2005

DOI: 10.1007/s11182-005-0113-2

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Thermodynamics of the Early Universe

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Cited by 5 publications

(4 citation statements)

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“…Originality and irreversibility of time are due to the originality and irreversibility of the processes of tunneling of the Planckian particle and production of matter during decay of the Lemaître primordial atom [11]. Homogeneity of space and time underlying the laws of conservation of energy and momentum is due to constancy of the scalar-field potential energy ( )…”

Section: A C C a A C Cmentioning

confidence: 99%

The causality principle in relativistic gravitation theory

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2007

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“…Originality and irreversibility of time are due to the originality and irreversibility of the processes of tunneling of the Planckian particle and production of matter during decay of the Lemaître primordial atom [11]. Homogeneity of space and time underlying the laws of conservation of energy and momentum is due to constancy of the scalar-field potential energy ( )…”

Section: A C C a A C Cmentioning

confidence: 99%

The causality principle in relativistic gravitation theory

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2007

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“…Φ ϑ = Φ Φ ϑ satisfy the equation similar to the first thermodynamics law[6] The amplitude of ( ) C l versus odd harmonic number l = (solid curve) and ( )…”

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confidence: 97%

Anisotropy of a relict scalar field

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2009

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It is shown that anisotropy of relict radiation can be caused by anisotropy of a relict scalar field, and largescale structures of the relict scalar field can lead to large-scale structures of baryon matter.

“…It follows from Eqs. (5) and (6) that the relation between the initial variables , x p and new variables , J ϑ depends on the equations…”

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confidence: 99%

“…Earlier, in [5], a gravitational analog of the classical Liouville equation describing the Universe filled with a constant, homogeneous, negative scalar field was derived. Its exact solution was found, which is largely similar to solution (14).…”

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confidence: 99%

Spontaneous violation of symmetry of the classical Liouville equation

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2007

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An exact solution to the classical Liouville equation is derived. It is found that it can have a partial solution with a broken symmetry with respect to time. Thus, in the general case, it does not follow from the invariance of the fundamental Liouville law concerning time reversal that the past and future play similar roles.It is believed that the Liouville equation cannot describe irreversible processes, since the equation is reversible. Generally, this is not the case. For example, one knows a means for introducing of the gauge field mass through its interaction with a scalar field of matter. This method is based on the so-called mechanism of spontaneous symmetry violation. This is violation of symmetry of the solution rather than that of the Lagrangian, and, hence, of the differential equation [1].In this connection, we will show that the Liouville equation reversible with respect to time can have a partial solution whose symmetry is violated with respect to time. To this end, we will study a heated oscillator in terms of the classical Liouville equation.At present, individual quantum objects have become the subject of experimental studies (one electron in a magnetic trap, one-electron devices). Therefore, interpretation of a wave function as an ensemble becomes unnecessary. We discard this in the classical theory as well.We assume that within the classical theory a state can be attributed to a particle only with a certain probability, that is, by analogy with quantum theory, the dynamic processes of one classical particle will be treated as probable rather than the ensemble of the particle replicas. To do so, we postulate the distribution function ( ) , , f x p t using no principle of abridged description [2]. The function is proportional to the probability density of location of the particle in the phase space ( ) , x p at the time t.

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