Transcript The role of energy conservation and vacuum energy in the evolution of the Universe Jan Greben Council for Scientific and Industrial Research Pretoria South Africa Presented at.

The role of energy conservation and
vacuum energy in the evolution of the
Universe
Jan Greben
Council for Scientific and Industrial Research
Pretoria
South Africa
Presented at the Evo Devo Universe Conference
Paris
8 October 2008
Outline
1.
Introduction 1-7
2.
Solution Einstein equations for the vacuum universe
3.
Properties of vacuum universe
4.
Addition of matter and radiation
5.
Further results of the cosmological model 1-2
6.
Evolution and development of the universe in this theory
1-2
7.
Analogies with biology 1-4
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Introduction-1
Major problems in Quantum Field Theory (QFT) and Cosmology
with little progress over the last thirty years:
• Cosmological Constant Problem: QFT vacuum energy 10120
larger than measured value 4x10-47 GeV4
• QCD perfect but other elements of Standard Model are
inelegant, incomplete or conceptually flawed
• Too many free parameters in Standard Model
• Role Higgs not understood
• Unification quantum gravity and QFT remains unresolved
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Introduction-2
Major problems in Quantum Field Theory (QFT) and Cosmology
continuation:
• No fundamental understanding of masses of particles
• Transition QFT→ NRQM→ classical physics poorly described
• No understanding of wave function collapse
• Problems with current cosmologies: dark energy; dark matter;
flatness; homogeneity; energy conservation
• Summary: No coherent view of Nature (Lederman)
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Introduction-3
Consequences of this lack of success: hypes/fashions pushed
• Extreme emphasis on one development, namely string theory.
This theory has considerable chance of failure and has met with
very little progress for the effort expanded
• Segmentation of fields and consequential ignorance of
fundamental problems, e.g. cosmological constant problem,
collapse of wave function
• In cosmology the unlikely mechanism of inflation has become
fashionable but is now loosing credibility
• Large number of possible universes (multiverses) is seen as a
success rather than a failure (e.g. Susskind, Weinberg)
• Few theorists keep clear perspective (Dirac, Penrose, Smolin)
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Introduction-4 How to solve this deadlock?
• Bold new physics approaches are required which question
existing hypotheses or tacit assumptions.
• New approaches should profit from other disciplines and should
not ignore fundamental problems by diverting responsibility to
other fields
Our approach is based on a formulation in terms of creation and
annihilation operators, which was traditionally used in QFT and has
been more fully developed and modified in its treatment of anti-
particles so as to guarantee symmetry between particles and antiparticles.
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Introduction-5 General consequences of this
theory
• Solution of non-linear QFT field equations: allows QFT solutions
without boson exchange (→ finite physical elementary particles)
• Sidesteps unification of QFT with gravity as exchange
mechanism through gravitons is not obligatory
• Shows that QFT contributions to vacuum energy are zero
• Unification of Nature by postulating single elementary particle
• Forces are necessarily diverse
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Introduction - 6
Consequences of these new foundations for
cosmology
•
Problems with current cosmologies: dark energy; dark
matter; flatness; homogeneity; cosmological constant
problem; energy conservation must be addressed
•
Proposed solution to a number of these problems:
(1) Assume QFT contributions to vacuum energy are zero
(2) Solve equations of general relativity without imposing
Robertson-Walker metric
(3) Impose energy conservation of total energy
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(4) Model locality of matter distribution
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Introduction - 7: Results
•
Resolution cosmological constant problem
•
Natural representation of Big Bang with vacuum universe
•
(Linear) expansion of universe is consequence of cosmic
energy conservation
•
Natural linking of cosmology to local Newtonian gravity
•
Possible explanation of dark matter
•
Excellent prediction of number of observables/phenomena
•
Explanation of particle physics scale
•
Dual representation of Nature
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2. Solution Einstein equations for a vacuum
universe
• QFT arguments against vacuum contributions based on a
formulation in terms of creation and annihilation operators
 0 TQFT 0   0
• Our proposal: classical vacuum energy ε:
T   g 
• Solve equations of general relativity using conformal form
g   g (t )  
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t s2
 2  
t
 1 0 0 0 


