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The conservation of energy-momentum and the mass for the graviton
In this work we give special attention to the bimetric theory of gravitation
with massive gravitons proposed by Visser in 1998. In his theory, a prior
background metric is necessary to take in account the massive term. Although in
the great part of the astrophysical studies the Minkowski metric is the best
choice to the background metric, it is not possible to consider this metric in
cosmology. In order to keep the Minkowski metric as background in this case, we
suggest an interpretation of the energy-momentum conservation in Visser's
theory, which is in accordance with the equivalence principle and recovers
naturally the special relativity in the absence of gravitational sources.
Although we do not present a general proof of our hypothesis we show its
validity in the simple case of a plane and dust-dominated universe, in which
the `massive term' appears like an extra contribution for the energy density.Comment: 9 pages, accepted for publishing in GR
as parameter of Minkowski metric in effective theory
With the proper choice of the dimensionality of the metric components, the
action for all fields becomes dimensionless. Such quantities as the vacuum
speed of light c, the Planck constant \hbar, the electric charge e, the
particle mass m, the Newton constant G never enter equations written in the
covariant form, i.e., via the metric g^{\mu\nu}. The speed of light c and the
Planck constant are parameters of a particular two-parametric family of
solutions of general relativity equations describing the flat isotropic
Minkowski vacuum in effective theory emerging at low energy:
g^{\mu\nu}=diag(-\hbar^2, (\hbar c)^2, (\hbar c)^2, (\hbar c)^2). They
parametrize the equilibrium quantum vacuum state. The physical quantities which
enter the covariant equations are dimensionless quantities and dimensionful
quantities of dimension of rest energy M or its power. Dimensionless quantities
include the running coupling `constants' \alpha_i; topological and geometric
quantum numbers (angular momentum quantum number j, weak charge, electric
charge q, hypercharge, baryonic and leptonic charges, number of atoms N, etc).
Dimensionful parameters include the rest energies of particles M_n (or/and mass
matrices); the gravitational coupling K with dimension of M^2; cosmological
constant with dimension M^4; etc. In effective theory, the interval s has the
dimension of 1/M; it characterizes the dynamics of particles in the quantum
vacuum rather than geometry of space-time. We discuss the effective action, and
the measured physical quantities resulting from the action, including
parameters which enter the Josepson effect, quantum Hall effect, etc.Comment: 18 pages, no figures, extended version of the paper accepted in JETP
Letter
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