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Register a new userCosmological constant, matter, cosmic inflation and coincidence
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She-Sheng Xue
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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.
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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.
Informed by a quantum information perspective, we interpret cosmological expansion of space as growing entanglement between underlying degrees of freedom. In particular, we focus on inflationary cosmology, which, while being a successful empirical paradigm for early universe physics, is riddled with ambiguities when one traces its quantum mechanical origins. We show, by deriving a modified cosmological continuity equation, that by properly accounting for new degrees of freedom being added to space by quantum entanglement, inflation can naturally be driven by quantum mechanics without having to resort to novel, unknown physics. While we explicitly focus on inflation in our discussion, we expect this approach to have possible broad implications for cosmology and quantum gravity.
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.
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).
An earlier paper points out that a quantum treatment of the string landscape is necessary. It suggests that the wavefunction of the universe is mobile in the landscape until the universe reaches a meta-stable site with its cosmological constant $Lambda_0$ smaller than the critical value $Lambda_c$, where $Lambda_c$ is estimated to be exponentially small compared to the Planck scale. Since this site has an exponentially long lifetime, it may well be todays universe. We investigate specific scenarios based on this quantum diffusion property of the cosmic landscape and find a plausible scenario for the early universe. In the last fast tunneling to the $Lambda_0$ ($<Lambda_c$) site in this scenario, all energies are stored in the nucleation bubble walls, which are released to radiation only after bubble collisions and thermalization. So the $Lambda_0$ site is chosen even if $Lambda_0$ plus radiation is larger than $Lambda_c$, as long as the radiation does not destabilize the $Lambda_0$ vacuum. A consequence is that inflation must happen before this last fast tunneling, so the inflationary scenario that emerges naturally is extended brane inflation, where the brane motion includes a combination of rolling, fast tunnelings, slow-roll, hopping and percolation in the landscape. We point out that, in the brane world, radiation during nucleosynthesis are mostly on the standard model branes (brane radiation, as opposed to radiation in the bulk). This distinction may lead to interesting dynamics. We consider this paper as a road map for future investigations.
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