Lecture 7(cont d):our Universe 1. Traditional Cosmological tests Theta-z Galaxy counts Tolman Surface Brightness test 2. Modern tests HST Key Project (H o ) Nucleosynthesis (Ω b ) BBN+Clusters (Ω M ) SN1a (Ω M & Ω Λ ) CMB (Ω k & Ω R ) 3. Latest parameters 4. Advanced tests (conceptually) CMB Anisotropies Galaxy Power Spectrum Course Text: Chapter 6 & 7 Wikipedia: Dark Energy, Cosmological constant, Age of Universe
Advanced tests: CMB The CMB contains significantly more information that the horizon scale( 1 st peak) and radiation density. In fact all cosmological parameters can be derived from detailed fitting of the anisotropies alone but needs to be calculated via Monte-Carlo simulations. Anisotropies are measurements of variance on specific angular scales or multi-pole number (l)., e.g.,
By exploring all scales (multipoles) one builds up the full anisotropy plot with different features relating to distinct cosmological params.
Fit to data very good.
Dependencies Height of 1 st peak is dominated by where The Baryons are at decoupling. Location of 1 st peak dominated by total curvature and current expansion rate 2 nd peak is dominated by where The dark matter is which has had time to collapse Other peaks are interfering harmonics and have no singular culprit. Try online tool at: http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html To gain an appreciation of the dependencies. Its really really good.
Fit to data very good.
WMAP yr 5 constraints http://lambda.gsfc.nasa.gov/
Advanced tests: P(k) Galaxies are not randomly distributed in space Can measure their correlation function Fourier transform is the Power spectrum k=wavenumber dp = n -2 (1 +!(r 12 )) dv 1 dv 2!(r) = 1! k 2 P(k) sin(kr).dk 2" 2 kr ξ(r)=probability of finding an excess of galaxies in volume V 2 from volume V 1 (zero on all scales = random)
Bubbly galaxies on boundaries between voids ~1985 CfA Redshift Survey z = 0.05 Coma Cluster Huchra, Geller, de Laparet
The Great Wall z = 0.05 Fingers of God
2dF = 2 degree Field CfA
Numerical simulations required to calibrate bias of the galaxy population Steps Conduct major galaxy survey Measure P(k) Measure P(k) for a simulation Calibrate out the bias (galaxies not equal to dark matter) Extract cosmological params.
Numerical Predictions Galaxies AS 3011 15
Numerical Predictions Galaxies AS 3011 16
Numerical Predictions Galaxies AS 3011 17
Galaxy Power Spectrum P(k)
Consistency with Other Constraints Cluster baryon fraction Nucleosynthesis CMB anisotropies Galaxies AS 3011 19
Lec 8: Inflation 1. Problems with the Big Bang - The Flatness Problem - The Horizon Problem - Cross-over conspiracy - Age conspiracy 2. Inflation - Λ again - Stopping inflation 3. Tired Light Cosmology 4. Summary/Review Course Text: Chapter 12 Wikepedia: Inflation
Flatness Problem From Friedmann Eqn: H 2 (t) = 8!G"! kc2 3 R 2 (t) Let: "(t) = 8!G" 3H 2 (t) # H 2 (t) = "(t)h 2 (t)! kc2 R 2 (t) # "(t)!1 = 1 H 2 (t)r 2 (t) = R2!R 2 R 2 = 1! R 2 For Matter Dominated Universe: R $ t 2 3 1 % "(t)!1 $ & d(t 2 3 ) $ t 2 3 $(1+ z)!1 2 ( ) + '( dt * + # "(t)!1 =1! " M!1 (1+ z) =1! 0.8 1000 = 0.9998 at decoupling 0.999999999999999<" M <1.000000000000000 at Nucleosynthesis
Why so close to 1? Anthropic principle Fluke Fundamental Physics Flatness Problem
Horizon Problem Our Horizon Bs Horizon B has never known of A but shares similar properties, i.e., same Temp, same anisotropies Implies once were in thermal equilibrium which is impossible
Relic monopole problem In the standard particle model some massive particles could be stable. Topological defects caused by phase transitions in a rapidly cooling Universe Should dominate mass today Need to find a way to reduce their abundance
Inflation Proposed by Alan Guth in 1981 to explain both problems. Want A & B to be in causal contact and afterwards rapidly expand the Universe prior to decoupling i.e.,!! R(t) > 0 From F2, as abefore only! can do this. " $ #!R R % ' & 2 R = e " $ # =! 3! 3 t % & or!r =! 3 R ', i.e., exponential expansion
Inflation fixes both problems Rapid Expansion But, it can do too good a job and easily set Ω M =1 unless it stops. A. B A. B In Casual Contact No longer in casual contact
Stopping inflation Inflation will solve these problems but will also accelerate the Universe so fast no structure can form. Inflation must stop at some point. The term phase-transition is used but there is no real insight here, ρ Λ must suddenly drop in value. Inflation may also plant the seeds for structure growth with quantum fluctations amplified to produce the anisotropies. Problems: Speculative idea only The good old cosmological constant to the rescue again Why did it stop after ~70 e-folding times (70 doublings) Why is the Universe just starting to inflate again (Dark Energy) Cosmological constant = Dark Energy = inflation Alternative is Universe simply started flat and in equilibrium, i.e., set initial conditions instead of inflation.
Summary Expansion Observed and Required (Olber s Paradox) 4 He explained, CMB and other phenomina predicted Cosmological model: CP+GR+RWM distances, ages, volumes and angles 1980s Inflation introduced 1990s Open Universe favoured 2000s Dark Energy required by SNIa 2001 Era of precision cosmology (multiple independent measurements) Era of CMB anisotropy missions (COBE, WMAP, PLANK) Outstanding problems: Did the Universe really inflate? What is the dark matter particle mass and nature What is dark energy, w=-1 or w(t)? Is there a problem with GR, i.e., rather than add new contents need to do more with the existing contents. Multiverse? Quantum-Gravity?
Multiverse?