Isotropic distribution of galaxies

Transcription

1 Isotropic distribution of galaxies APM (Automatic Plate Measure) Survey of a 100x50 sq region close to the southern Galactic pole (based on Schmidt plates taken with the UK Schmidt telescope in Siding Springs, Australia). Color codes galaxy density. Maddox et al. 1990

2 Jarrett MASS all sky data in Galactic coordinates. Blue: z<0.01, green: 0.01<z<0.04, red: 0.04<z<0.1

3 The universe is homogeneous

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5 Age of globular clusters The age of globular clusters (metal poor pop. II stars): ~1.2x1010yrs This imposes a lower limit on the age of the Universe He Flash Horiz. Bran ch Red gian t MS 47 Tuc

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10 Kinematic description: comoving coordinates Consider a homogeneous, isotropic sphere which is expanding or contracting (retaining its homogeneity): Choose a coordinate system with the origin in the center of the sphere and an observer at time t0: At a later time t>t0, the position will have followed the radial expansion, such that: a(t): cosmological scale factor

11 Expansion rate and Hubble law We can calculate the expansion rate by calculating the derivative of r(t): Now consider two different comoving observers: We have recovered a general form of the Hubble law: v=h0d with H0=H(t0)

12 Dynamics of the expanding sphere Let's look at the gravitational pull of the enclosed mass This gives us a relation for the matter density as a function of time: The gravitational pull can then be written:

13 Dynamics contd. Re-writing this for a(t) by replacing r=ax, effectively cancelling x!

14 The Friedmann-Lemaître equation In GR, we can derive the FL equations based upon the GR field equations and the Robertson-Walker metric (see e.g. Peacock exercise 3.1) Extra term not found in the Newtonian approximation Pressure term: not included in the Newtonian approximation

15 Critical density For K=Λ=0, the expansion stops when the density has a critical value Taking t=t0, we can calculate the critical density today (da/dt=h0, a(t=t0)=1) Commonly, densities are normalized to the critical density (unitless -but not useless) number)

16 Re-write the FL equation We express the densities in units of critical density This can be included in the FL equation For t=t0 (a(t=t0)=1, H(t=t0)=H0

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18 Overview of the thermal history of the Universe Early Universe: Inflation produces flat, homogeneous & isotropic Universe Primordial Plasma: Baryogenesis & Nucleosynthesis take place (t 100 s). Radiation dominated Universe Matter dominated (still ionised) Universe: Dark Matter Structures start to form (t> yrs) Recombination: Hydrogen&Helium ATOMS form (t= yrs) Matter dominated (neutral) Universe: The Dark Ages (no stars!)

19 Sakharov Conditions for Baryogenesis Partial Annihilatio n Asymmetry between Particle and AntiParticle (CP violation) Particle number conservation broken Deviation from thermal equilibrium Over abundance of baryons: nb n B = n

20 Discrete Symmetries Original picture White horses left Black horses right Parity changed White horses right Black horses leftparity not conserved! Charge changed White horses left Black horses CP rightconserved!

21 Original picture White geese right Black geese left Parity changed White geese left Black geese right Parity not conserved! Charge changed White geese right Black geese left: but look at the tail..

22 (naïve) estimate of η Total number of Baryons in the Universe: Number of galaxies: Ngal 1011 Typical mass of galaxy: Mgal 1011 M Number of baryons per M =2x1033 g, mostly hydrogen: NAM =1.2 x 1057 H-atoms Total number of baryons: Ngal Mgal NAM 1.2x1079 Density of Baryons in Universe: nbar=1.2x1079/v with V=4π/3 R3=1.4x1086 cm3 nbar 8.5x10-8 cm-3 nγ=410 cm-3 nb n B 10 = 2 10 n

23 How to get the right CP violation In electroweak interactions: CP violation has been observed In strong interactions: CP violation absent (electric dipole of neutron) In Quantumchromodynamics: CP violation possible, but not dynamic and too strong (=requires fine-tuning) What to do? Introduce the axion (as seen on tv) Electroweak Baryogenesis Spotaneous Baryogenesis Baryo-through-lepto-genesis Baryogenesis in black hole evaporation Baryogenesis by topological defects Antimatter-Universe

24 Hot Big Bang Nucleosynthesis It lasted 3 minutes (title of S. Weinbergs famous book) After Baryogenesis: p,n (n/p~exp(-q/t)~1/6 with Q=1.293 MeV) undergoing the following reactions: Neutron decay (t1/2=615 s): Deuterium production (t~100 s) when kt<0.1 MeV (n/ p~1/7) Once d: He3, He4, H3 are formed until Coulomb repulsion stops nucleosynthesis (t~3 minutes)

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27 Temporal evolution of mass abundances Fields&Sarkar 2006 η=3x x109 K 8

28 Comoving coordinates We define a comoving coordinate system The comoving density The velocity field Using these rules to modify the fluid equations: r =a x d =d t = t r x a x x a

29 Fluid equations in comoving coordinates Continuity equation Euler equation

30 Continuity equation in comoving coordinates We can rewrite the continuity equation when using Now, we have a set of equations for the evolution We can look at the linear case (small δ)

31 Linear approximation Consider the linear set of equations (neglecting higher order terms in v,δ, or δv terms)

32 Solution for δ Solution of the form: With D+/- solving the ODE: Some implications/discussions: D+/- are two modes, one growing (D+), one decaying (D-) D+ is the growth factor Shape of fluctuations is constant, amplitude is growing Neglected pressure terms (relativistic photon gas etc.)->follow a more general (more complicated) approach for early universe

33 Peacock

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