Dark matter and dark energy The dark side of the universe. Anne Ealet CPPM Marseille

Transcription

1 Dark matter and dark energy The dark side of the universe Anne Ealet CPPM Marseille

2 Lectures Lecture I Lecture II Basis of cosmology An overview: the density budget and the concordance model An history of the universe The dark matter mystery Lecture III The CMB Lecture IV The dark energy

3 Each lecture will be followed by a discussion on a given subject some basic references: Books: Peebles Principle of physical cosmology (princeton) Liddle An introduction to modern cosmology Weinberg Gravitation and cosmology Review papers: Freedmann astro-ph/6 Trodden/Carroll astro-ph/41547 Peebles astro-ph/9861 Web sites: astron.berkeley.edu/~mwhite/ site index ww.damtp.cam.ac.uk/user/gr/public/cos_home.html

4 The Standard model of Cosmology Hu & White Scientific American 4 4

5 The Standard Cosmological model Evolution of an homogeneous fluid composed of all kind of particles (relativistic and not relativistic) with small inhomogeneities in an expanding univers At different stages of the evolution of the universe different physics interplay: particle physic nuclear physic general relativity linear perturbation theory (and non-linear) hydrodynamic, boltzmann and compare to observations 5

6 This lecture The cosmological principle Hubble s law and Friedmann equations Geometry of the universe Weighing the universe The current universe budget The story of the universe 6

7 Cosmological distances Alternative unit : 1 parsec ~ 3.61 lyr Mean distance Earth-Sun 1 Astronomical Unit (AU) ~ 1 11 meters 1 pc = 1 AU / tan(1 arcsecond) 1 arcsecond = 36 degrees / 36 Nearest stars Few light years ~ 1 16 meters Milky Way galaxy size ~ 13 kpc ~ 1 meters ~ 4 light years 7

8 Large-scale structure of the universe galaxies clusters of galaxies LSS closest similar galaxy : Andromeda Millions of light years ~ 1 Mpc After.. Use the redshift as an indicator (see definition later..) 8

9 Cosmological principle At large scale (> ~ 5 Mpc), the Universe is isotropic = look the same in all direction homogeneous= look the same at each point ( we are not particular) was used to do calculations In GR nearly proved later with large scale structure and CMB. Angular distribution of 31 radio sources 9

10 Observational Cosmology Cosmic Background Radiation (CMB) Large Scale Structure (LSS) Supernovae Ia 1

11 Hubble s Great Discovery - The Universe Recessional Velocity (km/sec) is Expanding! Distance Mpc) Edwin Hubble velocity distance v = H o r Historical Note: Hubble was off by a factor of 8 in his measurement of H. In 199 Hubble measured the red shift of nearby galaxies and found that nearly all were moving away from us. He used Cepheid variables as standard candles to measure distances. Result: The faster they are moving, the farther away they are. The Universe is expanding! Einstein declares L his Biggest Blunder. Lesson: Beware of systematic errors! H : Hubble s constant 11

12 Methods and distance ladder users/kenton/c185/ 1

13 Hubble parameter from supernovae H = h 1 Kms -1 Mpc -1 Age ~ 1/H ~ yrs

14 Hubble s law is just what one would expect for a homogeneous expanding universe; each point in the universe sees all objects rushing away from them with a velocity proportional to distance We conclude that in the distant past everything in the Universe was much closer together: Consequence: The universe was denser and hotter in the past It starts with a mechanism known as the big bang The left over of this dense phase is a radiation background called the cosmic microwave background (CMB) 14

15 CMB 15

16 The theory (framework) Gravitation and then the dynamic of the Universe are governed by the Einstein equations of general relativity: R 1 µν R gµν = 8πG Tµν + Λ gµν R µν g µν G Ricci Tensor -> space-time curvature Metric tensor -> space time distances Gravitational constant = m 3 s - kg-1 R = g µν Rµν ds = g µ ν µν dx dx Ricci scalar T µν Λ Energy-momentum tensor -> mass,energy Cosmological constant 16

17 R Objects appear to be in different 1 positions µν R gµν = 8πG Tµν + Λ gµν Space is curved by matter 17

18 This is a non linear theory This is a gauge theory but the measurements not depend of the gauge choice We can choose the referentiel and the metric as we want, results will be the same.. 18

19 Cosmology : an application of GR General relativity + cosmological principle Friedmann-Lemaitre model Homogeneity The spatial curvature Can be different at different times And symetric (3 solutions) Isotropy The space-time is the same in all directions. This curvature give the expansion Define a metric with this properties Relate it to the matter density with Einstein equation (at the universe scale, describe it as a perfect fluid) 19

