International Journal of Theoretical Physics

, Volume 28, Issue 9, pp 967-981

First online:

Is the cosmological singularity thermodynamically possible?

  • Jacob D. BekensteinAffiliated withPhysics Department, Ben-Gurion University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


The four broad approaches that have been suggested heretofore to eliminate the initial singularity from cosmology are briefly reviewed. None is satisfactory, basically because one does not know enough about the microphysics involved in the process. Thermodynamics has often been used in such dilemmas, and it is proposed to answer the question of whether there was a Friedmann-like singularity in the universe by exploiting the bound on specific entropy that has been established for finite system. It is made applicable to the universe by considering only a causally connected spacelike region within the particle horizon of a given observer. It is found that the specific entropy of radiation in such a region can exceed the bound if the observer is too early in the universe. Faith in the bound leads to the conclusion that the Friedmann models cannot be extrapolated back to nearer than a few Planck-Wheeler times from the singularity. The Friedmann initial singularity thus appears to be thermodynamically unacceptable.