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Register a new userThe Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl geometrical Universe
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Added by
Francesco De Martini
Publication date
2017
fields
Physics
and research's language is
English
Authors
Francesco De Martini
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The standard electroweak theory of leptons and the conformal groups of spacetime Weyls transformations are at the core of a general relativistic, conformally covariant scalar tensor theory aimed at the resolution of the most intriguing enigma of modern Physics: the cosmological constant paradox (hereafter: Lambda paradox. A Higgs mechanism within a spontaneous symmetry breaking process offers formal connections, via an effective potential V(eff), between some relevant properties of the elementary particles and the dark energy content of the Universe. The nonintegrable application of the Weyls geometry leads to a Proca equation accounting for the dynamics of a vector-meson proposed as an optimum candidate for Dark Matter. The average vacuum-energy density in the Universe and the cosmological constant are evaluated on the basis of the recent experimental data of the PLANCK Mission. The resolution of the paradox is found for all exponential inflationary potentials and is consistent with the experimental data. The result of the theory: Lambda=6|V(eff)|shows that the paradox is determined by the algebraic mismatch between two large counteracting functions of the scalar field contributing to V(eff). The critical stability of the Universe is discussed.
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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.
We discuss the cosmological constant problem, at the minisuperspace level, within the framework of the so-called normalized general relativity (NGR). We prove that the Universe cannot be closed, and reassure that the accompanying cosmological constant $Lambda$ generically vanishes, at least classically. The theory does allow, however, for a special class of $Lambda ot=0$ solutions which are associated with static closed Einstein universe and with Eddington-Lema^{i}tre universe.
Deriving the Einstein field equations (EFE) with matter fluid from the action principle is not straightforward, because mass conservation must be added as an additional constraint to make rest-frame mass density variable in reaction to metric variation. This can be avoided by introducing a constraint $delta(sqrt{-g}) = 0$ to metric variations $delta g^{mu u}$, and then the cosmological constant $Lambda$ emerges as an integration constant. This is a removal of one of the four constraints on initial conditions forced by EFE at the birth of the universe, and it may imply that EFE are unnecessarily restrictive about initial conditions. I then adopt a principle that the theory of gravity should be able to solve time evolution starting from arbitrary inhomogeneous initial conditions about spacetime and matter. The equations of gravitational fields satisfying this principle are obtained, by setting four auxiliary constraints on $delta g^{mu u}$ to extract six degrees of freedom for gravity. The cost of achieving this is a loss of general covariance, but these equations constitute a consistent theory if they hold in the special coordinate systems that can be uniquely specified with respect to the initial space-like hypersurface when the universe was born. This theory predicts that gravity is described by EFE with non-zero $Lambda$ in a homogeneous patch of the universe created by inflation, but $Lambda$ changes continuously across different patches. Then both the smallness and coincidence problems of the cosmological constant are solved by the anthropic argument. This is just a result of inhomogeneous initial conditions, not requiring any change of the fundamental physical laws in different patches.
We consider a non singular origin for the Universe starting from an Einstein static Universe in the framework of a theory which uses two volume elements $sqrt{-{g}}d^{4}x$ and $Phi d^{4}x$, where $Phi $ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field $phi$ are considered in the action. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for $phi rightarrow infty$ relevant for the non singular origin of the Universe and $phi rightarrow -infty$, describing our present Universe. Surprisingly, avoidance of singularities and stability as $phi rightarrow infty$ imply a positive but small vacuum energy as $phi rightarrow -infty$. Zero vacuum energy density for the present universe is the threshold for universe creation. This requires a modified emergent universe scenario, where the universe although very old, it does have a beginning.
The nature of the scalar field responsible for the cosmological inflation, the qo{inflaton}, is found to be rooted in the most fundamental concept of the Weyls differential geometry: the parallel displacement of vectors in curved space-time. The Euler-Lagrange theory based on a scalar-tensor Weyl-Dirac Lagrangian leads straightforwardly to the Einstein equation admitting as a source the characteristic energy-momentum tensor of the inflaton field. Within the dynamics of the inflation, e.g. in the slow roll transition from a qo{false} toward a qo{true vacuum}, the inflatons geometry implies a temperature driven symmetry change between a highly symmetrical qo{Weylan} to a low symmetry qo{Riemannian} scenario. Since the dynamics of the Weyl curvature scalar, constructed over differentials of the inflaton field, has been found to account for the quantum phenomenology at the microscopic scale, the present work suggests interesting connections between the qo{micro} and the qo{macro} aspects of our Universe.
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