20 The Robertson-Walker metric ds = dt a dr ( t) + r dθ + r sin θ dφ 1 kr Spatial curvature r,θ,φ are co-moving coordinates x = a(t) r a(t) is a function of time and r is a constant coordinate. a(t) is known as the scale factor of the universe and it measures the universal expansion rate a(t ) = 1 where t is today The comoving coordinates preserve today distance

21 The k parameter: the curvature Closed: k=+1 (Ω tot >1) spherical geometry Recollapse, Big Crunch Flat: k= (Ω tot =1) Euclidean geometry Open: k< (Ω tot < 1) hyperbolic geometry a+b+c > 18 a+b+c = 18 a+b+c < 18 1

22 The tensor T µν T µν = ρ p p p Assuming a Perfect Homogeneous fluid ρ is the total density of the fluid p is the total pressure The Ricci tensor R µν is calculated from the metric g µν

23 From Einstein field equations: a& a a&& a a&& a + k a = 4πG = ρ 3 8πG 3 ρ 1 a& + = 4πGp a ( ) + 3p 1st Friedmann equation k a Acceleration equation Relate the expansion rate to the total energy density of all components in the universe d Friedmann equation Definition: w=p/ρ equation of state parameter 3

24 Reduced density definition Critical density at any time Ω i Ω total Ω i = = ρ ρ = i c ρ cρ H k a ρ c putting a = H = & with a 3H 8πG H is the Hubble parameter which is time dependent. k Ωk = Ω = 1 H a i Be carefull..often defined as the density today with t=t and the is dropped. I will use the same convention.. Ω m will be the matter density TODAY otherwise specify (idem Ω r, Ω Λ, Ω tot ) 4

25 Fluid equation ( ) µ ν µν T = ρ + p U U + pg µν U µν is the fluid four velocity From energy-momentum conservation : µν µ T = ρ& a& + 3 ρ + p = a ( ) The expansion of the universe can lead to local changes in the energy density 5

26 The cosmological constant T µν Λ = g 8πG µν This is like a prefect fluid with ρ Λ Λ Λ = 8πG p = ρ w= 1 Λ This a constant component through spacetime It is equivalent to a vacuum energy 6

27 ρ& Some solutions of the fluid equation a& + 3 p = a ( ρ + ) p = (matter dominated) ρ m = 1 a 3 p = ρ/3 (radiation dominated) ρ r = 1 a 4 p = w ρ ρ w = 1 3(1 w) a + For the cosmological constant ρ Λ = cste 7

28 Radiation - Matter - Vacuum (Dark Energy?) ρ(a) a -4 a -3 const Early Universe today a 8

29 What is dominant when? Matter dominated (w=): ρ a -3 Radiation dominated (w=1/3): ρ ~ a -4 Dark energy (w~-1): ρ ~constant Radiation density decreases the fastest with time Must increase fastest on going back in time Radiation must dominate early in the Universe Dark energy with w~-1 dominates last Radiation domination Matter domination Dark energy domination 9

30 Putting it all together ρ tot = ρ r + ρ m + ρ Λ (...+ ρ w ) ρ r = ρ r a -4 = ρ c Ω r a -4 since ρ / a -4 and a today is 1 ρ = radiation density today use Ω r = ρ r / ρ crit by definition (and is dropped ) sim ρ m, ρ Λ Therefore for k= and an unknown energy X (X= Λ is w=-1): ρ tot = ρ c [ Ω r a - + Ω m a -3 + Ω w a -3(1+w) ] 3

31 Evolution of the universe: H a = & a = 8πG 3 ρ( t) Freidmann eqn1 for k= ρ(t) = ρ c [ Ω r a - + Ω m a -3 + Ω w a -3(1+w) ] Putting these together and using a& H = a H = H ( Ω r a - + Ω m a -3 + Ω w a -3(1+w) ) 31

32 First summary The Universe can be caracterized by The Hubble parameter in function of time The densities of each component Ω i = ρ ρ i c H a = & a = 8πG 3 ρ( t) ΩT = 1 Ω k = Ω r + Ω m + Ω Λ H + ( a) 3 3(1 w) = ( Ωra + Ωma + Ωwa ) H General assumptions: :Ω r can be neglected and Ω T = 1 (flatness) 3

