ISSN:
1572-9532
Keywords:
Inflation
;
axion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A simple, consistent inflationary cosmology is developed from the basic structure of the Σ-model expansion in string theory, which corresponds to the low energy effective (α′ → 0) limit. The classical dilaton background solution φ is subject to stochastic vacuum fluctuations near the Planck scale. The motivation here is that the coupling of stochastic noise to a classical field theory often provides workable and powerful methodologies with which to explore quantum behaviour, turbulence and pattern and structure formation. The dilaton fluctuations induce random (Weyl) conformal fluctuations in the Einstein frame metric. The additional vacuum stress-energy tensor—which the fluctuations induce within the string derived Einstein-dilaton field equations—can be interpreted and described in terms of a "turbulent perfect fluid" with a fluctuating negative pressure. A (stochastic) de-Sitter solution describes a turbulent, inflating vacuum bubble whose exponential expansion is future-eternal and unbounded; but the vacuum turbulence breaks the spherical symmetry and homogeneity usually associated with a smooth de-Sitter solution. Consequently, the strong energy condition (SEC) is violated for the turbulent perfect fluid tensor describing the (false) vacuum—this suggests that there is no initial singularity. With a suitable "rollover" dilaton potential V(φ) there can then be a phase transition to a hot Friedmann expanding universe at the minima of the potential as φ → φo. Assuming an instantaneous decay of the inflaton to a perfect fluid of thermal radiation, the de-Sitter and Friedman solutions are matched using a step function. However, the residual vacuum turbulence carried over from inflation, breaks the usual homogeneity and symmetry of the FRW solutions. The induced cosmological constant plays a role somewhat like a Reynold's number for a non-linear, turbulent fluid. The SEC—and therefore the Hawking singularity theorem—is obeyed only after inflation, so it appears that the universe is singular only within the perspective of a matter or radiation fluid dominated era; but past directed matter worldlines do not converge in the past since they cannot be extrapolated beyond the (phase) transition at which the turbulent vacuum bubble decayed. On cosmic time scales, the vacuum "turbulence" augments both cosmic acceleration (the Hubble parameter) and distances with respect to the standard, classical Friedman RW cosmologies.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1001938319441
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