CMBR anisotropy: Theoretical approaches
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TESTS OF NEW PHYSICS IN RARE PROCESSES AND COSMIC RAYS (Elementary Particles and Fields: Theory)
CMBR Anisotropy: Theoretical Approaches* B. M. Barbashov1), V. N. Pervushin1)** , A. F. Zakharov1), 2), 3), 4) , and V. A. Zinchuk1) Received November 23, 2005
Abstract—A version of the cosmological perturbation theory based on exact resolution of the energy constraint is developed. In this version, the conformal time is invariant with respect to the diffeomorphisms of general relativity, and the scalar perturbations are the potential ones in accordance with the Dirac minimal surface constraint. The exact resolution gives one a possibility to fulfill the Hamiltonian reduction and to explain the “CMBR primordial power spectrum” and other problems of modern cosmology by quantization of the energy constraint and cosmological creation of matter. PACS numbers : 98.80.Bp DOI: 10.1134/S1063778807010243
1. INTRODUCTION One of the basic tools applied for analysis of modern observational data including cosmological microwave background radiation (CMBR) is the cosmological perturbation theory in general relativity (GR) [1, 2]. The main role in this perturbation theory is played by the separation of the cosmological scale factor by the transformation gµν = a2 g µν . In the present paper, we discuss the problem of the relation between the cosmological perturbation theory [1, 2] and the Hamiltonian approach [3, 4] to GR, where the similar scale factor a was considered in [5– 7] as the homogeneous invariant evolution parameter in accordance with the Hamiltonian diffeomorphism 0 = x 0 (x0 ) [8], meaning in fact that subgroup x0 → x the coordinate evolution parameter x0 is not observable. The content of the paper is the following. In Section 2, the status of the cosmological perturbation theory in GR is described. In Section 3, the Hamiltonian approach is formulated in a finite spacetime. In Section 4, a number of variables and constraints are discussed. Section 5 is devoted to the cosmological
model that follows from the Einstein correspondence principle as low-energy expansion of the reduced theory. The applications and a comparison of the Hamiltonian theory with Lifshitz’s one are given Sections 6 and 7, respectively. 2. STATUS OF COSMOLOGICAL PERTURBATION THEORY The Einstein GR is given by the Hilbert action ϕ20 4 √ S[ϕ0 ] = d x −g − R(g) + L(M) (ϕ0 |g, f ) 6 (1) and the spacetime geometric interval ds2 = gµν dxµ dxν , where the fundamental parameter 2 /(8π) (2) ϕ0 = 3/(8πG0 ) = 3MPl scales all masses, and G0 is the Newton coupling constant. The Hamiltonian approach to GR is formulated by means of a geometric interval ds2 = gµν dxµ dxν ≡ ω(0) ω(0) − ω(1) ω(1)
The text was submitted by the authors in English. Bogolyubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia. 2) National Astronomical Observatories of CAS, Beijing, China. 3) Institute of Theoretical and Experimental Physics, Bol’shaya Cheremushkinskaya ul. 25, Moscow, 117259 Russia. 4) Astro Space Center
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