877 0015-9018/03/0600-0877/0 © 2003 Plenum Publishing Corporation Foundations of Physics, Vol. 33, No. 6, June 2003 (© 2003) The Global Arrow of Time as a Geometrical Property of the Universe Mario Castagnino, 1 Olimpia Lombardi, 2 and Luis Lara 3 1 CONICET, Instituto de Astronomía y Física del Espacio, Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires, Argentina; e-mail: mariocastagnino@citynet.net.ar 2 CONICET, Departamento de Filosofía de la Ciencia, Universidad Autónoma de Madrid, Ctra. Colmenar Km 15, 28049, Madrid, España; e-mail: olimpiafilo@arnet.com.ar 3 Departamento de Física, Universidad Nacional de Rosario, Av. Pellegrini 250, 2000, Rosario, Argentina; e-mail: lplara@arnet.com.ar Received January 24, 2003; revised March 11, 2003 Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But the definition of the entropy of the universe is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space- time provide a more fundamental and less controversial way of defining an arrow of time for the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic consid- erations, ‘‘the global arrow of time.’’ In this paper we will argue that: (i) if certain conditions are satisfied, it is possible to define a global arrow of time for the uni- verse as a whole, and (ii) the standard models of contemporary cosmology satisfy these conditions. 1. INTRODUCTION Scientific cosmology is an empirical discipline whose objects of study are the large-scale properties of the universe. In this context, it is usual to call the direction of the expansion of the universe ‘‘the cosmological arrow of time.’’ This arrow is global in an expanding model of the universe, but in an expanding-contracting model it has a divided nature, pointing in differ- ent directions at different phases of the evolution of the universe. However,