Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant

Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant

26 Jun 2000 | Raphael Bousso, Joseph Polchinski
The paper discusses the quantization of four-form fluxes in M theory and their role in the cosmological constant problem. It argues that four-form fluxes, although often assumed to be continuous, are actually quantized, leading to a discrete set of possible cosmological constants. This quantization arises from the generalized Dirac quantization condition, which ensures that the fluxes take discrete values. In M theory compactifications on manifolds with non-trivial three-cycles, multiple four-form fluxes can lead to a sufficiently dense 'discretuum' of cosmological constants, allowing some values to fall within the observational range. The paper also explores the dynamics of membrane nucleation, which can dynamically generate regions with a small cosmological constant. The cosmological constant can be neutralized by the nucleation of membranes, leading to a picture similar to eternal inflation, where the cosmological constant takes different values in different expanding bubbles. The paper addresses the 'gap problem', which arises when the spacing between allowed values of the cosmological constant is too large to be compatible with observations. It shows that with multiple four-forms, this spacing can be reduced to an acceptable value. The paper also discusses the stability of the compactification and the role of moduli in the four-form energy density. It concludes that the cosmological constant can be small for anthropic reasons, as the universe can have different cosmological constants in different regions, with galaxies only forming in regions of small cosmological constant. The paper also considers the implications of large extra dimensions and the role of the inflaton field in reheating the universe after membrane nucleation.The paper discusses the quantization of four-form fluxes in M theory and their role in the cosmological constant problem. It argues that four-form fluxes, although often assumed to be continuous, are actually quantized, leading to a discrete set of possible cosmological constants. This quantization arises from the generalized Dirac quantization condition, which ensures that the fluxes take discrete values. In M theory compactifications on manifolds with non-trivial three-cycles, multiple four-form fluxes can lead to a sufficiently dense 'discretuum' of cosmological constants, allowing some values to fall within the observational range. The paper also explores the dynamics of membrane nucleation, which can dynamically generate regions with a small cosmological constant. The cosmological constant can be neutralized by the nucleation of membranes, leading to a picture similar to eternal inflation, where the cosmological constant takes different values in different expanding bubbles. The paper addresses the 'gap problem', which arises when the spacing between allowed values of the cosmological constant is too large to be compatible with observations. It shows that with multiple four-forms, this spacing can be reduced to an acceptable value. The paper also discusses the stability of the compactification and the role of moduli in the four-form energy density. It concludes that the cosmological constant can be small for anthropic reasons, as the universe can have different cosmological constants in different regions, with galaxies only forming in regions of small cosmological constant. The paper also considers the implications of large extra dimensions and the role of the inflaton field in reheating the universe after membrane nucleation.
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