De sitter space and perpetuum mobile
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ELEMENTARY PARTICLES AND FIELDS Theory
De Sitter Space and Perpetuum Mobile* Emil T. Akhmedov1), 2) , P. V. Buividovich1), 3) , and Douglas A. Singleton4), 5) Received March 18, 2011; in final form, October 3, 2011
Abstract—The general arguments that any interacting nonconformal classical field theory in de Sitter space leads to the possibility of constructing a perpetuum mobile is given. The arguments are based on the observation that massive free falling particles can radiate other massive particles on the classical level as seen by the free falling observer. The intensity of the radiation process is not zero even for particles with any finite mass, i.e., with a wavelength which is within causal domain. Hence, we conclude that either de Sitter space cannot exist eternally or that one can build a perpetuum mobile. DOI: 10.1134/S1063778812040023
1. INTRODUCTION It is generally believed that de Sitter space is stable at least on the classical level. The belief relies on the following arguments: (i) de Sitter space has a big isometry group [1, 2]; (ii) there are no exponentially growing linearized fluctuations over de Sitter space [3]. The question is whether these arguments are sufficient to prove the classical stability of de Sitter space. In this note we argue that the answer on this question is negative. Indeed, the situation changes if one turns on interactions. Let us ask the following question of a classical6) interacting field theory on de Sitter background: “Does an inertially moving charged particle in de Sitter space emit radiation or not?” Because the space in question is conformally flat, we consider a field theory which is not conformaly invariant, otherwise the behavior of fields is not much different from fields in Minkowski space. amplitude7)
of the corCalculating the classical responding process and observing that it is not zero, we obtain an affirmative answer to the above question.
Our point is that even in a classical field theory on de Sitter space, massive particles can radiate other massive particles with a wavelength within the causal domain. Quantum particle production by another particle in de Sitter space was addressed in [4–7]. Classical electromagnetic radiation was considered in [8, 9]. On general physical grounds one can expect that the characteristic wavelength of the radiation of the massless fields and the wave creation length in such a process are of the order of the size of the cosmological horizon. This is one of the reasons why we consider radiation of massive particles with wavelengths smaller than the cosmological horizon. Our main point in this paper is to show that there is a problem with the stability of de Sitter space even on the classical level—if the vacuum energy is truly fixed then one can create a perpetuum mobile. 2. FIELD THEORY IN DE SITTER SPACE The D-dimensional de Sitter space is a hyperboloid [1, 10, 2] −z02
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The text was submitted by the authors in English. Institute of Theoretical and Experimental Physics, Moscow, Russia. 2) Moscow Institute of Physics and Technology,
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