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Home , Flatness problem, Horizon problem

Lecture 7(cont’d):Our

1. Traditional Cosmological tests – Theta-z – Galaxy counts – Tolman Surface Brightness test 2. Modern tests

– HST Key Project (Ho)

– Nucleosynthesis (Ωb)

– BBN+Clusters (ΩM)

– SN1a (ΩM & ΩΛ)

– CMB (Ωk & ΩR) 3. Latest parameters 4. Advanced tests (conceptually) – CMB – Galaxy Power Spectrum

Course Text: Chapter 6 & 7 Wikipedia: , , Age of Universe Advanced tests: CMB

• The CMB contains significantly more information that the horizon scale( 1st 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 plot with different features relating to distinct cosmological params.

Fit to data very good. Dependencies

Height of 1st peak is dominated by where The Baryons are at .

Location of 1st peak dominated by total curvature and current expansion rate

2nd peak is dominated by where The dark 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 -2 dP = n (1 + !(r12 )) dV1 dV2 • Fourier transform is the Power spectrum 1 sin(kr) !(r) = k 2P(k) .dk 2" 2 ! kr • k=wavenumber

• ξ(r)=probability of finding an excess of galaxies in volume V2 from volume V1 (zero on all scales = random) “Bubbly” ~1985 CfA Survey galaxies on z = 0.05 boundaries between voids

Coma Cluster

Huchra, Geller, de Laparet “The Great Wall”

z = 0.05

“Fingers of God” 2dF = 2 degree

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

Nucleo- synthesis

CMB anisotropies

Galaxies – AS 3011 19 Lec 8:

1. Problems with the - The - The - Cross-over conspiracy - Age conspiracy 2. Inflation - Λ again - Stopping inflation 3. Tired Light 4. Summary/Review

Course Text: Chapter 12 Wikepedia: Inflation Flatness Problem From Friedmann Eqn: 2 2 8!G" kc H (t) = ! 3 R2 (t) Let: 8!G" "(t) = 3H 2 (t) kc2 # H 2 (t) = "(t)H 2 (t)! R2 (t) 1 R2 1 # "(t)!1 = = = H 2 (t)R2 (t) R! 2 R2 R! 2 2 For Matter Dominated Universe: R $ t 3 1 2 % "(t)!1 $ $ t 3 $(1+ z)!1 2 2 &d(t 3 )) ( + '( dt *+ " !1 0.8 # "(t)!1 =1! M =1! = 0.9998 at decoupling (1+ z) 1000

0.999999999999999<"M <1.000000000000000 at Nucleosynthesis Flatness Problem

• Why so close to 1? – – Fluke – Fundamental Physics 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 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. 2 " R! % ! ! $ ' = or R! = R # R & 3 3

" ! % $ t' R = e# 3 &, i.e., exponential expansion Inflation fixes both problems

Rapid Expansion

• But, it can do too good a job and easily set ΩM=1 unless it stops.

A . B A . B

In Casual No longer in Contact 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, ρΛ 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) • 4He 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. – ? – Quantum-? Multiverse?