On the Adiabatic Expansion of the Visible Space in a Higher-Dimensional Cosmology

Abstract

In the context of higher-dimensional cosmologies we study the conditions under which adiabatic expansion of the visible external space is possible, when a time-dependent internal space is present. The analysis is based on a reinterpretation of the four-dimensional stress-energy tensor in the presence of the extra dimensions. This modifies the usual adiabatic energy conservation laws for the visible Universe, leading to a new type of cosmological evolution which includes large-scale entropy production in four dimensions.

Higher-dimensional models in gravitational theories of quartic Lagrangians

“…Thus, the external space is radiation-dominated, while the internal one is pressureless. It has been recently shown that, in this case, the two subspaces are completely disjoint 4,31 . The time-evolution of the total mass-energy density ρ is accordingly given by Eq.(2.7).…”

On spinless null propagation in five-dimensional space-times with approximate space-like Killing symmetry

“…In this context, q/c 2 represents a conversion constant between the gravitational and the electromagnetic field. The 5D field equations imply that A μ (i.e., N μ ) satisfy Maxwell-type equations [8][9][10].…”

“…First, studies of field equations (e.g., see [8][9][10]) and geodesic motion [6,8] claimed that the existence of extra dimensions manifests as new physics in ordinary 4D spacetime. The relationship between geodesic motion and the classical tests of general relativity adapted for 5D space-times may be found in Ref.…”

“…Geodesic propagation in five dimensional (5D) space-times remains, lately, a topic of great interest [1][2][3][4][5][6][7][8]. Particular attention has be devoted to 5D space-times, with a space-like fifth dimension which is neither compact nor Planckian, where the metric is independent of the fifth dimension [7][8][9][10]. It has been shown that, in this case, 5D null-path propagation may be interpreted as anomaly-free 4D propagation both in the classical and quantum regimes [7,8,11,12].…”

Particle creation, renormalizability conditions and the mass-energy spectrum in gravity theories of quadratic Lagrangians

“…Indeed, the metric ( 6) is an exact solution of the classical gravitational field equations when the pressure of the internal (one-dimensional) space equals to zero (p int = 0). According to Kleidis and Papadopoulos (1997a), as regards the thermodynamical description of two subspaces (the external space and the internal one), this condition corresponds to an adiabaticity criterion and therefore, no radiation (massless particles) is allowed to be transfered from one space to the other. Both subspaces represent closed thermodynamical systems (see also Prigogine et al 1989).…”