We study the back-reaction effect of a massless minimally coupled scalar field at finite temperatures in the background of an Einstein universe. Substituting for the vacuum expectation value of the components of the energy-momentum tensor on the right hand side of the Einstein equation, we deduce a relationship between the radius of the universe and its temperature. This relationship exhibits a maximum temperature, below the Planck scale, at which the system changes its behavior drastically. The results are compared with the case of a conformally coupled field. An investigation into the values of the cosmological constant exhibits a remarkable difference between the conformally coupled case and the minimally coupled one.

• Received 9 September 2002

DOI:https://doi.org/10.1103/PhysRevD.67.044018