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Register a new userThe cosmological constant and the size of the Physical Universe
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Authors
Enrique Gaztanaga
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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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A Universe with finite age also has a finite causal scale. Larger scales can not affect our local measurements or modeling, but far away locations could have different cosmological parameters. The size of our causal Universe depends on the details of inflation and is usually assumed to be larger than our observable Universe today. To account for causality, we propose a new boundary condition, that can be fulfill by fixing the cosmological constant (a free geometric parameter of gravity). This forces a cancellation of vacuum energy with the cosmological constant. As a consequence, the measured cosmic acceleration can not be explained by a simple cosmological constant or constant vacuum energy. We need some additional odd properties such as the existence of evolving dark energy (DE) with energy-density fine tuned to be twice that of dark matter today. We show here that we can instead explain cosmic acceleration without DE (or modified gravity) assuming that the causal scale is smaller than the observable Universe today. Such scale corresponds to half the sky at z=1 and 60 degrees at z=1100, which is consistent with the anomalous lack of correlations observed in the CMB. Late time cosmic acceleration could then be interpreted as the smoking gun of primordial Inflation.
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).
Our goal is to interpret the energy equation from Doubly Special Relativity (DSR) of Magueijo-Smolin with an invariant Planck energy scale in order to obtain the speed of light with an explicit dependence on the background temperature of the expanding universe. We also investigate how other universal constants, including the fine structure constant, have varied since the early universe and, thus, how they have evoluted over the cosmological time related to the temperature of the expanding universe. For instance, we show that both the Planck constant and the electron charge were also too large in the early universe. However, we finally conclude that the fine structure constant has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data.
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.
Based on the equivalence of the two different types of measurement protocols and the asymmetry between the Schrodinger and Heisenberg pictures, it has been previously proposed that negative sea fills the universe as a nondeterministic computation - a time-reversal process of the irreversible computations presented since the big bang. The goal of this paper is to extend the proposed subjective universe model, i.e., the universe as a quantum measurement: Motivated by the relationship between quantum theory and classical probability theory with continuity, it is argued that the frame of reference of the observer may be identified with classical probability theory where its choice, along with big bang singularity, should correspond to the quantum observable. That is, the physical version of singularity resolution corresponds to the case, where big bang singularity is equivalent to the continuity of the negative sea, or aether, filling the universe as a frame of reference of the observer. Moreover, based on the holographic principle, we identify the choice of the observer with the degrees of freedom proportional to the Planck area on the horizon. We also discuss that the continuity or infinity present in every formal language of choice acceptable in nondeterministic computation may be associated with the universal grammar proposed by Chomsky in linguistics.
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