Thermal and Dynamical Particle Creation in a Curved Geometry.pdf

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Thermal and Dynamical Particle Creation in a Curved Geometry.pdf

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Thermal and Dynamical Particle Creation in a Curved Geometry

a r X i v : h e p - t h / 9 6 1 0 1 1 6 v 1 1 6 O c t 1 9 9 6 THERMAL AND DYNAMICAL PARTICLE CREATION IN A CURVED GEOMETRY Carlos E. Laciana Instituto de Astronom??a y F??sica del Espacio Casilla de Correo 67 - Sucursal 28, 1428 Buenos Aires, Argentina E-mail: laciana@iafe.uba.ar Abstract A generalization of Termo Field Dynamics to a curved geometry is proposed. In particular a neutral scalar field minimally coupled to gravity is considered as matter content in a Robertson-Walker metric. A non linear amplification in the particle creation is obtained, due to the altogether action of thermal and geometric effects. As a consequence the frequencies in the system look like red shifted with respect to the case where the thermal creation is not taken into account. 1. Introduction A realistic description of the dynamics of our universe must take into account all the possible interactions. But that is practically impossible. An approach that we can used is to separate the universe in system and enviroment. Then we supouse degrees of freedom with different hierarchy, some of them considered as quantum degrees of freedom and the other ones constitute the classical background. The interaction between both kinds of degrees of freedom can be produced through the changes in the spacetime which are driven by the dynamical Einstein equations and by spontaneous thermal fluctuations of the enviroment which acts as a thermal reservoir. In the cosmological semiclassical approach (see ref. [1]) the role of the classical background is played by the gravitational field. This background can also play the role of thermal reservoir, as is shown in ref. [2] and the conformal quantum thermal fluctuation of the gravitational field can be interpreted as the tilde fields of the formalism of Thermo Field Dynamics (TFD) [3]. However the tilde fields “inhabit” also in a curved geometry, then they are also affected by the changes in 1 the metric. So we will consider a matter field in a thermal b