The quantum theory is studied by setting to zero on the boundary the magnetic field, the gauge-averaging functional, and hence the Faddeev--Popov ghost field. Electric boundary conditions are also studied. On considering two gauge functionals which involve covariant derivatives of the 4-vector potential, a series of detailed calculations shows that, in the case of flat Euclidean 4-space bounded by two concentric 3-spheres, one-loop quantum amplitudes are gauge independent and their mode-by-mode evaluation agrees with the covariant formulae for such amplitudes and coincides for magnetic or electric boundary conditions. By contrast, if a single 3-sphere boundary is studied, one finds some inconsistencies, i.e. gauge dependence of the amplitudes.

SPIN-

Abstract We calculate the reduced density matrix for the inflaton field in a model of chaotic inflation by tracing out degrees of freedom corresponding to various bosonic fields. Apart from the standard decoherence factor there also arises a contribution from the Euclidean effective action of quantum fields. We regularise the ultraviolet divergences in the decoherence factor. Dimensional regularisation does not work because it would lead to a density matrix which does not define a bounded operator. A conformal redefinition of the environmental fields leads to a bounded density matrix. This redefinition is essentially fixed by the requirement that decoherence be absent for vanishing particle creation. Off-diagonal elements of the reduced density matrix become negligibly small for non-conformally invariant fields, so that due to bosonic fields the Universe can acquire classical properties near the onset of inflation.

\frac{3}{2}

We investigate the contributions of matter fields to the Hartle-Hawking wave function of the Universe in the one-loop approximation. The values ζ(0), which describe the scaling behavior of the wave function calculated on the background representing the part of four-dimensional DeSitter sphere, are calculated for scalar, electromagnetic, graviton, spin-1/2 and spin-3/2 fields. The ζ-function technique is used and developed for these calculations. The obtained results can be applied to a detailed investigation of the structure of the Hartle-Hawking wave function.

POTENTIALS IN BACKGROUNDS WITH BOUNDARY

The discrepancy between the results of covariant and noncovariant one-loop calculations for higher-spin fields in quantum cosmology is analyzed. A detailed mode-by-mode study of perturbative quantum gravity about a flat Euclidean background bounded by two concentric three-spheres, including nonphysical degrees of freedom and ghost modes, leads to one-loop amplitudes in agreement with the covariant Schwinger-DeWitt method. This calculation provides the generalization of a previous analysis of fermionic fields and electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a well-defined 3+1 decomposition.