33 Acceleration Acceleration parameter is defined by aa && q = a& Today we have: q = i (3(1 + w) ) Ω For an universe with k= and a cosmological constant i q = Ω m ΩΛ 33

34 Time evolution first Friedmann equation, H a = & a = 8πG 3 ρ( t) assuming a(t) = t α Expansion evolutiondepend ofthe densitycontent: p= matter dominated a(t) t /3 p=ρ/3 radiation dominated a(t) t 1/ Generalisation w a(t) t /3(1+w) Cosmological constant a(t) e Ht 34

35 Destiny ο Ω m =1 and Ω Λ = Einstein de Sitter universe : a(t) = (3/H t) /3 t = /3H ο Ω m = and Ω Λ = empty universe a(t) =H t t = 1/H ο Ω m = and Ω Λ =1 a( t) = exp( Λ / 3t) 35

36 + flat or not flat. Without Λ: k=+1 expand from a singularity and recollapse later (big Crunch) k=-1 (=k=) expand for ever With Λ dominant: all solutions expand exponentially (de Sitter) Experimental evidence of flatness with high accuracy (WMAP) (see lecture 3) Interesting to be aware if it is not completely true 36

37 Destiny 37

38 Measurements in an expanding Universe (or how photons are traveling in the expanding Universe) 38

39 Redshift and scale factor time t radius a(t)r time t, a(t )=1 radius R t t Redshift z ν λ 1 + = ν λ a a ( t ) ( t) z 39

40 In Practice All radiation and all wavelengths are redshifted here Hα is 656 nm In a model, we can calculate z = (75-656)/656 =.14 t ~ billions years D ~ 6 Mpc when the light has been emitted and the distance of the source 4

41 comoving distance Comoving distance Using dx= c dt = a dr D c = a dr = a cdt a da aa& = a = a a da H ( a) D a a C ( z) H ( z) H 1 = 1+ z z z dz' = = H ( z') H = ( Ω da a m = (1 + z) dz a 3 + Ω ( Ω w m (1 + (1 + Ω z) z') T 3 = 1 3(1+ w) dz' + Ω ) w (1 + z') 3(1+ w) ) 1 41

42 Luminosity and observed flux L is the intrinsic luminosity of a given object at a redshift z, on geodesic: ds = = cdt a(t) dr /(1-kr ) Propagation of light from the object to us x x 1 1 = = a r 1 NB : case a r 1 dr k = a dr (1 kr t t 1 ) cdt a( t) 1/ = a a da H( a) = dz H( z) x 1 is the present day distance of the object

43 Observed flux Take into account Spatial distance between photons increased with a factor (1+z) Photons are distributed on a surface of 4πx 1 l = π L (1 + ) 1 4 x z l is the observed flux at a redshift z, related to cosmological parameters through r 1 43

44 Luminosity distance Definition l = L 4πd L d L can be measured directly from the observed flux and is related to the cosmological parameter via l d L = D c (1+z) we will see later an application with supernovae (lecture 4)

45 Angular distance Defined such that θ=r / d A r=physical size of object θ= angular size on sky d A = d (1 + L z) = D C (1 + ( z) z) Application with the CMB (lecture 3) 45

46 The age of the Universe H = H (Ω m a -3 + Ω w a -3(1+w) ) (neglect radiation, flatness ) Integrate t = 1 = 1 3 3(1+ da ah( a) H o ( Ω m a da + Ω w a w) 1 ) If w=-1 (so Ω x =Ω Λ ): If w - 1 (given k= assumption) t= / 3(1+w) H 46

47 Measurements of the age of universe Krauss + Chaboyer (3) Fit globular cluster age with a monte carlo approach to take uncertainties into account stars age = 1.6 Gyr t >1.4 Gyr 95 % From the density estimation with CMB data + flatness -> t ~13.4 Gyr 47

48 a 48

49 The current budget 49

50 A Revolution in Cosmology Inflation Big Bang Nucleosynthesis Flat universe Ω total = 1.+/-. Baryon Density Ω B =.44+/-.4 Ω M -Ω Λ = C Ω DE =.7, Ω M =.3 for a flat universe WMAP Weak lensing mass census Large scale structure measurements Ω M =.3 Ω M +Ω Λ = C New Standard Cosmology: 73±4% Dark Energy 7±4% Matter.5% Bright Stars Matter: % CDM, 4.4% Baryons,.3% ns 5