2
ts  0 1 0 0 
 2
0 010 
t


 0 0 01 


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t s2 
3
8  G
3. Properties of a vacuum universe
• Energy Vacuum Universe:
ts3
Etot   d x g11 g 22 g33   3  V
t
V
3
• To conserve energy we must demand that:
t3
V  Vs 3
ts
• Another way of expressing this is that the scale factor
behaves linearly:
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R(t )  a(t ) 
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t
ts
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4. Addition of Matter and Radiation
• Normally matter density is defined in the Friedmann models as
dependent only on time (ideal fluid), however, matter is localized:


Mi
 matter ( t , x )  
3
i

(3)

( x  xi ) ,

gˆ ( t , x )
• Resulting correction to the vacuum metric:

gˆ  ( t , x )  g( t ){  h ( x )}
where
h( x)  2G
t
ts
M
i
i
1
 
x  xi
• It looks like h increases linearly with time, but….
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1
h( x)  2G  M i  
i
xˆ  xˆi
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 t 
where x  xˆ
ts
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5. Further results cosmological model-1
• Linear expansion continues in the presence of matter and
radiation
• Dual variables
 t ~
x x
ts
 t ~
p s p
t
~
~
x and p are com ovingm easurem ent variables
• Measuring of time
t measured 
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ts
t
t0
Hubbletime 
1
1
 t0  measured  t s  13.7 109 yrs
H0
H0
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5. Further results cosmological model-2
• Particle epoch
1/ 6
G
tc   
 
 1 / 125 MeV 1
• Dark energy = vacuum energy (w = -1)
• Possible dark matter explanation: due to screening of black
hole from matter metric
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6. Evolution of the Universe in this theory - 1
• Universe starts out classically with infinite classical vacuum energy
t s3
 3 
t
for t  0
• Initial entropy zero and universe is perfectly homogeneous
• Entropy becomes non zero and increases forever after first particles
are created in particle epoch ( tc )
• Quantum fluctuations ensure spatial diversity and inhomogeneity of
later Universe
• Statistical imbalance due to quantum fluctuations creates
preponderance of electrons and protons or positrons and antiprotons
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6. Evolution of the Universe in this theory - 2
• Gravity multiplies inhomogeneities caused by quantum fluctuations
• Expansion is linear, but perturbed by creation and annihilation
processes, e.g. inflationary period after creation epoch
• Later stages of evolution follow usual scenarios, however, time
periods are shifted
• First galaxies created much later than in standard formulation
• Formalism has no horizon problem → no inflation required
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7. Analogies with biology-1
• Evolution requires randomness of quantum fluctuations. Only
this ensures a non-trivial universe with diversity. Similar to
randomness in mutations.
• Collapse of the wave function also plays a role since only
certain possibilities are realized. This may in some sense
represent the survival of species in a particular environment
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7. Analogies with biology-2
• Hierarchy plays an essential role in particle physics and
cosmology, just like in biology. Particles are small units that form
complex non-linear systems and then interact perturbatively with
other particles.
• The hierarchy is enabled by complex systems (such as
particles) emerging as simple entities. In nuclear physics this
distinction is captured by two fields: reaction theory (linear) and
structure theory (non-linear). In QFT the latter has not (yet) been
developed
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7. Analogies with biology-3
• Development can be seen as the non-random component of
evolution. In physics and cosmology this also plays an important
role through the emergence of simple entities from complex
non-linear systems.
• The main example of emergence is the physical elementary
particle. It is a product of a complex system involved in all the
interactions of the standard model plus GR
• Nature seems to allow for functional and beautiful emerging
structures without requiring a historical random pathway or
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adaptation to the environment
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7. Analogies with biology - 4
• Other examples of emergence and development are galaxies,
stars, black holes, etc
• Particle creation at present mimics aspects of the historical
development (particle epoch) right after the Big Bang. This is
key to a more satisfactory understanding of the nature of
particles and of renormalization.
• Reminiscent of the biological principle of recapitulation
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8. Comparison to observables
46
45
44
43
42
41
40
Data
Vacuum Universe
39
38
37
36
35
34
33
32
0
0.25
0.5
0.75
1
1.25
1.5
1.75
z
•
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Figure 1: Comparison between Supernovae data and our
description of red shifts. Plotted are the distance moduli
against the red shift z.
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