A COSMOLOGICAL FIELD-THEORY

Field theory is used to describe the material content of the universe throughout its entire history, and an oscillating cosmological model without a singularity is presented. The "cosmological fluid" is described by a single scalar field that undergoes a series of phase transitions, each of which denotes a change in the equation of state of the field. We find that an inflationary equation of state (rho almost-equal-to -p) is required in the early universe if the later epochs are to resemble the standard model. We find that H-0 = 33-44 km s-1 Mpc-1 is the value of the Hubble parameter at the current epoch that is least sensitive to initial conditions. Unlike most other inflation models, the onset of inflation in our theory is independent of an earlier radiation-dominated era. Instead, inflation arises as a consequence of boundary conditions which are expressed in terms of the fundamental Planck quantities. The theory describes a universe that is very cold at its minimum radius, although it heats quickly. The heating mechanism follows from very basic physical considerations and does not depend on the fine-tuning of free parameters. The heating occurs during inflation, and this imposes a thermodynamic constraint on a more complete theory of matter for the early universe. Inflation continues until a maximum possible physical temperature (the Planck temperature) is attained, at which point a phase transition occurs and the standard model begins. No fine-tuning of free parameters is necessary to end inflation. For an arbitrary equation of state, we show that the scalar field potential V(phi) may be derived from the solution of Riccati's equation. This result may be useful beyond its specific application in our theory. We use this result to find the scalar field Lagrangian for the entire history of the universe. The expression that we obtain for V(phi) also may assist in the development of a more complete theory of matter for the early universe.