The Standard Model of Cosmology

The Standard Model of Cosmology

Chad A. Middleton, Ph.D.Mesa State CollegeOctober 11, 2007

“The most incomprehensible thing about the world is that it is comprehensible.”

-A. Einstein

Cosmologyis the scientific study of the large scale

properties of the Universe as a whole.

addresses questions like:

Is the Universe (in)finite in spatial extent? Is the Universe (in)finite in temporal

extent? What are the possible geometries of the

Universe? What is the fate of the Universe?

Ancient Greek Worldview: A Geocentric Cosmos

Rotating spheres carry the moon, sun, planets, & stars around a stationary Earth

Perfect, eternal & unchanging celestial region

Universe is finite

Keplerian Orbits

Based on Tycho Brahe’s astronomical measurements

Copernican circular Heliocentric orbits must be abandoned

Kepler’s 3 Laws of Planetary Motion

1. The planets move in elliptical orbits with the Sun at one focus.

2. A line drawn from the Sun to any planet sweeps out equal areas in equal time intervals.

3. The square of the period of a planet is proportional to the cube of the semi-major axis of its orbit.

€

T 2 ∝ a3

Olbers’ Paradox

Kepler believed:

space must be finite # of stars must be

finite space surrounded

by some kind of dark wall

If the Universe in infinite, unchanging, and everywhere the same, shouldn’t the entire night sky be bright?

Newton’s Universal Law of Gravitation

Successes Described the motion

of massive bodies… …on earth

…in the heavens

€

rF = −

Gm1m2

r2ˆ r

So what keeps the stars fixed?

Newton’s view of the Cosmos: a perfect balance?

Newton envisioned an infinitely large universe stars were placed at just the right distances

so their attractions cancelled.

In 1915, Einstein gives the world his General Theory of Relativity

describes the curvature of space

describes the matter & energy

€

Gμν = 8πGTμν

€

Gμν

€

Tμν

Space is not an empty void but rather a dynamical structure whose shape is determined by the presence of matter and energy.

Matter tells space how to curve

Space tells matter how to move

Einstein’s Static Universe

General Relativity does NOT allow for a static cosmological model

Einstein introduces a Cosmological Constant

Static Universe if:

€

Gμν + gμν Λ = 8πGTμν

vacuum energy

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ρΛ =1

2ρ M

In 1929, Edwin Hubble discovers that the Universe is expanding!

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v = H ⋅d

Einstein calls Λ the “greatest blunder” of his life!

Doppler Shift allows for determining the velocity of approaching/receding galaxies!

Cosmological Principle On sufficiently large distance scales, the

Universe is

1. Isotropic2. Homogeneous

Maximally Symmetric Space

For a Homogeneous & Isotropic Universe…

… 3 possible Geometries

Recent data indicates

that the Universe

is flat

Friedmann-Robertson-Walker (FRW) Cosmology

Choose the Robertson-Walker metric*

€

ds2 = −dt 2 + a2(t)dr2

1−κr2+ r2dΩ2

⎡

⎣ ⎢

⎤

⎦ ⎥

3 non-interacting components: pressureless matter radiation vacuum

* the Robertson-Walker metric describes a

spatially

homogeneous, isotropic Universe evolving in

time

The FRW Equations are…

density (ρ) & pressure (p) of the Universe determine the evolution of the scale factor (a)€

ρ + Λ =3˙ a 2

a2+ 3

κ

a2

p − Λ = − 2˙ ̇ a

a+

˙ a 2

a2

⎛

⎝ ⎜

⎞

⎠ ⎟−

κ

a2

Solutions for the scale factor when = 0

Radiation dominated:

Matter dominated:

Vacuum dominated:

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a(t) ~ t 2 / 3

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a(t) ~ t1/ 2

€

a(t) ~ eHt

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ρ(a) = ρ crit Ωv +Ωm

a3+

Ωr

a4

⎛

⎝ ⎜

⎞

⎠ ⎟

NOTICE: As t 0, a(t) 0

Solutions for a non-static Universe: an abstract theoretical

curiosity?

Georges Lemaître suggests the Universe had a temporal beginning..

Belgian Astrophysicist/ Catholic Priest

1927 paper in Annals of the Brussels Scientific Society

Lemaître… showed that the universe had to be either contracting or

expanding. suggested that the Universe had a definite beginning in

which all its matter and energy were concentrated at one point.

Did the Universe begin with a “Big Bang”??

is not an explosion that happened at one point in space

Big Bang - a time of infinite density, infinite temperature, and infinite spacetime curvature

The “Big Bang” ...

occurred at every place in space @ one moment in time

In the early 1960’s, the Princeton group in gravitational physics…

finds that the Universe should be uniformly bathed in a background microwave radiation

predicts a blackbody spectrum of the background radiation w/ T ~ 10K

In 1965, observational evidence for the Big Bang!!

Arno Penzias & Robert Wilson

Bell Lab Physicists calibrating the Bell Labs microwave antenna designed for satellite communications

Awarded the 1978 Nobel Prize in physics for discovery of the Cosmic Microwave Background Radiation

Yeah, but does this microwave background radiation have a

Blackbody Spectrum?In Nov ‘89, NASA

launches the Cosmic Background Explorer (COBE) to measure…

the spectrum the anisotropies

of the cosmic background radiation.

Spectrum of the Cosmic Microwave Background

Radiation

The excellent agreement with Planck’s law is the best fit ever measured!

John Mather & George Smoot

Awarded the 2006 Nobel Prize in physics “for their discovery of the blackbody form and anisotropy discovery of the CMB”

COBE image of the Cosmic Microwave Background

Radiation

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TB = 2.726K ±18μK Light from when the Universe was 380,000 years

old… Map of K anisotropies

Conclusions

Theory & observational evidence indicate that:

the Universe is infinite in spatial extent

the Universe began w/ a “Big Bang” ~ 13.7 billion years ago

the Universe is flat

the Universe will continue to expand indefinitely

Models of the Expansion of the Universe

An Alternative:“Steady State” Cosmology

Proposed by Hoyle, Bondi, & Gold Perfect Cosmological Principle

- Universe is not only homogeneous in space but also in time Universe has NO beginning or end to time new matter is continuously being created as Universe

expands Expansion rate is constant

Steady State vs Big Bang

Big Bang Predicts the correct abundance of H (~75%) & He

(~25%) Universe only ~few Billion years old?

Steady State Space & Time treated symmetrically What about Olbers’ Paradox?

Inflation Why is the Universe so spatially flat homogeneous & isotropicWhere did the temperature

anisotropies come from?

€

a(t) ~ eHt

The Standard Model of CosmologyThe Standard Model of Cosmology

Chad A. Middleton, Ph.D.Mesa State CollegeOctober 11, 2007

“The most incomprehensible thing about the world is that it is comprehensible.”

-A. Einstein