26. Cosmology• Significance of a dark night sky• The Universe is expanding• The Big Bang initiated the expanding Universe• Microwave radiation evidence of the Big Bang• The Universe was initially hot & opaque• The importance of the shape of the Universe• The Universe seems filled with dark energy• The Universe’s expansion rate is accelerating• Dark matter & dark energy determine the future

Significance of a Dark Night Sky• Physical cosmology

– Science of the structure & evolution of the Universe• One fundamental expectation

– Universe is large enough to fill the sky with stars• Night sky should be filled with light• Night sky is not filled with light Olber’s ⇒

paradox• The model of an infinite static Universe cannot be correct

• One possible solution– Einstein’s special theory of relativity

• Distance, mass & time are all relative to all observers– Einstein’s general theory of relativity

• Space is warped by massive objects• Einstein introduced the cosmological constant

L– Introduced to produce the preconceived static Universe

The Dark Sky Anomaly

The Universe Is Expanding• The Hubble law 1920

– Galaxy clusters are moving away from each other• Pervasive galaxy cluster redshift is compelling evidence• The Hubble law is a linear relationship

– Tenfold distance increase Tenfold recessional speed increase⇒– Expansion of space, not velocity through space

• Cosmological redshift rather than Doppler redshift• Space does not expand in objects tightly bound by gravity

– Model of solid objects on an inflating balloon

• One fundamental conclusion– The center of expansion cannot be identified

• Everything is moving away from everything else• Every viewing location observes the same expansion

The Expanding Balloon Analogy

The Hubble Law & Expansion

Fundamental Assumptions• Assumptions in scientific method

– Any reasonable assumptions can be made• Assumptions are presumed unproveable for some reason• Future observations may prove some assumptions invalid

• Assumptions in cosmology– Observations can verify only one Universe

• Cosmologists imagine but cannot produce other universes– The cosmological principle

• The Universe is assumed to be homogeneous– At the largest scale, all regions of space are

identical• The Universe is assumed to be isotropic

– At the largest scale, all directions in space lookidentical

Big Bang & the Expanding Universe• Observational evidence

– Inverse of the Hubble law• In the distant past, the Universe was very small• Far enough back, all matter & energy were in one point• 1/H0 Age of the Universe⇒

– The Universe began 13.8 Bya if H0 = 75 km . sec–1 . Mpc– This assumes that H0 is now & has always been constant

– One major problem• Stars cannot be older than the Universe

– Observational evidence suggests this may not be the case• Recent evidence may resolve this issue

• The Big Bang– “Cosmic singularity” may be a better term

• Remarkably similar to the singularity in a black hole

The Observable Universe• Expected size of the Universe

– Almost certainly far larger than what we can see

• Observational limits– We only see as far back as the Universe is old

• This results from the finite speed of EMR in vacuum

– Presume the Universe is 13.8 billion years old• We can only see objects < 13.8 Bly away in all directions• This is our cosmic particle horizon

– As the Universe ages, we see back even farther

The Changing Observable UniverseEntire

Universe

Microwave Radiation As Evidence• The overabundance of He

– Theoretically, there is too much He in the Universe• Can be accounted if the early Universe was extremely hot• If so, there should be evidence

– This would be severely redshifted to ~ 1.1 mm l

• Cosmic background microwave radiation– Penzias & Wilson at Bell Labs

Early 1960s• Observed microwave background radiation from space

– This radiation is about 1% the strength of analog TV noise

– Earth’s atmosphere is largely opaque at 1.1 mm l• Satellites are a better option

– Cosmic Background Explorer (CoBE)

1989

Tri-Color Noise

Noise

Bell Labs Horn Antenna

Microwave Background Spectrum

Blackbody curveT = 2.725 K

Microwave Background Temperature

Our Motion Through the Universe

Density Dominance in the Universe• Radiation - dominated Universe

– Prevailed in the earliest stages of the Universe• This corresponds to a cosmic redshift of z = 25,000

– Since then, l’s have been stretched by a factor of 25,000

• This occurred when the Universe was ~ 2,500 years old– EMR had l = 40 nm in the UV part of the spectrum

• Matter - dominated Universe– Prevailed since the Universe was ~ 2,500 years old

• This may prevail for all time in the future

The Universe Began Hot & Opaque• Basic physical processes

– High temperatures tend to ionize atoms & molecules• Hydrogen has only 1 proton in its nucleus

