arXiv subjects

A. Yu. Kamenshchik

Publications and source records attributed to A. Yu. Kamenshchik.

68 records · Page 4Linked to original sources

arXiv1998

Effective equations of motion and initial conditions for inflation in quantum cosmology

We obtain effective equations of inflationary dynamics for the mean inflaton and metric fields in the no-boundary and tunneling quantum states of the Universe. In the slow roll approximation (taking the form of the local Schwiger-DeWitt expansion) effective equations follow from the Euclidean effective action on the DeSitter gravitational instanton. Effective equations are applied in the model of the inflaton scalar field coupled to the GUT sector of matter fields and also having a strong nonminimal coupling to the curvature. The inverse of its big negative nonminimal coupling constant, serves as a small parameter of the slow roll expansion and semiclassical expansion of quantum gravitational effects. As a source of initial conditions we use a sharp probability peak recently obtained in the one-loop approximation for the no-boundary and tunneling quantum states and belonging (in virtue of a strong nonminimal coupling) to the GUT energy scale much below the Planck scale. The obtained equations in the tunneling quantum state predict a finite duration of inflationary stage compatible with the observational status of inflation theory, whereas for the no-boundary state they lead to the infinite inflationary epoch with a constant inflaton field.

hep-th↗

arXiv1998

Simplest cosmological model with the scalar field II. Influence of cosmological constant

Continuing the investigation of the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity we study an influence of the cosmological constant on the behaviour of trajectories in closed minisuperspace Friedmann-Robertson-Walker model. The transition from chaotic to regular behaviour for large values of cosmological constant is discussed. Combining numerical calculations with qualitative analysis both in configuration and phase space we present a convenient classification of trajectories.

gr-qc↗

arXiv1998

Simplest cosmological model with the scalar field

We investigate the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity. The classification of trajectories in closed minisuperspace Friedmann-Robertson-Walker model is presented.The fractal nature of a set of infinitely bounced trajectories is discussed. The results of numerical calculations are compared with those obtained byperturbative analytical calculations around the exactly solvable minisuperspace cosmological model with massless scalar field.

gr-qc↗

arXiv1998

Complex inflaton field in quantum cosmology

We investigate the cosmological model with the complex scalar self-interacting inflaton field non-minimally coupled to gravity. The different geometries of the Euclidean classically forbidden regions are represented. The instanton solutions of the corresponding Euclidean equations of motion are found by numerical calculations supplemented by the qualitative analysis of Lorentzian and Euclidean trajectories. The applications of these solutions to the no-boundary and tunneling proposals for the wave function of the Universe are studied. Possible interpretation of obtained results and their connection with inflationary cosmology is discussed. The restrictions on the possible values of the new quasi-fundamental constant of the theory-non-zero classical charge-- are obtained. The equations of motion for the generalized cosmological model with complex scalar field are written down and investigated. The conditions of the existence of instanton solutions corresponding to permanent values of an absolute value of scalar field are obtained.

gr-qc↗

arXiv1996

Quantum origin of the early inflationary Universe

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 tunneling 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 tunneling model 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 $H\simeq 10^{-5}m_P$, its quantum width $ΔH/H\simeq 10^{-5}$ and the number of inflationary e-foldings $N\geq 60$) 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.

gr-qc↗

arXiv1996

Hamiltonian BFV-BRST theory of closed quantum cosmological models

We introduce and study a new discrete basis of gravity constraints by making use of harmonic expansion for closed cosmological models. The full set of constraints is splitted into area-preserving spatial diffeomorphisms, forming closed subalgebra, and Virasoro-like generators. Operatorial Hamiltonian BFV-BRST quantization is performed in the framework of perturbative expansion in the dimensionless parameter which is a positive power of the ratio of Planckian volume to the volume of the Universe. For the (N+1) - dimensional generalization of stationary closed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out, that certain relationship between dimensionality of the space and the spectrum of matter fields emerges from the requirement of quantum consistency of the model.

hep-th↗

arXiv1996

Rarita-Schwinger Potentials in Quantum Cosmology

This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional Riemannian backgrounds with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing the background is Ricci-flat, in agreement with previous results in the literature. However, the preservation of boundary conditions under such gauge transformations leads to a restriction of the gauge freedom. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then applied. The equations for the secondary potentials, jointly with the boundary conditions, imply that the background four-geometry is further restricted to be totally flat.

