Some Remarks on Dark Energy

Rong-Gen CaiInstitute of Theoretical PhysicsChinese Academy of Sciences （ Huangshan, April 9, 2011)

Godfather of Dark Energy: M.S. Turner

Turner, M.S. 1999, The Third Stromlo Symposium: The Galactic Halo, 165, 431

Inflation Big Bang ⊕ ⊕Dark Matter ⊕ Dark Energy (A.Guth, 1981) 4% 23% 73% ⊕

Challenges: Inflation model ? Dark matter ? Dark Energy ?

SNE + CMB + LSS (since 1998):

E. Komatsu et al, 2010:

The Concordance Model of the Universe

Observational evidence from supernovae for an accelerating universe and a cosmological constant.By Supernova Search Team (Adam G. Riess et al.). May 1998. 36pp. Published in Astron.J.116:1009-1038,1998. e-Print: astro-ph/9805201

Cited 4934 times

Measurements of Omega and Lambda from 42 high redshift supernovae.By Supernova Cosmology Project (S. Perlmutter et al.). LBNL-41801, LBL-41801, Dec 1998. 33pp. The Supernova Cosmology Project. Published in Astrophys.J.517:565-586,1999. e-Print: astro-ph/9812133

Cited 5071 times 2010.8.25

It is dark, but very hot!

Papers entitled “ dark energy”: 2154Papers entitled “ cosmological constant”: 1735

Papers in SLAC databases

0

50

100

150

200

250

300

350

1999 2001 2003 2005 2007 2009

4000in total

exponential growth stabilized

2009.12.09

SN Ia is not enough!

(M. Kowalski et al 2008)

SN Ia only SN Ia + CMB +BAO

Equation of state： w= p /ρ

M. Kowalski et al, 2008 BAO (z=0.2,0.35) +WMAP-5+SN Ia

E. Komatsu et al, 2010 BAO +WMAP-7 +H_0(=74.2±3.6 km/s/Mpc)

E. Komatsu et al, 2010 BAO +WMAP-7 +SNIa +H_0(=74.2±3.6 km/s/Mpc)

at 68% CL

at 68% CL

Cosmic acceleration dark energy?

Dynamics equations:

/ 3p (Violate the Strong Energy Condition: exotic energy component)

What is the nature of the dark energy?

Dark Energy?Observational Data

Theoretical Assumptions

General Relativity Cosmological Principle

G 8πGT (Λ)

Model I Model II Model III

R G Cai, 2007 HEP&NP

Model I: Modifications of Gravitational Theory

1) GR’s test

UV: ~ 0.1 mm

IR: ~ solar scale

2) Modify GR

UV: quantum gravity effect

IR: cosmic scale

Brane world scenarios

Scalar-tensor theory……

１ ) “ Is Cosmic Speed-up due to New Gravitational Physics ” by S. M. Carroll et al. astro-ph/0306438, Phys.Rev. D70 (2004) 043528

Consider a modification becoming important at extremely low curvature

gr-qc/0511034:An alternative explanation of the conflict between 1/R gravity and solar system testsC.G. Shao, R.G. Cai, B. Wang and R.K. SuPhys.Lett. B633 (2006) 164-166

Making a conformal transformation yields a scalar field with potential:

(1) Eternal de Sitter; (2) power-law acceleration; (3) future singularity

Viable f(R) dark energy models:

(Hu and Sawicki, 2007)

(Starobinsky, 2007)

They satisfy f (R=0)=0, the cosmological constant disappears in flat spacetime.

n >0.9 local gravity constraints can be satisfied (S.Tsujikawa,2008)

f(T) model, 2010: Linder, Geng, Yu….

２ ) Brane World Scenarios:

y

X 1) N. Arkani-Hamed et al, 1998 factorizable product

2) L. Randall and R. Sundrum, 1999 warped product in AdS_5

4 x nM T

RS1:

RS2:

14 2

4

x S /

x R

cM Z

cM

3) DGP model, 2000 a brane embedded in a Minkovski space

a) A popular model: RSII scenario

5 5

5 41 15 5 416 8( 2 ) ( )G GS d x g R d x g K

2 242 3 44 5

8 4( ) ( )

3 3 3H

M M a

where2

4 53 35 5

25

4 5

4 4( )

3

3( )

4

M M

MM M

= 0

Fine-Tuning

b) DGP Model

3 5 (5) 2 4 ( )mS M d x G R m d x g R L

Then corresponding Friedman equation:

