Lecture 3: Modified matter models of dark energy Shinji Tsujikawa (Tokyo University of Science)
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Transcript of Lecture 3: Modified matter models of dark energy Shinji Tsujikawa (Tokyo University of Science)
Lecture 3:Modified matter models of dark energy
Shinji Tsujikawa(Tokyo University of Science)
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, …
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
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
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) .
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
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
String Landscape
We may live in a vacuum with a small energy density (related with anthropic selection).
10 upliftedvacua!
500
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
€
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)
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’
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.
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
(iii) Pseudo-Nambu Goldston Boson (PNGB) models (Friemann et al)
The filed starts to evolve only recently.
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
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.
Dynamical system approach to quintessence
Dynamical equations
The fixed point responsible for the cosmic acceleration is
Phase space
Attractor(cosmic acceleration)
Saddle(matter point)
General potentials
where
(tracking condition)
Tracking always occurs.
Numerical simulations for
K-essenceK-essence is described by the action
where
The models that belong to k-essence is
Conformal transformation
or
Equation of state for k-essence
Stability condition for k-essence
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)
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:
Past:
Future:
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.