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Register a new userQuantum effects of black holes and cosmological constant problem
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Authors
Yoshimasa Kurihara
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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.
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We propose the generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics as a quantum mechanical framework for the minimal length uncertainty at the Planck scale. We demonstrate that the GUP parameter, $beta_0$, could be best constrained by the the gravitational waves observations; GW170817 event. Also, we suggest another proposal based on the modified dispersion relations (MDRs) in order to calculate the difference between the group velocity of gravitons and that of photons. We conclude that the upper bound reads $beta_0 simeq 10^{60}$. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non-gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant $Lambda$ (apparently manifesting gravitational influences on the vacuum energy density), known as {it catastrophe of non-gravitating vacuum}, we suggest a possible solution for this long-standing physical problem, $Lambda simeq 10^{-47}~$GeV$^4/hbar^3 c^3$.
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.
We calculate the Hawking temperature for a self-dual black hole in the context of quantum tunneling formalism.
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.
The relevant physics for the possible formation of black holes in the LHC is discussed.
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