Dark Energy.ppt

1、Dark Energy,Shinji Tsujikawa (辻川 信二) Tokyo University of Science (東京理科大学）,Dark energy,Observations suggest that more than 70% of the energy density of the current universe is dark energy that gives an accelerated expansion.,The energy components in the present universe,72 %: Dark Energy: Negative pr

2、essure,23%: Dark Matter: Pressure-less dust,Responsible for cosmic acceleration,Responsible for the growth of large-scale structure,4.6%: Atoms,Responsible for our existence!,0.01 %: Radiation,Remnants of black body radiation,Supernova Ia,The current universe is accelerating!,Large-scale structure,C

3、osmic microwave background,Equation of state,Energy fraction,Negative pressure P of dark energy,Friedmann equation：,Continuous equation：,Equation of state：,When w is constant,exponential expansion,is a constant,(Cosmological constant),: accelerated expansion,:,: pressure,: energy density,Current obs

4、ervational constraints on dark energy,(95% confidence level),(for constant w),Komatsu et al (2008),Observational evidence for dark energy,The existence of dark energy is supported by,Supernovae Ia (SN Ia) The age of the oldest stars Cosmic Microwave background (CMB) Baryon oscillations Large-scale s

5、tructure (LSS) etc,Supernovae observations,The luminosity distance,is used for the distance measure of SN Ia observations.,L,s,: The absolute luminosity of a source,F: observed flux,where,and,For z 1 we have,K0: closed K=0: flat K0: open,In the presence of dark energy with the luminosity distance ge

6、ts larger.,The luminosity distance,Flat universe without dark energy,Open universe without dark energy,Flat universe with dark energy,Perlmutter et al and Riess et al (1998),They showed that cosmological constant is present at the 99 % confidence level.,(Perlmutter et al),The rest is dark energy.,Mo

7、re data over the past 10 years,The age of the oldest stars (globular clusters),Cosmic age,where,In the flat Universe without dark energy we have,Smaller than the age of the oldest stars (Cosmic age problem),Flat universe with cosmological constant,Cosmic age gets larger in the presence of cosmologic

8、al constant.,(age problem is solved),The WMAP bound,for h=0.70,Cosmic Microwave Background (CMB),Dark energy affects the CMB temperature anisotropies in two ways:,The change of the position of acoustic peaks The Integrated Saches Wolfe (ISW) effect,ISW effect,Larger,The change of the position of aco

9、ustic peaks,The characteristic angle of the first peak is,Comoving angular diameter distance,Sound horizon,The multipole moment that corresponds to this angle is,(CMB shift parameter),where,decreases for larger,Observational bound on,(WMAP 5-yr data),For w = -1 we have,DE,CMB data alone do not provi

10、de strong constraints on dark energy.,ISW effect on the CMB,Perturbed metric:,The l-th multiple moment of the present temperature anisotropy is,(Hu and Sugiyama, 1995),_,ISW contribution,Non-negligible when the gravitational potentials vary.,Only the large-scale modes with low l contribute to the IS

11、W effect.,Baryon acoustic oscillations (BAO),Before the recombination, baryons are tightly coupled to photons.,The oscillations of the sound wave are imprinted in baryon oscillations as well as CMB anisotropies.,In 2005 Eisenstein et al found baryon oscillations in the large-scale correlation functi

12、on measured from 46, 748 luminous galaxies.,This provides another independent test of dark energy.,In the presence of dark energy the gravitational potentials vary.,Accelerated epoch,ISW effect,However this is not powerful enough to place constraints on the property of dark energy.,Percival et al. o

13、btained the following quantity at two redshifts from the 2dF survey:,where,(The redshift at which baryons are released from photons),: comoving angular diameter distance,The observational constraint is,Useful to constrain the nature of dark energy,The BAO distance ratio,(,),The BAO data supports the

14、 presence of cosmological constant.,Combined analysis of CMB, SNIa and BAO for constant equation of state of dark energy,(95% confidence level),What is the origin of dark energy?,The simplest candidate: Cosmological constant,However this suffers from a fine-tuning problem if it originates from vacuu

15、m energy.,Many other dark energy models,Quintessence, k-essence, chaplygin gas, tachyon, phantom, f (R) gravity, scalar-tensor theories, Braneworld,These models generally give the dynamically changing equation of state w.,Simplest model of dark energy,Cosmological constant,This corresponds to the en

16、ergy scale,If this originates from vacuum energy in particle physics,Huge difference compared to the present value!,(Equation of state: ),Cosmological constant problem,(known even before the discovery of dark energy),There are two approaches to dark energy.,(i) Modified gravity,(ii) Modified matter,

17、f(R) gravity models, Scalar-tensor models, Braneworlds, .,Quintessence, K-essence, Tachyon, Chaplygin gas, .,Many other models of dark energy,(Einstein equations),Example of modified matter models,Quintessence (fifth matter),Chiba, Sugiyama, Nakamura (1997),X matter,Caldwell, Dave, Steinhardt (1998)

18、,Cosmic acceleration is realized by the potential energy of a slow-rolling scalar field (like cosmic inflation),There are some pioneering works before 1997.,Fujii (1982), Wetterich (1988), Ratra and Peebles (1988),Quintessence,They discussed cosmological dynamics in the presence of a scalar field an

19、d matter.,Quintessence: French wine!,Potential of quintessence,Cosmic acceleration is realized for a flat potential.,Energy density:,Pressure:,The equation of state is,In the slow-roll limit,we have,Quintessence,phantom,Tracking condition,If the quantity,This condition translates into,The exponentia

20、l potential,gives a border of acceleration and decceleration.,For the potential that is flatter than the exponential, e.g.,Tracking occurs at late times and cosmic acceleration is realized.,decreases, the energy density,of the scalar field dominates over a background fluid at late times.,Potential:,

21、The field mass squared:,The Hubble parameter:,The accelerated stage:,(present field),Compatible with the energy scale in particle physics,(Caldwell et al),for,To get the present acceleration, most of these models are based upon scalar fields with a very light mass:,In super-symmetric theories the fl

22、atness of the potential is easily spoiled by loop corrections to the potential. (Kolda and Lyth),Difficulty of quintessence,The quintessence field should interact with standard model particles because of a light mass (Carroll).,It is still a challenge to construct viable quintessence models in the f

23、ramework of particle physics.,Phantom scalar fields,The observations allow the equation of state,Quintessence does not give rise to this equation of state.,It is possible to have if the kinetic energy of the scalar field is negative.,However phantom fields are generally plagued by severe UV quantum

24、instabilities. The vaccum is unstable against the chatestrophic production of ghosts and normal fields.,The negative kinetic energy is problematic !,Modified gravity models,1. f(R) gravity,2. Scalar-tensor theories,DGP Braneworld models (a brane embedded in a 5-dimensional Minkowski bulk),In some of

25、 these models it is possible to have w -1 without having the instability problem of a vacuum.,Modified gravity models can be generally more strongly constrained compared to modified matter models.,1. Modifying gravity leads to the change of Newtons law.,Models are constrained by local gravity tests,

26、 e.g., Solar-system tests and the violation of equivalence principle.,2.,The evolution of the matter perturbation is also modified.,_,Modified in f(R) gravity 4/3 times compared to GR,This leads to changes of the matter power spectrum as well as the spectrum of weak lensing.,Current status of modified gravity,1. f(R) gravity,After the burst of activities over the past 5 years, many forms of f(R) have been excluded.,Viable form:,for,2. Scalar-tensor gravity,Fine as long as the scalar-field coupling with Ricci scalar is not so strong.,3. DGP braneworld,Under strong observati