Astro 101 Fall 2013 Lecture 12 Cosmology T. Howard

Astro 101Fall 2013

Lecture 12

Cosmology

T. Howard

Cosmology = study of the Universe as a whole

• ? What is it like overall?

• ? What is its history? How old is it?

• ? What is its future?

• ? How do we find these things out from what we can observe?

• In 1996, researchersat the Space TelescopeScience Institute usedthe Hubble to make avery long exposure ofa patch of seeminglyempty sky.

Q: What did they find?

A: Galaxies “as far as The eye can see …”

(nearly everything inthis photo is a galaxy!)

40 hour exposure

What do we know already (about the Universe) ?• Galaxies in groups; clusters; superclusters• Nearby universe has “filament” and void type of structure• More distant objects are receding from us (light is redshifted)• Hubble’s Law:

V = H0 x D (Hubble's Law)

Structure in the Universe

What is the largest kind of structure in the universe? The ~100-Mpc filaments, shells and voids? On larger scales, things look more uniform.

600 Mpc

Olbers’ Paradox• Assume the universe is homogeneous, isotropic, infinte, and static• Then:

Why don’t we see light everywhere?

Why is the night sky (mostly) dark?

• We believe the universe is homogeneous and isotropic

• So, either it isn’t infinite OR it isn’t static

• “Big Bang” theory – universe started expanding a finite time ago

Olbers’ Paradox (cont’d.)

The Cosmological Principle

On the largest scales, the universe is roughly homogeneous (same at all places) and isotropic (same in all directions). Laws of physics are everywhere the same.

Given what we know of structure in the universe, assume:

If there is a center, there must be a boundary to define it => a finite universe. If we were at center, universe would be isotropic (but only from our location) but not homogeneous:

Us

Finite volume of galaxies expanding away from us into...what, empty space?

Then part of universe hasgalaxies and part doesn’t.

Hubble's Law might suggest that everything is expanding away from us, putting us at center of expansion. Is this necessarily true?

So if the CP is correct, there is no center, and no edge to the Universe!

Best evidence for CP comes from Cosmic Microwave Background Radiation (later).

Us

But if we were not at center, universe would be neither isotropic nor homogeneous:

The Big Bang

All galaxies now moving away from each other.

A galaxy twice as far away from us, is moving twice as fast (Hubble's Law).

So, how old is the Universe?

Reversing the Hubble expansion, all separations go back to zero. How long ago?

At time zero, all separations were infinitely small. Universe then expanded in all directions. Stars, galaxies formed as expansion continued.

H0 gives rate of expansion. Assume H0 = 75 km / sec / Mpc. So galaxy at 100 Mpc from us moves away at 7500 km/sec. How long did it take to move 100 Mpc from us?

time =

=

= 13 billion years

distancevelocity100 Mpc7500 km/sec

(Experts note that this time is just ).

The faster the expansion (the greater H0), the shorter the time to get to the present separation.

1H0

We can do this samecalculation forgalaxies at other distances,getting a similar answer.

Age of universe is relatedto H0. Note, H0 may bein range 65 – 75km/sec/Mpc

Redshift vs. “Lookback Time”• Astronomers (and physicists) denote redshift by “z”

= amount light has shifted relative to its (laboratory, at rest) wavelength= direct measure of speed of recession of distant galaxies

Time (now) since Big Bang = 13.860 Gyr using H0 = 70 km/sec/Mpc Flat universe

z light travel time Age at redshift (Gyr) (Gyr)

0.037 0.5 13.3600.075 1.0 12.8600.254 3.0 10.8600.488 5.0 8.8601.04 8.0 5.8601.74 10 3.8606.54 13 0.86010.13 13.38 0.480

1 Gyr = 1,000,000,000 years.

But this is not galaxies expanding through a pre-existing, static space. That would be an explosion with a center and an expanding edge.

If CP is correct, space itself is expanding, and galaxies are taken along for the ride. There is no center or edge, but the distance between any two points is increasing.

A raisin bread analogy provides some insight:

But the bread has a center and edge. Easier to imagine having no center or edge by analogy of universe as a 2-d expanding balloon surface (this is only one possible analogy for our universe’s geometry):

(To understand what it would be like in a 2-d universe, read Flatland by Edwin Abbott: www.ofcn.org/cyber.serv/resource/bookshelf/flat10 )

Now take this analogy "up one dimension". The Big Bang occurred everywhere at once, but "everywhere" was a small place.

The Cosmic Microwave Background Radiation (CMBR)

A prediction of Big Bang theory in 1940's. "Leftover" radiation from early, hot universe, uniformly filling space (i.e. isotropic, homogeneous). Predicted to have perfect black-body spectrum.

Photons stretched as they travel and universe expands, but spectrum always black-body. Wien's Law: temperature decreases as wavelength of brightest emission increases => was predicted to be ~ 3 K now.

Points are data on the spectrum of the CMBR from the COBE satellite (1989). Curve is a black-body spectrum at T=2.735 K.

Found in 1964 by Penzias and Wilson. Perfect black-body spectrum at T = 2.735 K. Uniform brightness (and thus temperature) in every direction.

1% of the “snow” on a blank TV channel is this radiation!

Deviations are -0.25 milliKelvin (blue) to +0.25 milliKelvin(red) from the average of 2.735 Kelvin.

All-sky map of the CMBR temperature, constant everywhere to one part in 105 ! For blackbody radiation, this means brightness is very constant too (Stefan’s law).

(WMAP satellite)

The First Matter

At the earliest moments, the universe is thought to have been dominated by high-energy, high-temperature radiation. Photons had enough energy to form particle-antiparticle pairs. Why? E=mc2.

annihilation

pair production

The Early Universe

At time < 0.0001 sec, and T > 1013 K, gamma rays could form proton-antiproton pairs.

