Symmetry behavior of the static Taub universe: Effect of curvature anisotropy
Using the static Taub universe as an example, we study the effect of curvature anisotropy on symmetry breaking of a self-interacting scalar field. The one-loop effective potential of a lambdaphi/sup 4/ field with arbitrary coupling (xi) is computed by zeta-function regularization. It is expressed as a perturbative series in a small anisotropy parameter ..cap alpha.. measuring the deformation from the spherical Einstein universe with radius of curvature a. This result is used for analyzing the symmetry behavior of such a system as a function of the geometric (a,..cap alpha..) and field (xi,lambda) parameters. The result is also used to address the question of whether and how curvature anisotropy can affect the inflationary scenario, old or new. We find that for a massless scalar field conformally coupled to the background with a prolate configuration (negative scalar curvature) the phase transition is of second order, in which case inflation to the extent necessary for cosmological purposes becomes highly unlikely. For the massless minimally coupled scalar field, first-order phase transitions can occur for a certain range of the radius and deformation parameter. If the curvature radius in the axisymmetric direction is held fixed, increasing deformation can restore the symmetry, whereas if the shape is held constant but the size is allowed to vary, decreasing the radius of the universe can induce symmetry breaking. For the minimally coupled field in a closed universe with high curvature a term linear in the background field in the effective potential appears. The barrier thus generated in the effective potential replaces the broad plateau of the flat-space Coleman-Weinberg potential. The meaning and implication of these results are discussed.
- Research Organization:
- Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
- OSTI ID:
- 5693054
- Journal Information:
- Phys. Rev. D; (United States), Vol. 31:10
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
UNIVERSE
SPACE-TIME
SYMMETRY BREAKING
COSMOLOGICAL MODELS
HIGGS MODEL
METRICS
PHASE TRANSFORMATIONS
PHI4-FIELD THEORY
SCALAR FIELDS
FIELD THEORIES
MATHEMATICAL MODELS
PARTICLE MODELS
QUANTUM FIELD THEORY
640106* - Astrophysics & Cosmology- Cosmology