Structures in the early Universe
Particle Astrophysics chapter 8 Lecture 4 overview • problems in Standard Model of Cosmology: horizon and flatness problems – presence of structures
• Need for an exponential expansion in the early universe • Inflation scenarios – scalar inflaton field
• Primordial fluctuations in inflaton field • Growth of density fluctuations during radiation and matter dominated eras
• Observations related to primordial fluctuations: CMB and LSS
2011-12 Structures in early Universe 2 •Galactic and intergalactic magnetic fields as source of structures? •problems in Standard Model of Cosmology related to initial conditions required: horizon and flatness problems PART 1: PROBLEMS IN STANDARD COSMOLOGICAL MODEL
2011-12 Structures in early Universe 3 Galactic and intergalactic B fields
cosmology model assumes Non-uniformity observed uniform & homogeous in CMB and galaxy medium distribution,
• Is cltilustering of matter ithin the universe dtdue to galtilactic and intergalactic magnetic fields? • At small = stellar scales : intense magnetic fldfieldsare onlyimportant in later stages of star evolution • At galtilacticscale: magnetic fie ld in Milky Way ≈ 3G3µG • At intergalactic scale : average fields of 10-7 –10-11 G • → itinterga lac ticmagnetic fie ldsprobblbably have very small role in development of large scale structures • DlDevelopmen toflf large scallleesstttructures mailinly dtdue to gravity
2011-12 Structures in early Universe 4 Horizon in static universe • Particle horizon = distance over which one can observe a particle by exchange of a light signal vvc=c • Particle and observer are causally connected • In flat universe with k=0 : on very large scale light travels nearly in straight line
• In a static universe of age t photon emitted at time t=0 would travel STATIC t < 14 Gyr DctH =
• Would give as horizon distance today the Hubble radius SSCTATIC DtctGpcH ( 00)==424.2
2011-12 Structures in early Universe 5 Horizon in expanding universe
• In expanding universe, particle horizon for observer at t0
t0 R(t0 ) DdDH (tc0 )= dt ∫0 Rt() • EdiExpanding, fla t, ra dia tion ditddominated universe 1 2 Rt() ⎛⎞t Dt( )= 2 ct = ⎜⎟ H 00 Rt()0 ⎝⎠t0 • Expanding,flat,, flat, matter dominated universe 2 3 Rt() ⎛⎞t DtH ()00= 3 ct = ⎜⎟ Rt( 0 ) ⎝⎠t0 DtH ()00= 3.3 ct • expanding, flat, with Wm=0.24, WΛ=0.76 ~ 14Gpc
2011-12 Expanding Universe 6 Summary lecture 1
4 radiationρ c2 ∼ (1+ z) 3 matterρ c2 ∼ ()1+ z vacuumρ c2 ∼ cst 2 curvatureρ c2 ∼ ()1+ z
2011-12 Structures in early Universe 7 Horizon problem • At time of radiation-matter decoupling the particle horizon was much smaller than now • Causal connection between photons was only possible within this horizon • We expect that there was thermal equilibrium only within this horizon • Angle subtented today by horizon size at decoupling is abt1bout 1° • Why is CMB uniform (up to factor 10-5) over much larger angles, i.e. over full sky? • Answer : short exponential inflation before decoupling
2011-12 Structures in early Universe 8 Horizon at time of decoupling • Age of universe at matter-radiation decoupling
5 tydec =×410 zdec ≈1100 • Optical horizon at decoupling static Dtγγ ()dec= ct dec Dt=+ ct1 z • This distance measured today γγ ()0 dec ( dec ) • angle subtended today in flat matter dominated universe
Dtγγ ()0 ctdec()1+ z dec θdec ∼∼ ∼1° DtHdec()003 ctt()−
2011-12 Structures in early Universe 9 Flatness problem 1 • universe is flat today, but has been much flatter in early universe • How come that curvature was so finely tuned to Ω=1 in very early universe? kc2 • Friedman equation rewritten Ω−=()t 1 22 Rt( ) Ht( )
radiation domination Ω−()tt1~ ∼ n Rt( ) t 2 matter domination Ω−()tt1~ 3
−16 • At time of decoupling Ω−1~10 • At GUT time (10 -34s) Ω −1101 ~ 10−52
2011-12 Structures in early Universe 10 Flatness problem 2 • How could Ω have been so closely tuned to 1 in early universe? • Standard Cosmology Model does not contain a mechanisme to explain the extreme flatness • The solution is INFLATION ? Big Bang Planck scale GUT scale today
ts=10−44 ts=10−34
2011-12 Structures in early Universe 11 Horizon Flatness problem problem
Non-homogenous universe
The solution is INFLATION
2011-12 Structures in early Universe 12 The need for an exponential expansion in the very early universe PART 2 EXPONENTIAL EXPANSION
2011-12 Structures in early Universe 13 Accelerated expansion domination of Dark Energy
Steady state expansion Radiation and matter dominate Described by SM of Cosmo
Exponential expansion inflation phase © Rubakov 2011-12 Structures in early Universe 14 Constant energy density = exponential expansion
• Assume that at Planck scale the energy density is given by a cosmological constant Λ ρ ==ρ tot Λ 8 G • AconstantA constant energy density causes an exponentialπ expansion
• For instance between t1 and t2 in flat universe