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What is the Origin of the Universe?. What is the Fate of the Universe?. How Old is the Universe?. 1644: Dr. John Lightfoot, Vice Chancellor of Cambridge University, uses biblical genealogies to place the date of creation at September 21, 3298 BC at 9 AM (GMT?)

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What is the Origin of the Universe?

What is the Fate of the Universe?


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How Old is the Universe?

  • 1644: Dr. John Lightfoot, Vice Chancellor of Cambridge University, uses biblical genealogies to place the date of creation at September 21, 3298 BC at 9 AM (GMT?)

  • 1650: James Ussher, Archbishop of Armagh and Primate of All Ireland, correlates Holy Writ and Middle Eastern histories to “correct” the date to October 23, 4004 BC

  • Current Jewish calendar would “suggest” a date of creation about Sep/Oct 3760 BCE


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Cosmological Principle

At any instant of time, the universe must look homogeneous and isotropic to any observer.

Perfect Cosmological Principle

…….and indistinguishable from the way it looked at any other instant of time.


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How Old is the Universe?

  • 1760: Buffon uses cooling of Earth from its molten state to estimate age as 7.5x104 years

  • 1831: Charles Lyell uses fossils of marine mollusks to estimate age as 2.4x108 years

  • 1905: Lord Rutherford uses radioactive decay of rocks to estimate age as > 109 years (later refined to 4.3x109 years)


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Equivalence Principle

Consider a test particle with mass m and charge q

Electrostatic force on q due to Q @ r is Fe = q (kQ/r2)

 acceleration = Fe/m = q/m (kQ/r2)

Gravitational force on m due to M @ r is Fg= m (GM/r2)

 acceleration = Fg/m = m/m (GM/r2) = GM/r2

if gravitational and inertial masses are equivalent


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… but the equilibrium is unstable. In order to prevent the universe from either expanding or contracting, Einstein introduced a scalar field that was called

The Cosmological Constant

in order to keep the universe static.


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Astronomical Redshifts

λ = observed wavelength

λo = “laboratory” or “rest” wavelength

Δλ = λ – λo

= (1 + z) λ

z = redshift = √[(c+v)/(c-v)] - 1 →v<<c v/c


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The Age of the Universe

No gravity: v = Hor  to = r/v = Ho-1

Newtonian gravity for a flat universe:

½ mv2 - GmM/r = 0  v = dr/dt = (2GM/r)½

so we can integrate r½dr = (2GM)½dt to get

to = 2/3 (r3/2GM)½ = 2/3 (r/v) = 2/3 Ho-1


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fromAn Essay on Criticism

by Alexander Pope

A little Learning is a dang'rous Thing;

Drink deep, or taste not the Pierian Spring:There shallow Draughts intoxicate the Brain,And drinking largely sobers us again.


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Cosmological Principle

At any instant of time, the universe must look homogeneous and isotropic to any observer.

Perfect Cosmological Principle

…….and indistinguishable from the way it looked at any other instant of time.


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Steady-State Theory

The expansion of the universe is balanced

by the spontaneous production of bubbles

of matter-anti-matter, so that the Perfect

Cosmological Principle is preserved.

Nucleosynthesis in stars can account for

the abundances of all the elements except

the very lightest – is that a problem?


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Gamow’s Test for a Big Bang versus a Steady State Universe

  • If there was a Big Bang, there should be some cooling remnant radiation (now maybe 5K?) that pervades the universe

  • If, instead, the universe is always the same, there should NOT be any cooling radiation


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Evidence for the Hot Big Bang

Hubble flow

Ho measures the universe at approximately t= 1010 yrs

Cosmic microwave background radiation

CMB measure the universe at approximately t = 4 x105 yrs

Abundances of the light elements

BBN measures the universe at approximately t = 200 s


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So What’s the Problem(s)?

The horizon problem

How did the universe become so homogeneous on large scales?

The flatness problem

Why is density of the universe so close to the critical density?

The structure problem

Is there a physical origin for the density perturbations?


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Critical Energy Density of the Universe

Total energy associated with a galaxy of mass m: ½ mv2 - GmM/r

 0 if barely bound

M = 4/3 πr3ρnow= 4/3 πr3ρo

r (t) = a(t) = H-1(t)v(t)

 r = Ho-1v

ρo= ¾ M/(πr3) = 3/8 v2/(πGr2) = 3Ho2/(8πG)

Ω = ρ/ρo 1 if the universe is flat


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The current value of Ω….

…and it’s value at any time in the past

…must be exactly 1.00000000000…..


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Standard Model circa 1990

Hot Big Bang from Cosmic Background Radiation (CMB)

Horizon and flatness suggest inflation

Inflation demands that Ω = 1 very precisely

But ΩB < .05 from light element nucleosynthesis

Where is the other > 95% of the mass?

DARK MATTER


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Galactic Rotation Curves

For a star of mass m a distance r from the center of

a galaxy, where the total mass interior to r is M(r):

mv2/r = GM(r)m/r2

so that we would expect

v= [GM(r)/r] ½ so that v should go like r -½



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Oscillations on many scales

Source: Wayne Hu: background.chicago.edu


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Early Universe Acoustics

Sound speed cs ≈ √w = √(p/ρ) ≈ c/√3

Density fluctuations

are they random (Gaussian, scale-independent…?)

Measure cross-correlation in spherical harmonics


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Wtot = 1.0

WL = 0.0

h = 0.65

n = 1.0

Wb = 0.12

Wb= 0.08

Wb= 0.05

Wb= 0.03

Wm = 0.3

Wm= 0.7

Wm= 1.0

Wm= 0.3

WL = 0.7

WL = 0.3

WL = 0.0

WL = 0.0

Wb = 0.05

h = 0.65

n = 1.0

CMB Anisotropy Power Spectra

Dependence on Cosmological Parameters

Angular Scale

90°

0.5°

0.2°

6000

4000

2000

6000

Anisotropy Power (µK2)

4000

2000

0

2

10

40

100

200

400

800

1400

Multipole moment


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Power Spectrum

cosmic variance

limited for l<354

S/N>1

for l<658


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The Top Ten

to = 13.7 ± .2 Gyr

tdec = 379 ± 8 kyr zdec = 1089 ± 1

Tcmb = 2.725 ± .002 K

ns = 0.93 ± .03

mν < .023 eV

tr = 180 ± ~100 Myr zr = 20 ± 10

Ho = 71 ± 4 km/s-Mpc

Ωtot = 1.02 ± .02

ΩΛ = .73 ± .04

 Ωm = .27 ± .04

Ωb = .044 ± .004


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