MODERN COSMOLOGY LECTURE FYTN08

Transcription

1 1/43 MODERN COSMOLOGY LECTURE Lund University bijnens Lecture Updated 2015

2 2/43

3 3/ Some problems with a simple expanding universe Credit many pictures: ESA, NASA, WMAP, Planck, Scientific American

4 I: Flatness problem Rewrite Friedman-Lemaître equation as 3H 2 8π = 3k2 8πR 2 + ρ H = Ṙ R k = 0 or flat defines critical density ρ c 3H2 8π measure all components of ρ in units of ρ c : Ω i = ρ i ρ c Time evolution k R(t) 2 = H(t)2 (Ω(t) 1) e.g. Matterdominated (Ω(t) 1) kt 2/3 Ω 1 does not stay there Flatness problem: close to 1 now, really close to 1 in early universe For cosmological constant dominated: R(t) e αt = (Ω(t) 1) e 2αt 4/43

5 I: Flatness problem Rewrite Friedman-Lemaître equation as 3H 2 8π = 3k2 8πR 2 + ρ H = Ṙ R k = 0 or flat defines critical density ρ c 3H2 8π measure all components of ρ in units of ρ c : Ω i = ρ i ρ c Time evolution k R(t) 2 = H(t)2 (Ω(t) 1) e.g. Matterdominated (Ω(t) 1) kt 2/3 Ω 1 does not stay there Flatness problem: close to 1 now, really close to 1 in early universe For cosmological constant dominated: R(t) e αt = (Ω(t) 1) e 2αt 4/43

6 II 5/43 We see the universe as the same from all directions Not all these spots have had time to talk to each other Homogeneity problem Many phase transitions possible Create defects: vortices (cosmic strings), domain walls,... All of these contain large amounts of energy None seen, so either no phase transitions or they have had time to align Monopole problem

7 II 5/43 We see the universe as the same from all directions Not all these spots have had time to talk to each other Homogeneity problem Many phase transitions possible Create defects: vortices (cosmic strings), domain walls,... All of these contain large amounts of energy None seen, so either no phase transitions or they have had time to align Monopole problem

8 III 6/43 The early universe was very smooth Where does the observed structure come from? Much structure seen: galaxies, voids, sheets, the great wall,... How are these formed? Structure formation problem

9 7/43 At some point very early in the universe we had a period dominated by Λ This is not the present Λ or dark energy Blow up a small region that had fully homogeneized to enormous size Solves homogeneity problem Solves monopole problem (for earlier first order phase transitions) That bit also gets really flat Solves flatness problem During the blowup: quantum fluctuations get very big, become real Possible seeds of structure Can solve structure problem

10 credit NASA/IPAC 8/43

11 9/43 Matter ρ M R 3, radiation ρ R R 4 In addition all momenta were bigger earlier since λ 1 p R(t) Early universe dominated by radiation Present: Matter+cosmological constant (dark energy) t years or T 1eV : decoupling/recombination Accident: becomes radiation dominated at about the same time t a few minutes or T 1 MeV: Primordial nucleosynthesis (BBN) Much earlier T >> 100 GeV:

12 ladder 10/43 Main problem in cosmology: Measuring distances ladder: Parallax: triangulation easy in principle take base: Earth orbit main problem: how accurate to measure the angles Note old debate: if earth moves around sun, why don t the stars move? Now dominated by satellite: Hipparchos, Hubble, Gaia (to come) Redshift distance: simply take the redshift as a measure of distance Luminosity distance

13 ladder 11/43 Luminosity distance Flux (in flat space) goes like 1/d 2 Know Luminosity at source, measure luminosity at earth know the distance Small correction: if curvature take into account (example all the light emitted in a sphere surface from Southpole arrives at Northpole) Essentially start close by and then work further out Cepheid variables: period Luminosity... Supernovae Ia: Luminosity decay period Luminosity

14 Expansion Nobel Prize /43

15 Three main satellites 13/43 COBE: up Final data 1996 WMAP : up Final data 2012 Planck: up Final data??? (3rd batch February 2015) Also many ground based measurements, galaxy surveys,...