51 Λcdm Cosmological constant Or a dark energy We don t know Cold dark matter That we dont know = standard model Ω Λ = /3 Ω m = 1/3 + Initial adiabatic perturbations with an Harrison Zeldovitch spectrum n=1 (inflation) Ω tot = 1 h.7 Ω b.4 Ω ν =.5 Ω γ =.5 51

52 The story of the Universe 5

53 The universe : a question of temperature Expansion => volume increases a(t) 3 => temperature decreases as a(t) The radiation density is T 4 ( Stefan law) Matter as 1/Volume = 1/a 3 = T 3 => radiation dominates when T increases T 1/a(t) T = 1 1 K / vt (s) 53

54 At 1 s, the temperature is 1 1 K..only 1 Mev At early phases of creation, energy was sufficient to create huge numbers of MASSIVE particles and antiparticles, hence there was a lot of annihilation. (highly energetic photons). Upshot is that the photons we see then were created in the first second after the Big Bang. However, the photons actually trace the condition of the Universe at age 3, years. At this time we say matter decoupled from radiation. 54

55 Thermal story of the Universe Phases of Thermal story Temperature redshift Expansion scale a ~ exp[ Ht] ( ) a = 1/ 1+ z Inflation, GUT 1 1 GeV??????? End of inflation reheating Baryogenesis 1 TeV electroweak transition 1 MeV Neutrinos decoupling Nucleosynthesis Equivalence, à ev Photons decoupling (CMB) z=11 1 / a ~ t 3 / a ~ t z <1 Structures format Present T=.7 K z= 55

56 Stars and life Universe start atoms form Nucleosynthesis light elements neutrinos decoupling u u d Baryogenesis creation of proton and neutron Symmetry breaking antimatter disappear particles become massive Inflation Planck area 56

57 Visible matter: first budget Free H and He 4% Visible light from stars.5 % Neutrinos.5 % Heavy element.3% Nuclear processes to produce such abundance : a great success between Theory and observation

58 Start from the beginning.. t < 1-43 s Planck time physic law not applied 1-43 s < t < 1-3 s plasma of quarks etc..; Expansion of a factor 1 5..antimatter disappears 1-3 <t<1-6 s breaking strong and electroweak interaction 1-6 <t<1s formation of nuclei p,n,e,ν,γ 58

59 Nucleosynthesis p and n are interacting. As the Universe cools (expansion) (lower 1 MeV), they stop to interact : at this point, the number of neutrons relative to protons (neutrons are slightly heavier) is 1 n for 6 p. (Neutron have a life time of 1 mn and give n->p+e+n ) 3 3 n + p H +γ 3 H + H He + 3 He + n H + 4 H + H He+ n p n All neutrons end up in He and thus neutron/proton asymmetry determines primordial abundance of Helium and other light elements direct predictions For a radiation dominated epoch,the relative abundance of light element depend only on the baryon density This number has been measured by WMAP precisely 59

60 Big Bang Nucleosynthesis Theory vs. Observations: Remarkable agreement over 1 orders of magnitude in abundance variation Concordance region: Ω b h =. For h=.7, Ω b =.4. Deuterium: strongest constraint 4 He Ω b 6

61 15 mn after the Big Bang H,He,Li 7 as T decreases, not possible to continue. Heavier elements are produced later (bmillion of years..) from nuclear processes in stars as supernovae Wait 3 years. T allows photons to decouple. 61

62 Stellar nucleosynthesis Stars start with H et He gaz contraction T increases up to 1 6 K H burns T continues to increase K He burns 6

63 Next lecture Understanding the dark matter What we now from observationnal point of view What we expect from theory. 63

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65 Hubble radius and horizon Us t The universe is expanding with a radius which is the Hubble radius There are events outside our horizon and events which are inside but was outside the Hubble radius at a given time The light cone gives our horizon recombinaison Big bang A structure with a size greater than the Hubble radius is only affected by the metric If the size is smaller than the Hubble radius, the structure is affected by causality (physic) This is a paradoxe with CMB we will explain it later 65

66 Distances dans l univers local expansion linéaire Loi de Hubble distance lumineuse f = L/4πd L f = flux mesuré et L = flux émis d L = a r(1+z) = c(1+z)/h 1+ z =λ obs /λ emis =a /a(t) On utilise la relation distance-luminosité m-m=5log(d/1pc)-5 Distances d une chandelle standard (M=const.) m=5log(z)+b b = M+5+5log(c)-5log(H ) logh =log(z)+5+log(c)-.(m-m) Magnitude mesurée Normalisation absolue 66