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Register a new userDimensionality and the Cosmological Constant
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Authors
Z.C.Wu
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In the Kaluza-Klein model with a cosmological constant and a flux, the external spacetime and its dimension of the created universe from a $S^s times S^{n-s}$ seed instanton can be identified in quantum cosmology. One can also show that in the internal space the effective cosmological constant is most probably zero.
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Self tuning is one of the few methods for dynamically cancelling a large cosmological constant and yet giving an accelerating universe. Its drawback is that it tends to screen all sources of energy density, including matter. We develop a model that tempers the self tuning so the dynamical scalar field still cancels an arbitrary cosmological constant, including the vacuum energy through any high energy phase transitions, without affecting the matter fields. The scalar-tensor gravitational action is simple, related to cubic Horndeski gravity, with a nonlinear derivative interaction plus a tadpole term. Applying shift symmetry and using the property of degeneracy of the field equations we find families of functions that admit de Sitter solutions with expansion rates that are independent of the magnitude of the cosmological constant and preserve radiation and matter dominated phases. That is, the method can deliver a standard cosmic history including current acceleration, despite the presence of a Planck scale cosmological constant.
Based on Eddington affine variational principle on a locally product manifold, we derive the separate Einstein space described by its Ricci tensor. The derived field equations split into two field equations of motion that describe two maximally symmetric spaces with two cosmological constants. We argue that the invariance of the bi-field equations under projections on the separate spaces, may render one of the cosmological constants to zero. We also formulate the model in the presence of a scalar field. The resulted separate Einstein-Eddington spaces maybe considered as two states that describe the universe before and after inflation. A possibly interesting affine action for a general perfect fluid is also proposed. It turns out that the condition which leads to zero cosmological constant in the vacuum case, eliminates here the effects of the gravitational mass density of the perfect fluid, and the dynamic of the universe in its final state is governed by only the inertial mass density of the fluid.
We derive a model of dark energy which evolves with time via the scale factor. The equation of state $omega=(1-2alpha)/(1+2alpha)$ is studied as a function of a parameter $alpha$ introduced in this model. In addition to the recent accelerated expansion, the model predicts another decelerated phase. The age of the universe is found to be almost consistent with observation. In the limiting case, the cosmological constant model, we find that vacuum energy gravitates with a gravitational strength, different than Newtons constant. This enables degravitation of the vacuum energy which in turn produces the tiny observed curvature, rather than a 120 orders of magnitude larger value.
Theoretically, the running of the cosmological constant in the IR region is not ruled out. On the other hand, from the QFT viewpoint, the energy released due to the variation of the cosmological constant in the late universe cannot go to the matter sector. For this reason, the phenomenological bounds on such a running are not sufficiently restrictive. The situation can be different in the early universe when the gravitational field was sufficiently strong to provide an efficient creation of particles from the vacuum. We develop a framework for systematically exploring this ossibility. It is supposed that the running occurs in the epoch when the Dark Matter already decoupled and is expanding adiabatically, while baryons are approximately massless and can be abundantly created from vacuum due to the decay of vacuum energy. By using the handy model of Reduced Relativistic Gas for describing the Dark Matter, we consider the dynamics of both cosmic background and linear perturbations and evaluate the impact of the vacuum decay on the matter power spectrum and to the first CMB peak. Additionally, using the combined data of CMB+BAO+SNIa we find the best fit values for the free parameters of our model.
In this work we provide a link between a nearly vanishing cosmological constant and chiral symmetry. This is accomplished with a modification of General Relativity coupled to a topological field theory, namely BF theory by introducing fermions charged under the BF theory gauge group. We find that the cosmological constant sources a chiral anomaly for the fermions, providing a `technical naturalness explanation for the smallness of the observed cosmological constant. Applied to the early universe, we show that production of fermions during inflation can provide all the dark matter in the universe today, in the form of superheavy dark baryons.
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