22

1( )

6c

HH

r m 2 3/cr m M

Two branches: (+): normal one; phantom if Lambda=\0. (-): late-time acceleration

c) “Dark Energy” on the brane world scenario

“Braneworld models of dark energy” by V. Sahni and Y. Shtanov, astro-ph/0202346, JCAP 0311 (2003) 014

When m=0:

In general they have two branches:

“Crossing w=-1 in Gauss-Bonnet Brane World with Induced Gravity ” by R.G. Cai,H.S. Zhang and A. Wang, hep-th/0505186

Consider the model

Another brane world model with crossing –1:

“Super-acceleration on the Brane by Energy Flow from the Bulk”R.G. Cai, Y. Gong and B. Wang, JCAP 0603 (2006) 006, hep-th/0511301

Consider the action

Effective dynamic equations:

Model III: Back Reaction of Fluctuations

“Cosmological influence of super-Hubble perturbations” by E.W. Kolb, S. Matarrese, A. Notari and A. Riotto, astro-ph/0410541;

“Primordial inflation explains why the universe is accelerating today”by E.W. Kolb, S. Matarrese, A. Notari and A. Riotto, hep-th//0503117;

“On cosmic acceleration without dark energy” by E.W. Kolb, S. Matarrese, and A. Riotto, astro-ph/0506534

Inhomogeneous Model:

“Inhomogeneous spacetimes as a dark energy model”

D. Garfinkle, gr-qc/0605088, CQG23 (2006) 4811

Recently, many works on LTB model!

Another scenario:

arXiv:0709.0732PRL99:251101,2007 低密度区

（ void)

(1)

(2)

(3) The equation of state crosses –1?

(4) Interaction between dark matter and dark energy?

G 8πGT (Λ)

Model II: Various Dark Energy Models: Acts as Source of E’eq

Dark energy issues:

Model II: Various Dark Energy Models: Acts as Source of E’eq

G 8πGT (Λ)

Some aspects on dark energy ：

(1) Equation of state from observational data

(1) Various phenomenological models

(3) How to distinguish those models and new cosmic probers

（ 1 ） EOS from observational data

a) Cosmological constant: w = - 1

b) as a constant:

c) expansion by redshift ：

d) expansion by scale factor ：

parameterization of EOS

-0.11 < 1+w < 0.14

w = const. ， phantom ？

( R. Caldwell, astro-ph/9908168, Phys.Lett.B545:23-29,2002)

Note ： w <-1: phantom, w >-1: quintessence, w =-1:cosmological const

D. Huterer and A. Cooray, astro-ph/040462

In terms of bins:

S. Qi, F.Y. Wang and T. Lu, 0803.4304

By scale factor ：

D. Huterer and G. Starkman, astro-ph/0207517

B. Feng, X. Wang and X. Zhang, astro-ph/0404224

Quintom = quintessence + phantom

0903.5141

Om (z) diagnostic:

0904.2832

(Gong, Cai, Chen and Zhu, 0909.0596)

(Gong, Cai, Chen and Zhu, 0909.0596)

0908.3186

0905.1234

DE: constant w and CPL paramertrization

Probing the dynamical behavior of dark energyR.G. Cai et al. 1001.2207, JCAP 2010

G 8πGT (Λ)

(1) Cosmological constant: w=-1

(2) Holographic energy

(3) Quintessence: -1<w<0

(4) K-essence: -1 <w<0

(5) Chaplygin gas: p=- A/rho

(6) Phantom: w<-1

(7) Quintom

(8) Hessence

(9) Chameleon, K-Chameleon

(10) Agegraphic model

(11) Interacting models ……

(2) Various dark energy models

3 4 29 3exp crit.

4 19 4 123theor. pl exp

70% (10 ) 10 /

( ) (10 ) 10

ev g cm

M Gev

QFT, a very successful theory

Dark energy : a very tiny positive cosmological constant ?

4 3 4~ ( ) ~ (10 )SUSYE Gev

This is a problem? I will come back again.

Old Problem on CC:

why S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)

0

(1)Supersymmetry; (2) Anthropic princple;(3) Self-tuning mechanism; (4) Modifying gravity(5) Quantum cosmology

New Problem on CC:

why crit0 and

Some remarks:

1) The cosmological constant is undistinguished from the vacuum expectation value of quantum fields

2) The cosmological constant problem is an issue in quantum gravity

3) The cosmological constant problem is an UV problem

4) The dark energy problem is an IR problem

5) To resolve the dark energy problem: quantum properties of gravity, UV/IR relation…..6) Of course, other viewpoints

Application of holography to dark energy ： UV/IR Relation

[A.Cohen, D. Kaplan and A. Nelson, PRL 82, 4971 (1999)]

Consider an effective quantum field with UV cutoff Lambda in a box with size L, its entropy

Black hole mass as an upper bound

Holographic principle?

