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§1 – Observational Cosmology – Hot Big Bang

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§1 – Observational Cosmology – Hot Big Bang 1 – Observational Cosmology – Hot Big Bang http://www.sr.bham.ac.uk/~smcgee/ObsCosmo/ Sean McGee [email protected] Outline • Reminder: • Y3 assessed problem set 1 (Due: Oct 30, 3:30 pm (TSO)) • Y4 assessment exercise (Due: Dec 13, 3:30 pm (TSO)) • Discussion of Unit 1 topics: • Redshift • Hubble Expansion • Comoving frame/peculiar velocities • Isotropy/homogeneity; galaxy distributions; cosmological principle • Distance scale / Hubble parameter • CMB • Nucleosynthesis http://www.star.sr.bham.ac.uk/~smcgee/ObsCosmo Observational overview • Observations in visible light: • Stars – 1030 kg; sourced by nuclear fusion; 1 pc = 3.2 Lyrs • Galaxies – 1011 stars/solar masses; Milky way – 12.5 kpc in radius; 0.3 kpc high • The Local group – LMC, SMC, Andromeda – a few Mpc (1 Mpc = 3.086 X 1022 metres • Clusters of galaxies, supercluster, voids – rich structure on the scale of 100 Mpc • Smooth on large scales. Observational overview • Observations in microwaves – CMB • Radio Waves – galaxies, AGN, reionization • Infrared – dust obscured star formation • X-rays – hot plasmas; Galaxy clusters, AGN Cosmological principle Cosmological principle – We do not occupy a unique position in the Universe. At each epoch, the universe is the same at all locations and in all directions, except for local irregularities. The universe is isotropic and homogeneous at any given time, and its dynamics should be the same everywhere. Cosmological principle Cosmological principle – We do not occupy a unique position in the Universe. At each epoch, the universe is the same at all locations and in all directions, except for local irregularities. The universe is isotropic and homogeneous at any given time, and its dynamics should be the same everywhere. Homogeneity – The universe looks the same at each point Isotropy – The universe looks the same in all directions. Cosmological principle Cosmological principle – We do not occupy a unique position in the Universe. At each epoch, the universe is the same at all locations and in all directions, except for local irregularities. The universe is isotropic and homogeneous at any given time, and its dynamics should be the same everywhere. Homogeneity – The universe looks the same at each point Isotropy – The universe looks the same in all directions. Note: different from Perfect Cosmological Principle, which states the Universe appears the same at all times and is unchanging. Homogeneous and Isotropric Homogeneous and Isotropric But, this is not true on smaller scales Luminosity distance Angular diameter distance ds2 = c2dt2 + a(t)2[dr2 + S (r)2(d✓2 + sin2✓ dφ2)] − k Sk(r)=r (for k =0),R0sin(r/R0)(fork =+1),R0sinh(r/R0)(fork = 1) , ds2 = c2dt2 + a(t)2[dr2 + S (r)2(d✓2 + sin2✓ dφ2)] − − k a˙ 2 8⇡G⇢ kc2 H2 = , Sk(r)=r (for k =0),R0sin(0r/R1 0)(fork =+1),R2 20sinh(r/R0)(fork = 1) , ⌘ a 3 − R0a @ A − 2 2 2 2 2 2 2 2 2 ds = c dt + a(t) [dr + Sk(r) (d✓ + sin ✓ dφ )] a¨ 42⇡G 2 2 − Distances 2 = a˙ (8⇢⇡+3G⇢P/ckc) , H a 0−1 3= 2 2 , ⌘ a 3 − R0a S (r)=r (for k =0),Rsin(r/R )(fork =+1),Rsinh(r/R )(fork = @1) ,A k Distances0 0 0 0 3−a˙ ⇢˙ = a¨ (⇢ +4⇡P/cG 2) ,P= w⇢c2 . With the above definition of the comoving coordinates,− a= the( ⇢proper+3P/c distance2) , to an 2 2 a − 3 object (measured2 a˙ along8⇡G a⇢ geodesickc at time t) is simply H 0 1 = 2 2 , ⌘ a 3 − R0a r @ A d (t)=a(t) dr = a(t)3rda˙ = 2d (t )(1+z) 2 d = d (t )/(1 + z) p 0 ⇢˙ = (⇢ + LP/c )p ,P0 = w⇢c .A p 0 a¨ 4⇡G Z − a = (⇢ +3P/c2) , a − 3 t t r dt0 dt0 and for a flat universe (k=0) thedp(t rluminosity)=hor(ta)=(t) c dr distance= a(t) rddhoris ( t )=L =ad(tp)(tr0hor)(1+(t) zd) hor(dt)=A =ad(pt)(ct0)/(1 + z) 3a˙ Z0 Z a(t ) Z a(t ) ⇢˙ = (⇢ + P/c2) ,P= w⇢c2 . 0 0 0 0 − a 2 t 3H t dt0 ⇢c = dt0 r rhor(t)=c dhor(t)=a(t8)⇡rGhor(t) dhor(t)=a(t)c dp(t)=a(t)anddr the= a angular(t) rd diameterL = dp(t0)(1+ distancez) dA = d0Zp(at(0t)0/)(1 + z) . 0Z a(t0) Z0 a¨ 4⇡G = ⇢3(1H2 + 3w) , t t a −⇢ 3= dt0 dt0 c 8⇡G rhor(t)=c dhor(t)=a(t) rhor(t) dhor(t)=a(t)c 0Z a(t0) 0Z a(t0) 8⇡G⇢ a(t) a¨eHt 4⇡GH2 = v = ⇤/3 / = ⇢(1 + 3w3 ) , 3H2 a − 3 ⇢c = 8⇡G l δT 1 m (✓,Htφ)= 2 a8lm⇡GYl⇢v(✓, φ) T m=0 a¨ 4⇡G a(t) e lX=0H X= = ⇤/3 = ⇢(1 + 3w) , / 3 a − 3 l δT 1 m (✓, φ)= almY (✓, φ) 8⇡G⇢v l a(t) eHt H2 = = ⇤/3 T lX=0 mX=0 / 3 l δT 1 m (✓, φ)= almYl (✓, φ) T lX=0 mX=0 Redshift Cosmological Redshift Comoving frame and peculiar velocities Hubble law defines a frame of reference Being at rest in this frame is said to be ‘comoving’ We have a peculiar velocity of ~ 350 km/s Comoving frame and peculiar velocities Hubble law defines a frame of reference Being at rest in this frame is said to be ‘comoving’ We have a peculiar velocity of ~ 350 km/s Velocity = H*x + peculiar velocity Distance scale and H0 Parallax – only model independent method Cepheids – evolved high-mass stars on the instability strip in H-R diagram RR Lyrae Stars – evolved old, low mass, low metallicity stars – short periods Supernovae – intrinsic brightness known – Ia (binary WD detonating) Tully-Fisher – luminosity related to rotation speed Cosmic microwave background .
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