Dirac Cosmology and the Acceleration of Contemporary Universe

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Dirac Cosmology and the Acceleration of
Contemporary Universe

• Ru-Keng Su
• Fudan University, Shanghai,China

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• Introduction
• Unified Theory of G.R. and Dirac Cosmology
• Numerical Solution with Matter and Radiation
• Summary and Discussion

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Introduction(1)

• Large number hypothesis
• The large dimensionless numbers provided by
  atomic physics and astronomy of our universe
  connect with each other
• the ratio of the electric to the gravitational
  force between an electron and proton
• the age of the universe expressed in the atomic
  unit

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Introduction(2)

• The mass of that part of the universe that is
  receding from with a velocity vltc/2, expressed in
  the unit of proton mass

• Varying gravitational constant
• Increase in the amount of matter in the universe

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Introduction(3)

• (B) Difficulties
• How to explain the contradiction between G.R. and
  Dirac cosmology
• Milne two time scale hypothesis
• Weyls geometry
• All experiments at the scales of solar system and
  galaxies have not found the variation of G

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Introduction(4)

• The conservation of energy and momentum (in local
  system)
• Dirac suggested
• Addition creation the new matter creates
  uniformly in whole space (Dark Energy?)
• Multiplication creation the new matter creates
  in the regions where the old matter exists (Dark
  Matter?)

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Introduction(5)

• Can we establish a possible unified theory of
  Dirac cosmology and G.R.?
• R.K. Su, S.W. Zhang, Proc of the 3rd Grassmann
  Meeting on G.R. P.1381 (1983)
• Acta. Math. Sci. 3 (1983) 321
• Kexue Tongbao (Sci. Bullium of China) 27
  (1982) 944.

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Introduction(6)

• Basic idea
• Though one would expect a constant value of G at
  the local system, it must be stressed that the
  cosmological observations still cannot put strong
  limits on the time variation of G in the
  cosmological scale
• Though Einstein G.R. has been proved to be
  correct by many experiments at the scales of
  local systems, it probably needs to be modified
  in the cosmological scale.

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Introduction(7)

• Local sys tem, , R , 0
• Cosmological scale, matter dominate area
• , 1/2

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Introduction

• Local system ,
• Cosmological scale Dirac Cosmology

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Unified Theory of G.R. and Dirac Cosmology (1)

• Constant curvature vacuum solution

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Unified Theory of G.R. and Dirac Cosmology (2)

• varying gravitational constant
• creation of energy momentum

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Unified Theory of G.R. and Dirac Cosmology (3)

• multiplication creation Dark matter
• addition creation Dark energy

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Unified Theory of G.R. and Dirac Cosmology (4)
In the flat R-W metric
baryon radiation
,
where
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Unified Theory of G.R. and Dirac Cosmology (5)
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Unified Theory of G.R. and Dirac Cosmology (6)
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Numerical Solution(1)

• By using the present cosmological parameters as
  the initial conditions.
• baryon to matter
• baryon to photon

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Numerical Solution(2)
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Numerical Solution(3)
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Numerical Solution(4)
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Numerical Solution(5)
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Numerical Solution(6)
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Numerical Solution(7)

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Numerical Solution(8)
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Summary and discussion

• We suggest a model to unify G.R. and Dirac
  cosmology.
• local system G.R.
• cosmological scale Dirac cosmology
• Supernova data adjust parameter
• addition creation Dark energy 0.8
• multiplication creation Dark matter 0.2
• negative pressure region
• Cannot be extended to the big bang epoch
• inflation epoch

Accelerating Universe
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Thank you