E,S

V,AR

i) Bekenstein Bound: 2S ER

ii) Holographic Bound: / 4S A G

iii) UV/IR Mixture:

R

UV/IR relation, effective cosmological constant and dark energy

A. Cohen et al, (1999): L~Hubble horizon S. Hsu (2004): L~Hubble horizon M. Li (2004): L~particle horizon, event horizon….

What is the IR cutoff L?

Holographic dark energy (Hsu, 2004, Li, 2004) ?

What is the IR Cutoff L for the universe?

(1) Hubble horizon? L=1/H(2) Particle horizon?(3) Event horizon? (4) Other Choices?

While the holographic energy with event horizon works well, however,

Issues here ：• The event horizon is a global concept for manifold;• It exists only for eternal accelerated universe;• It is determined by future evolution of the universe

New solution: Causal connection scale:

C.G. Gao et al: arXiv:0712.1394 R.G. Cai et al: arXiv:0812.4504 

A new idea on the dark energy: Agegraphic dark energy model

(RGC: arXiv:0707.4049, PLB 657:228-231,2007

Karolyhazy relation (F. Karolyhazy et al, 1966):

(1) General relativity: a classical theory(2) Quantum mechanics: Heisenberg uncertainty relation

the distance t in Minkowski spacetime cannot be known to a better accuracy than

The Karolyhazy relation together with the time-energy uncertainty relation in quantum mechanics leads to a energy density of quantum fluctuation of spacetime metric (Maziashvili, 2006, 2007)

(N. Sasakura, 1999, Y.J. Ng et al,1994; 2006,2007)

A few features: (1) energy density exists within a causal patch (2) obey the holographic entropy bound; (3) resemble the holographic dark energy

(X. Calmet: hep-th/0701073)

The new proposal is (arXiv:0707.4049)

As the dark energy density in the universe with age T.

A New model for the agegraphic dark energy (Wei and Cai: arXiv:0708.0884, PLB 660:113-117,2008 )

Dark energy: QCD ghost?

References: F. Urban and A. Zhitnitsky, 0906.2106; 0906.2165; 0906.3546; 0909.2684 N. Ohta, 1010.1339

Other arguments also lead to such a scaling!

Dynamical evolution: R.G. Cai et al, 1011.3212 

Data fitting:

Furthermore:

Interaction?

The case:

Interaction between dark matter and dark energy?

Interaction and coincidence problem

interaction ：

相互作用的分段参数化 :

（ R.G. Cai and Q.P. Su. 0912.1843, PRD 2010)

(3) How to distinguish those models and new cosmic probers

Current probes

New probes？

Einstein’s equations (1915):

18

2R g R g GT

18

2R g R GT

Two years later (1917),The cosmological constant

For a static, closed universe model !

(The Greatest Blunder ! ?)

Revisit the cosmological constant problem

EOS: CPL parameterization：

Komatsu et al, 1001.4538

WMAP-7+…

at 68% CL.

conclusion：A flat universe with atiny cosmologicalconstant is consistent with observational data so far!

Then why the cosmological constant is not good?

1) It is the greatest blunder?

2) The coincidence problem?

3) The worst prediction?

E. Bianchi and C. Rovelli, 1002.3966:Why all these prejudices against a constant?

Einstein’s equations (1915):

18

2R g R g GT

18

2R g R GT

Two years later (1917),The cosmological constant

For a static, closed universe model !

(The Greatest Blunder ! ?)

G. Gamow, My World Line, 1970

1) It is the greatest blunder?

What means by the greatest blunder?

18

2R g R g GT

2) The coincidence problem?

&

3) The vacuum energy in QFT

about 122 orders of magnitude larger the observed one

Consider:

The effective action:

At one-loop:

i) Planck scale => 122 ordersii) Tev scale => 55 orders

Do we understand the vacuum energy?

which gives the false result:

The vacuum energy does not gravitate;The shift of the vacuum energy does gravitate?

1) The dark energy problem is nothing, but a cosmological constant problem.

2) The cosmological constant is so far so good!

Possible answer:

Thanks!