A cosmological field theory
Date
2018-07-04
Authors
Starkovich, Steven Paul
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Abstract
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. In our theory, the “cosmological fluid” is described by a classical
scalar field that undergoes a series of phase transitions over the lifetime of the
universe. Each transition corresponds to a discontinuous change in the equation
of state of the field. In general, for an FRW universe and a given equation of
state, we show that the field potential V(Φ) may be derived from the solution of
Piccati’s equation. The resulting expression for V(Φ) includes parameters whose
values are determined from the boundary conditions. In our theory, we employ the
standard cosmological model and the fundamental Planck quantities to provide
these boundary conditions. We thereby determine the scalar field Lagrangian for
the entire history of the universe. The resulting cosmological model is free of any
singularities, and includes an early inflationary epoch. Inflation arises in our theory
as a consequence of the initial conditions. The theory describes a universe that
is very cold at its minimum radius, although it heats rapidly during the initial inflationary
era. This increase in the temperature of the scalar field during inflation
is a direct consequence of applying classical thermodynamics under the assumed
conditions for the early universe, and does not depend on the fine-tuning of free
parameters. Inflation continues until a maximum possible physical temperature
(the Planck temperature) is attained, at which point a phase transition occurs
and the standard model era begins. By relating the temperature of the scalar
field in our theory to the radiation temperature in the standard model universe,
it is possible to establish a thermodynamic constraint on a more complete theory
of matter for the early universe. Although, in principle, inflation occurs for any
equation of state where p < -(1/3)p, we find that the initial equation of state
must be p ≈ -p if the later epochs of the universe are to resemble the standard
model. In particular, we find that Ho = 33 - 44 km sec-1 Mpc-1 is the value
of the Hubble parameter a t the current epoch that is least sensitive to the initial
equation of state.
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Keywords
Field theory (Physics)