lecture 3: modified matter models of dark energy shinji tsujikawa (tokyo university of science)
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Lecture 3:Modified matter models of dark energy
Shinji Tsujikawa(Tokyo University of Science)
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What is the origin of dark energy?
The simplest candidate: Cosmological constant However this suffers from a fine-tuning problem
if it originates from a vacuum energy.
Dynamical dark energy models
Quintessence, k-essence, chaplygin gas, tachyon, f (R) gravity, scalar-tensor theories, Braneworld, Galileon, …
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Cosmological constant:
€
Λ Originally introduced by Einstein to realize the static Universe .
1917 (38 old) 1945 (66 old)
‘Biggest Blunder in my life’
1998 (119 old:heaven)
In 1929Hubble found the expansion of the Universe.
Static Universe
Big Bang Cosmology
Big Bang cosmology+cosmic acceleration
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Cosmological constant problem
The energy scale of dark energy today is
€
or, Cosmo-illogical constant problem (by Rocky Kolb)
If we take the Planck scale as a cut-off scale, the energy scale of the vacuum energy is
Problem even before 1998
See my review in 1989. by Steven Weinberg
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The cosmological constant is (i) sufficiently small to explain the energy scale of dark energy?(ii) or, completely zero?
Case (i): Both the cosmological constant and the dark energy problems are solved at the same time.
Economical
Case (ii): The cosmological constant problem is solved, but the dark energy problem has to be addressed.
This possibility remains.
`Modified matter’ (such as a scalar field) is introduced, or gravity is modified from Einstein gravity (Dynamical dark energy) .
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Example of case (i): de-Sitter vacua in string theory
Kachru-Kallosh-Linde-Trivedi (KKLT) scenario
Type II string theory compactified on a Calabi Yau manifold with a flux.
The KKLT scenario consists of three steps.
Potential: where
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We add uplifting potential generated by anti-D3 braneat the tip of warped throat:
uplifting
It is possible to explain dark energy if
The total potential is
AdS
dS
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String Landscape
We may live in a vacuum with a small energy density (related with anthropic selection).
10 upliftedvacua!
500
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Example of case (ii) [vanishing cosmological constant]
_________________ ______K: Kahler potentialW: Superpotential
In supersymmetric theories the vacuum energy is zero if supersymmetry is unbroken, but in real word supersymmetry is broken.
Cancellation is required
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€
We can classify the models into two classes .
(i) Modified gravity (ii) Modified matter
f(R) gravity,Scalar-tensor theory,Braneworlds,Gauss-Bonnet gravity,Galileon gravity,…..
Quintessence,K-essence,Chaplygin gas,Coupled dark energy,(including mass varying neutrinos)…..
Dynamical dark energy models
(Einstein equation)
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Modified matter models based on scalar fields
• Quintessence (‘fifth element’):
Chiba, Sugiyama, Nakamura (1997) ‘X matter’
Caldwell, Dave, Steinhardt (1998) ‘Quintessence’
• K-essence:
Accelerated expansion based on the potential energy
where
Chiba, Okabe, Yamaguchi (1999) ‘Kinetically driven quintessence’
Accelerated expansion based on the kinetic energy
Armendariz-Picon, Mukhanov, Steinhardt (2000) ‘k-essence’
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Quintessence: French wine!
_____________________________
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Potentials of Quintessence
As long as the potential is sufficiently flat, cosmic acceleration can be realized.
Energy density:
Pressure:
Equation of state for Quintessence
Quintessencephantom
Quintessence can be distinguishedfrom the LCDM.
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Particle physics models of quintessence
(i) Fermion condensate in globally supersymmetric QCD theories (Binetruy)
The inverse power-law potential was derived.
where
(ii) Supergravity models (Brax and Martin, Copeland et al)
The field potential in SUGRA theories is
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(iii) Pseudo-Nambu Goldston Boson (PNGB) models (Friemann et al)
The filed starts to evolve only recently.
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Classification of Quintessence potentials (Caldwell and Linder, 2003)
(A) Freezing models:
Since the potential tends to be flatter, the evolutionof the field slows down.
(B) Thawing models:
The field has been nearly frozen in the past, but it starts to evolve around today
.
.Example
Example
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Quintessence in the (w,w’) plane
.
LCDM
The current observations are not still enough tofind the evidence for the variation of the equation of state.
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Dynamical system approach to quintessence
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Dynamical equations
The fixed point responsible for the cosmic acceleration is
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Phase space
Attractor(cosmic acceleration)
Saddle(matter point)
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General potentials
where
(tracking condition)
Tracking always occurs.
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Numerical simulations for
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K-essenceK-essence is described by the action
where
The models that belong to k-essence is
Conformal transformation
or
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Equation of state for k-essence
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Stability condition for k-essence
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Some people tried to solve the coincidence problem of dark energy by considering a specific Lagrangian
However it is difficult to construct such models theoretically. Moreover they typically have the superluminal propagation speed.
k-essence density parameter
Armendariz-Picon, Mukhanov, Steinhardt (2000)
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Chaplygin gas model
Chaplygin gas Generalized Chaplygin gas
This corresponds to unified dark energy models in which darkmatter and dark energy are explained as a single component.
(pressureless matter)
(dark energy)
Continuity equation:
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Past:
Future:
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Chaplygin gas satisfies observational constrants ? No!
Matter power spectrum
_____________________
The sound speed term prevents the growth oflarge-scale structure.
Observational constraints
This cannot be distinguishedfrom the LCDM.