– The bond with the 1 electron is therefore relatively weak• Hydrogen ionizes at temperatures > 3,000 K

– This was true for ~ 300,000 years after the Big Bang– An ionized gas is called a plasma

• Plasma interacts very strongly with EMR– This makes a plasma opaque

– Cosmic redshift reduces energy content of EMR• Energy is inversely proportional to wavelength

• Recombination– Protons & electrons bind to form neutral hydrogen

• Misnomer because they were never previously combined

Radiation & Matter In the Universe• Two basic possibilities in the Universe

– Something is either energy or matter• Special relativity: They are two forms of the same entity

• Two important concepts– Universe’s average mass density of radiation

todayrrad = 4.6 . 10–31 kg . m–3

Equivalent to 550,000,000 photons per cubic meterExtremely low energy per severely redshifted photon

– Universe’s average density of mattertoday

rm = 2 to 11 . 10–27 kg . m–3

Equivalent to 1 to 6 hydrogen atoms per cubic meterExtremely high energy per hydrogen atom

Evolution of Density

Evolution of Radiation Temperature

Before & After RecombinationFree protons Bound protons& electrons & electrons

Microwave Temperature Variations

Importance of the Universe’s Shape• Three basic possibilities

– Positive curvature of space Spherical• Two parallel beams of EMR will converge• Three-dimensional analog of a sphere• The Universe’s expansion rate will decrease

– The Universe will eventually collapse upon itself– Zero curvature of space Flat

• Two parallel beams of EMR will remain parallel• Three-dimensional analog of a plane• The Universe’s expansion rate will remain constant

– The Universe will continue expanding forever– Negative curvature of space Hyperbolic

• Two parallel beams of EMR will diverge• Three-dimensional analog of a saddle• The Universe’s expansion rate will increase

– The Universe will continue expanding forever

Measuring the Universe’s Shape• Hypothetical

– Draw a huge triangle– Measure the three angles

• Practical– Count the number of extremely distant galaxies

• Spherical Concentration is highest nearby• Flat Concentration is uniform• Hyperbolic Concentration is highest far away

The Geometry of the Universe

Microwave Background & Curved Space

A Universe Filled With Dark Energy• The observational evidence

– Temperature variations A nearly flat Universe⇒– Galaxy clusters Matter density ⇒ Wm = 0.2 to 0.4

• This clearly suggests a non-flat Universe

• The tentative conclusion– There is substantial dark energy in our Universe

– Necessarily WL = 0.6 to 0.8• Presumed dark energy must be 60 – 80% of the Universe

Dark Energy

Dark Matter

Proportions of Mass & Energy

http://upload.wikimedia.org/wikipedia/commons/4/4b/DarkMatterPie.jpg

Universe’s Variable Expansion Rate

http://www.nasa.gov/images/content/56200main_dark_expansion-lg.jpg

Universe’s Matter & Energy Distribution

http://upload.wikimedia.org/wikipedia/commons/b/b9/Cosmological_composition.jpg

Universe’s Expansion is Accelerating• The observational evidence

– Type Ia supernovae in distant galaxies• A highly reliable standard candle

• The tentative conclusion– The expansion rate of the Universe is increasing

Einstein’s cosmological constantmay be correct after all ! ! !

Varying Rates of Cosmic Expansion

Distant Supernovae & Hubble Diagram

Limits on the Nature of the Universe

The Evolution of Density Revisited

The Growth of the Universe

• The expanding Universe– How can the sky be so dark?

• Stars should be literally everywhere– The Hubble Law (1920)

• Space itself is expanding• Concept of the Big Bang

– Matter & energy in a very small space– Explosion created space & time

• Space expanded faster than light– Expansion of space has slowed down

• Evidence for the Big Bang– The cosmological red shift– The cosmic background radiation

• Remnants of heat from the Big Bang– Big Bang produced excess helium

• Required extremely high temperatures– Milky Way moves amidst CBR

• The Great Attractor

• Characteristics of the Big Bang– Extremely hot & opaque plasma

• The primordial fireball– Hydrogen atoms eventually formed

• Temperature < 3,000 K• Universe became transparent

• The shape of the Universe– Three major possibilities

• Zero curvature =Flat

• Positive curvature =Closed

• Negative curvature =Open

– Two remarkable things• ~90% of all matter is “dark”• ~80% of all energy is “dark”

• The strangest thing yet– Universe’s expansion is accelerating

Chapter 28: Important Concepts