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Alexandre T. Filippov

Publications and source records attributed to Alexandre T. Filippov.

9 recordsLinked to original sources
arXiv2019

Constructing and solving cosmologies of early universes with dark energy and matter. I

The main purpose of this paper is to advance a unified theory of dark matter, dark energy, and inflation first formulated in 2008. Our minimal affine extension of the GR has geodesics coinciding with the pseudo Riemannian ones, up to parameterizations. It predicts a `sterile' massive vecton and depends on two new dimensional constants, which can be measured in the limit of small vecton velocity. In a special gauge, this velocity has an upper limit near which it grows to infinity. The linearized vecton theory is similar to the scalar models of inflation except the fact of internal anisotropy of the vecton. For this reason we study general solutions of scalar analogs of the vecton theory without restricting the curvature parameter and anisotropy by using previously derived exact solutions as functions of the metric. It is shown that the effects of curvature and anisotropy fast decrease in expanding universes. Our approach can be applied to anisotropic universes, which is demonstrated on an exactly solvable strongly anisotropic cosmology. To characterize different cosmological scenarios in detail we introduce three characteristic functions, two of which are small and almost equal during inflation and grow near the exit. Instead of the potential it is possible to use one of the two characteristic functions. This allows to approximately derive flat isotropic universes with `prescribed' scenarios, which is the essence of our constructive cosmology of early universes. The most natural application of our approach is in analytically constructing characteristic functions of inflationary models with natural exits. However, the general construction can be applied to other problems, e.g., to evolution of contracting universes.

gr-qc↗
arXiv2015

On solving dynamical equations in general homogeneous isotropic cosmologies with scalaron

We study general dynamical equations describing homogeneous isotropic cosmologies coupled to a scalaron $ψ$. For flat cosmologies ($k=0$), we analyze in detail the gauge-independent equation describing the differential, $χ(α)\equivψ^\prime(α)$, of the map of the metric $α$ to the scalaron field $ψ$, which is the main mathematical characteristic locally defining a `portrait' of a cosmology in `$α$-version'. In the `$ψ$-version', a similar equation for the differential of the inverse map, $\barχ(ψ)\equiv χ^{-1}(α)$, can be solved asymptotically or for some `integrable' scalaron potentials $v(ψ)$. In the flat case, $\barχ(ψ)$ and $χ(α)$ satisfy the first-order differential equations depending only on the logarithmic derivative of the potential. Once we know a general analytic solution for one of these $χ$-functions, we can explicitly derive all characteristics of the cosmological model. In the $α$-version, the whole dynamical system is integrable for $k\neq 0$ and with any `$α$-potential', $\bar{v}(α)\equiv v[ψ(α)]$, replacing $v(ψ)$. There is no a priori relation between the two potentials before deriving $χ$ or $\barχ$, which implicitly depend on the potential itself, but relations between the two pictures can be found by asymptotic expansions or by inflationary perturbation theory. Explicit applications of the results to a more rigorous treatment of the chaotic inflation models and to their comparison with the ekpyrotic-bouncing ones are outlined in the frame of our `$α$-formulation' of isotropic scalaron cosmologies. In particular, we establish an inflationary perturbation expansion for $χ$. When all the conditions for inflation are satisfied and $χ$ obeys a certain boundary (initial) condition, we get the standard inflationary parameters, with higher-order corrections.

gr-qc↗
arXiv2013

Unified description of cosmological and static solutions in affine generalized theories of gravity: vecton - scalaron duality and its applications