16 Perfect black body radiation 14/43

17 Perfect black body radiation 15/43

18 : homogeneity/isotropy 16/43 This is data, not a uniform picture Note: discovered 1960s, Nobel Prize 1978 Penzias Wilson

19 : homogeneity/isotropy 17/43 So v 600 km/s Originally discovered in 1970s

20 : homogeneity/isotropy 18/43 Nobel Prize 2006 Mather Smoot

21 : homogeneity/isotropy 19/43

22 WMAP/Planck 20/43 More frequencies (COBE 3, WMAP 5, Planck 9) Much better angular resolution Much better sensitivity Polarization Note: all-sky pictures have a fit of the foreground removed and a simualated spectrum across the galaxy

23 WMAP 5 year 21/43

24 Planck Nine months 22/43

25 Planck 2 years 23/43

26 Angular spectrum of fluctuations 24/43

27 WMAP 5 year 25/43 Plot temperature or intensity as a function of I (θ, φ) I (θ, φ) = C lm Yl m (θ, φ) lm For each l average the power over m: C l So we have an angular measure and fluctuations Ground based ones add at high l

28 Planck Two years 26/43 Note: SEVEN now visible

29 Everyone 27/43 Dl[µK 2 ] Planck WMAP9 ACT SPT l Can fit to nine

30 The source of the fluctuations 28/43 Small quantum fluctuations do exist blows them up so they cannot disappear again Expected power spectrum P s = A s ( k k 0 ) ns Tensor spectrum can come from priomordial gravitational waves P t = A t ( k k 0 ) nt predics n s 1 (scale invariant) and usually a little below 1. So then inflation stops, what now?

31 Growing and oscillating 29/43 Very long wavelength: frozen in, no time to interact As soon as within horizon (i.e. time to interact) Fluctuations grow: denser spots grow denser, rarer spots grow rarer (gravity is attractive) Then however: universe is dominated by radiation: we know the photon gas If too dense, pressure counteracts the compression by gravity, like sound waves (hence acoustic oscillations) Matter reacts much slower and in first hand only normal matter reacts with the photons So height first peak depends on photon density, we know that one, so get information on total matter and from the different sizes first second peak also on baryonic matter

32 How big is the first peak 30/43 We know the real size of the first peak plus the age, so the angle of view tells us flat, open (hyperbolical) or closed (spherical) from the shape of the triangles If neutrinos had mass: streaming kills of those so upper limit on neutrino mass. fluctuations should hook on to those measured from galaxy distributions (surveys) Number of neutrinos: how many radiation species: affects rate of also visible

33 Parameters 31/43 1 Ω ± Ω Λ ± Ω b h ± Ω c h ± H ± 0.46 km/s/mpc h ± Age ± Gyr n s ± ν m ν < ev w ± 0.045

34 Universe content (WMAP) 32/43 3 No Big Bang SNe: Knop et al. (2003) : Spergel et al. (2003) Clusters: Allen et al. (2002) 2 1 Ω Λ 0 Supernovae expands forever recollapses eventually Clusters closed 1 open flat Ω M

35 Universe content (WMAP) 33/43

36 34/43 Galaxy rotation curves: flat???

37 35/43 Globular clusters: also more matter needed than visible to bound them Seen in essentially all galaxies Clusters of galaxies needed for galaxy formation Weigh galaxies by gravitational lensing: see directly dark matter Colliding galaxies: dust interacts strongly, starsless, dark matter even less

38 36/43 Credit: X-ray: NASA/CXC/M.Markevitch et al. Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al. Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al.

39 Gravitational waves Copyright: Physics World IOP 37/43

40 Density Wave E-Mode Polarization Pattern Cold Hot Hot Cold Gravitational Wave Squeezes Space Cold Hot Temperature Pattern Seen by Electrons B-Mode Polarization Pattern Stretches Space Hot Cold Credit: BICEP collaboration 38/43

41 39/43 Credit: BICEP collaboration

42 Credit: Wikipedia commons 40/43

43 41/43 : E signal Simulation: E from lensed ΛCDM+noise µK 1.7µK µk Declination [deg.] : B signal 0.3µK Simulation: B from lensed ΛCDM+noise 0.3µK µk Right ascension [deg.] Credit: BICEP collaboration

44 B mode signal µK Declination [deg.] Right ascension [deg.] Credit: BICEP collaboration 42/43

45 43/ BICEP QUAD QUIET Q QUIET W CBI Boomerang DASI WMAP CAPMAP l(l+1)c l BB /2π [µk 2 ] r=0.2 lensing Multipole