An extension of Friedmann–Robertson–Walker theory beyond big bang

Abstract

Starting from the classic Friedmann–Robertson–Walker theory with big bang it is shown that the solutions of the field equations can be extended to negative times. Choosing a new cosmic time scale instead of proper time one achieves complete differentiability of the scale factor and of suitable thermodynamic quantities equivalent to pressure and energy density. Then, the singularity of big bang manifests itself only by the vanishing of the scale factor at time zero. Moreover, all solutions of the field equations are defined for all times from $-\infty$ to $+\infty$. In a separate section, the horizon structure of the extended theory is studied. Some weak assumptions guarantee that there are no horizons. Hence, the horizon problem in a strict sense disappears. An intensive discussion of the results is given at the end of the paper.