gr-qc↗

arXiv1995

Quantum Origin of the Early Universe and the Energy Scale of Inflation

Quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states is considered in the one-loop approximation of quantum cosmology. A universal effective action algorithm for the distribution function of chaotic inflationary cosmologies is derived for both of these states.The energy scale of inflation is calculated by finding a sharp probability peak in this distribution function for a tunnelling model driven by the inflaton field with large negative constant $ξ$ of nonminimal interaction. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant ${\mbox{\boldmath $H$}}\simeq 10^{-5}m_P$, its quantum width $Δ{\mbox{\boldmath $H$}}/{\mbox{\boldmath $H$}}\simeq 10^{-5}$ and the number of inflationary e-foldings ${\mbox{\boldmath $N$}}\simeq 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.

gr-qc↗

arXiv1995

Non-minimally coupled complex scalar field in classical and quantum cosmology

We investigate the cosmological model with complex scalar self-interacting inflaton field non-minimally coupled to gravity. The different geometries of the Euclidean classically forbidden regions are represented. The instanton solutions of the corresponding Euclidean equations of motion are found by numerical calculations. These solutions give a rather non-trivial examples of real tunnelling geometries. Possible interpretation of obtained results and their connection with inflationary cosmology is discussed.

gr-qc↗

arXiv1995

One-Loop Amplitudes in Euclidean Quantum Gravity

This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $ζ$-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 $ζ(0)$ 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.

gr-qc↗

arXiv1995

Relativistic Gauge Conditions in Quantum Cosmology

This paper studies the quantization of the electromagnetic field on a flat Euclidean background with boundaries. One-loop scaling factors are evaluated for the one-boundary and two-boundary backgrounds. The mode-by-mode analysis of Faddeev-Popov quantum amplitudes is performed by using zeta-function regularization, and is compared with the space-time covariant evaluation of the same amplitudes. It is shown that a particular gauge condition exists for which the corresponding operator matrix acting on gauge modes is in diagonal form from the beginning. Moreover, various relativistic gauge conditions are studied in detail, to investigate the gauge invariance of the perturbative quantum theory.

gr-qc↗

arXiv1994

Quantum scale of inflation and particle physics of the early universe

The quantum gravitational scale of inflation is calculated by finding a sharp probability peak in the distribution function of chaotic inflationary cosmologies driven by a scalar field with large negative constant $ξ$ of nonminimal interaction. In the case of the no-boundary state of the universe this peak corresponds to the eternal inflation, while for the tunnelling quantum state it generates a standard inflationary scenario. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant ${\mbox{\boldmath $H$}}\simeq 10^{-5}m_P$, its quantum width $Δ{\mbox{\boldmath $H$}}/{\mbox{\boldmath $H$}}\simeq 10^{-5}$ and the number of inflationary e-foldings ${\mbox{\boldmath $N$}}\simeq 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.

gr-qc↗

arXiv1993

Tunnelling geometries I. Analyticity, unitarity and instantons in quantum cosmology

We present a theory of tunnelling geometries originating from the no-boundary quantum state of Hartle and Hawking. We reformulate the no-boundary wavefunction in the representation of true physical variables and calculate it in the one-loop approximation. For this purpose a special technique is developed, which reduces the formalism of complex tunnelling geometries to the real ones, and also the method of collective variables is applied, separating the macroscopic collective degrees of freedom from the microscopic modes. The quantum distribution of Lorentzian universes, defined on the space of such collective variables, incorporates the probabilty conservation and represents the partition function of quasi-DeSitter gravitational instantons weighted by their Euclidean effective action. They represent closed compact manifolds obtained by the procedure of doubling the Euclidean spacetime which nucleates the Lorentzian universes. The over-Planckian behaviour of their distribution is determined by the anomalous scaling of the theory on such instantons, which serves as a criterion for the high-energy normalizability of the no-boudary wavefunction and the validity of the semiclassical expansion.

gr-qc↗

arXiv1993

The renormalization group for non-renormalizable theories: Einstein gravity with a scalar field

We develop a renormalization-group formalism for non-renormalizable theories and apply it to Einstein gravity theory coupled to a scalar field with the Lagrangian $L=\sqrt{g} [R U(ϕ)-{1/2} G(ϕ) g^{μν} \partial_μϕ\partial_νϕ- V(ϕ)]$, where $U(ϕ), G(ϕ)$ and $V(ϕ)$ are arbitrary functions of the scalar field. We calculate the one-loop counterterms of this theory and obtain a system of renormalization-group equations in partial derivatives for the functions $U, G$ and $V$ playing the role of generalized charges which substitute for the usual charges in multicharge theories. In the limit of a large but slowly varying scalar field and small spacetime curvature this system gives the asymptotic behaviour of the generalized charges compatible with the conventional choice of these functions in quantum cosmological applications. It also demonstrates in the over-Planckian domain the existence of the Weyl-invariant phase of gravity theory asymptotically free in gravitational and cosmological constants.

gr-qc↗