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Register a new userA fundamental explanation for the tiny value of the cosmological constant
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Authors
Claudio Nassif
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We will look for an implementation of new symmetries in the space-time structure and their cosmological implications. This search will allow us to find a unified vision for electrodynamics and gravitation. We will attempt to develop a heuristic model of the electromagnetic nature of the electron, so that the influence of the gravitational field on the electrodynamics at very large distances leads to a reformulation of our comprehension of the space- time structure at quantum level through the elimination of the classical idea of rest. This will lead us to a modification of the relativistic theory by introducing the idea about a universal minimum limit of speed in the space- time. Such a limit, unattainable by the particles, represents a preferred frame associated with a universal background field (a vacuum energy), enabling a fundamental understanding of the quantum uncertainties. The structure of space-time becomes extended due to such a vacuum energy density, which leads to a negative pressure at the cosmological scales as an anti-gravity, playing the role of the cosmological constant. The tiny values of the vacuum energy density and the cosmological constant will be successfully obtained, being in agreement with current observational results.
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In this work we suggest (in a formal analogy with Linde chaotic inflation scenario) simple dynamical model of the dark energy or cosmological constant. Concretely, we suggest a Lagrangian dependent of Universe scale factor and scalar field (with constant and positive total energy density as cosmological constant). Then, Euler-Lagrange equation for Universe scale factor is equivalent to the second Friedman equation for the flat empty space with cosmological constant (in this sense our model is full agreement with recent astronomical observations). Also there is Euler-Lagrange equation for scalar field that includes additional friction term and negative first partial derivative of unknown potential energy density (this equation is, in some way, similar to Klein-Gordon equation modified for cosmic expansion in Linde chaotic inflation scenario). Finally, total time derivative of the (constant) scalar field total energy density must be zero. It implies third dynamical equation which is equivalent to usual Euler-Lagrange equation with positive partial derivative of unknown potential energy density (this equation is formally exactly equivalent to corresponding equation in static Universe). Last two equations admit simple exact determination of scalar field and potential energy density, while cosmological constant stands a free parameter. Potential energy density represents a square function of scalar field with unique maximum (dynamically non-stable point). Any initial scalar field tends (co-exponentially) during time toward the same final scalar field, argument of the maximum of the potential energy density. It admits a possibility that final dynamically non-stable scalar field value turns out spontaneously in any other scalar field value when all begins again (like Sisyphus boulder motion).
The cosmological constant $Lambda$ is a free parameter in Einsteins equations of gravity. We propose to fix its value with a boundary condition: test particles should be free when outside causal contact, e.g. at infinity. Under this condition, we show that constant vacuum energy does not change cosmic expansion and there can not be cosmic acceleration for an infinitely large and uniform Universe. The observed acceleration requires either a large Universe with evolving Dark Energy (DE) and equation of state $omega>-1$ or a finite causal boundary (that we call Causal Universe) without DE. The former cant explain why $Omega_Lambda simeq 2.3 Omega_m$ today, something that comes naturally with a finite Causal Universe. This boundary condition, combined with the anomalous lack of correlations observed above 60 degrees in the CMB predicts $Omega_Lambda simeq 0.70$ for a flat universe, with independence of any other measurements. This solution provides new clues and evidence for inflation and removes the need for Dark Energy or Modified Gravity.
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We present a possible understanding to the issues of cosmological constant, inflation, matter and coincidence problems based only on the Einstein equation and Hawking particle production. The inflation appears and results agree to observations. The CMB large-scale anomaly can be explained and the dark-matter acoustic wave is speculated. The entropy and reheating are discussed. The cosmological term $Omega_{_Lambda}$ tracks down the matter $Omega_{_M}$ until the radiation-matter equilibrium, then slowly varies, thus the cosmic coincidence problem can be avoided. The relation between $Omega_{_Lambda}$ and $Omega_{_M}$ is shown and can be examined at large redshifts.
A quantum equation of gravity is proposed using the geometrical quantization of general relativity. The quantum equation for a black hole is solved using the Wentzel-Kramers-Brillouin (WKB) method. Quantum effects of a Schwarzschild black hole are demonstrated by solving the quantum equation while requiring a stationary phase and also by using the Einstein-Brillouin-Keller (EBK) quantization condition, and two approaches shows a consistent result. The WKB method is also applied to the McVittie-Thakurta metric, which describes a system consisting of Schwarzschild black holes and a scalar field. A possible interplay between quantum black holes and a scalar field is investigated in detail. The number density of black holes in the universe is obtained by applying statistical mechanics to a system consisting of black holes and a scalar field. A possible solution to the cosmological constant problem is proposed from a statistical perspective.
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