We briefly describe the simplest class of affine theories of gravity in multidimensional space-times with symmetric connections and their reductions to two-dimensional dilaton - vecton gravity field theories (DVG). The distinctive feature of these theories is the presence of an absolutely neutral massive (or tachyonic) vector field (vecton) with essentially nonlinear coupling to the dilaton gravity (DG). We show that in DVG the vecton field can be consistently replaced by an effectively massive scalar field (scalaron) with an unusual coupling to dilaton gravity. With this vecton - scalaron duality, one can use methods and results of the standard DG coupled to usual scalars (DGS) in more complex dilaton - scalaron gravity theories (DSG) equivalent to DVG. We present the DVG models derived by reductions of multidimensional affine theories and obtain one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully applicable to studying static and cosmological solutions in multidimensional theories as well as in general one-dimensional DGS models. We focus on global properties of the models, look for integrals and analyze the structure of the solution spaces. In integrable cases, it can be usefully visualized by drawing a `topological portrait' resembling phase portraits of dynamical systems and simply exposing global properties of static and cosmological solutions, including horizons, singularities, etc. For analytic approximations we also propose an integral equation well suited for iterations.

hep-th↗
arXiv1998

Quantization of the String Inspired Dilaton Gravity and the Birkhoff Theorem

We develop a simple scheme of quantization for the dilaton CGHS model without scalar fields, that uses the Gupta-Bleuler approach for the string fields. This is possible because the constraints can be linearized classically, due to positivity conditions that are present in the model (and not in the general string case). There is no ambiguity nor anomalies in the quantization. The expectation values of the metric and dilaton fields obey the classical requirements, thus exhibiting at the quantum level the Birkhoff theorem.

hep-th↗
arXiv1997

The Birkhoff Theorem in the Quantum Theory of Two-Dimensional Dilaton Gravity

In classical two-dimensional pure dilaton gravity, and in particular in spherically symmetric pure gravity in d dimensions, the generalized Birkhoff theorem states that, for a suitable choice of coordinates, the metric coefficients are only functions of a single coordinate. It is interesting to see how this result is recovered in quantum theory by the explicit construction of the Hilbert space. We examine the CGHS model, enforce the set of auxiliary conditions that select physical states a` la Gupta-Bleuler, and prove that the matrix elements of the metric and of the dilaton field obey the classical requirement. We introduce the mass operator and show that its eigenvalue is the only gauge invariant label of states. Thus the Hilbert space is equivalent to that obtained by quantum mechanical treatment of the static case. This is the quantum form of the Birkhoff theorem for this model.

hep-th↗
arXiv1995

Quantization of the Schwarzschild Black Hole

We quantize by the Dirac - Wheeler-DeWitt method the canonical formulation of the Schwarzschild black hole developed in a previous paper. We investigate the properties of the operators that generate rigid symmetries of the Hamiltonian, establish the form of the invariant measure under the rigid transformations, and determine the gauge fixed Hilbert space of states. We also prove that the reduced quantization method leads to the same Hilbert space for a suitable gauge fixing.

gr-qc↗
arXiv1994

Hamiltonian Formalism for Black Holes and Quantization

Starting from the Lagrangian formulation of the Einstein equations for the vacuum static spherically symmetric metric, we develop a canonical formalism in the radial variable $r$ that is time--like inside the Schwarzschild horizon. The Schwarzschild mass turns out to be represented by a canonical function that commutes with the $r$--Hamiltonian. We investigate the Wheeler--DeWitt quantization and give the general representation for the solution as superposition of eigenfunctions of the mass operator.

gr-qc↗
arXiv1994

A Schrodinger Equation for Quantum Universes

We discuss how to fix the gauge in the canonical treatment of Lagrangians, with finite number of degrees of freedom, endowed with time reparametrization invariance. The motion can then be described by an effective Hamiltonian acting on the gauge shell canonical space. The system is then suited for quantization. We apply this treatment to the case of a Robertson--Walker metric interacting with zero modes of bosonic fields and write a §equation for the on--shell wave function (Presented at the International Workshop ``Birth of the Universe and Fundamental Physics'', Rome, May 18-21, 1994).

gr-qc↗
arXiv1994

A SCHRÖdinger Equation for Mini Universes

We discuss how to fix the gauge in the canonical treatment of Lagrangians, with finite number of degrees of freedom, endowed with time reparametrization invariance. The motion can then be described by an effective Hamiltonian acting on the gauge shell canonical space. The system is then suited for quantization. We apply this treatment to the case of a Robertson--Walker metric interacting with zero modes of bosonic fields and write a §equation for the on--shell wave function.

gr-qc↗