At time < 15 sec, and T > 6 x 109 K, electron-positron pairs could form.

Annihilation occurred at same rate as formation, so particles coming in and out of existence all the time.

As T dropped, pair production ceased, only annihilation. A tiny imbalance (1 in 109) of matter over antimatter led to a matter universe(cause of imbalance not clear, but other such imbalances are known to occur).

Primordial Nucleosynthesis

Hot and dense universe => fusion reactions.

At time 100-1000 sec (T = 109 - 3 x 108 K), helium formed.

Stopped when universe too cool. Predicted end result: 75% hydrogen, 25% helium.

Oldest stars' atmospheres (unaffected by stellar nucleosynthesis) confirm Big Bang prediction of 25% helium.

We are now in a “Matter-dominated” epoch

Other Measurements Support the Big Bang Model of the Universe(Detailed Big Bang theory predicts some things we can measure)

(Now) … < -- Time … (Early Universe)

We can’t “see” all the way to the Big Bang

[we see its “echo”]

Radiation andMatter “decoupled”

Nuclei and electronscombine to formatoms (H, He)

More complex atomsform later fromfusion

This explains CMB

Galaxies –form around clumpsof Dark Matter ?

Opaque

Transparent

Computer simulations of structure formation around clumps of Dark Matterpredict a universe with shapes/sizes very similar to what we observe.

Time sinceBig Bang.

Big Bang cosmology + Dark Energy, WMAP valuesCurrent mass density ratio 0.27 (incl. Dark Matter)Current value of Dark Energy equivalent density ratio, 0.73H0 ~ 71 km/s-Mpc Era or Event Time Temp Planck Era < 5x10-44 > 1019 GeVPlanck transition 5 x 10-44 1019 GeV** Grand unification era **Grand unification of forces ends 10-36 1015 GeVInflation 10-36 to 10-34 1015 GeV** Electro weak era **Electroweak era ends 10-11 100 GeV** Quark era **Quark era ends 10-5 200 MeV

Cosmic expansion timelines (1)

Cosmic expansion timelines (2)

Neutrino decoupling 0.1 s 3 MeVe- e+ annihilation ends 1.3 s 1 MeVn-p ratio frozen 1.8 s 1010 KDeuterium formation begins 176 s 109 KMatter-dominated era begins 55000 year 8920 K z = 3233** Matter era **CMB visible ~300,000 yr 3000 K1st stars form 200Myr – 1 Gyr1st galaxies form 1 Gyr – 5 Gyruniversal expansion accelerates ~ 7.1 Gyr z= 0.76, R =0.57Dark Energy dominates ~ 9.5 Gyr z = 0.39, R = 0.72** Dark Energy era**Today ~ 13.7 Gyr z = 0, R = 1

Era or Event Time Temp redshift

InflationA problem with microwave background:

Temperature of background in opposite directions nearly identical. Yet even light hasn't had time to travel from A to B (only A to Earth), so A can know nothing about conditions at B, and vice versa. So why are A and B almost identical? This is “horizon problem”.

The Early Universe

Microwave background reaches us from all directions.

Solution: Inflation. Theories of the early universe predict that it went through a phase of rapid expansion.

Separation between two

points (m)

If true, would imply that points that are too far apart now were once much closer, and had time to communicate with each other and equalize their temperatures.

More on Dark Matter

• Dark matter thought to be necessary in cosmology theory to explain clumpy distributions of matter massive enough for galaxies to form

• Could have been either CDM or HDM• CDM = non-relativistic (speed << c)• HDM = relativistic (speed ~ c)

• Usual predictions of CDM candidates require modifications or extensions to Standard Model of particles

• Non-baryonic candidates• Neutrinos (neutrino oscillation implies neutrino mass)• WIMPs – hypothetical• Possibly “heavy” neutrinos or something equally exotic

• Axions

What Happens to the Universe?The Geometry of Curved Space

Net densityof matter

and

Fate of theUniverse arerelated

The universe asa curved space

Analogy usingthe Earth’s surface

What Happens to the Universe?The Geometry of Curved Space (cont’d.)

Possibilities:

1) Space curves back on itself (like a sphere). "Positive" curvature.

2) “Saddle-like”, with curvature in the opposite sense in different dimensions: "negative" curvature.

3) A more familiar “flat” geometry.

In general relativity, the geometry of the universe depends on the total mass and energy of the universe (including dark energy). Latest CMBR measurements are consistent with flat, infinite universe (curved, finiteuniverse still possible, with enormous radius of curvature).

Deviations are -0.25 milliKelvin (blue) to +0.25 milliKelvin(red) from the average of 2.735 Kelvin.

All-sky map of the CMBR temperature, constant everywhere to one part in 105 ! For blackbody radiation, this means brightness is very constant too (Stefan’s law).

(WMAP satellite)

Size of patches simply related to speed of light and age of universewhen CMBR photons started streaming freely. This we know quitewell. Also know how far away we are looking. Then angular sizeof patches tells us how light has traveled to us => curvature of space.

someknownsize

Sizes of patches in CMBR constrain geometry of universe.Curvature of universe makes it act like lens or pair of glasses

measure this angle ( 1°)

we know this distance

Example supernova remnant—Crab nebula in Taurus

Supernovae – extremely violent stellar explosions

• Several types & subtypes (called type “I”, “Ia”, “II”, etc.)• Different types arise from pre-explosion stellar conditions

• Type Ia has been shown to have a change in brightness over time that has a shape related to its total luminosity

Implies that SNe Ia can be used as “standard candles”

Time Br

ight

ness

Supernovae Ia – Standard Candles for Cosmology

The Cosmological “Distance Ladder”

Standard candles:Type IaSupernovae

[SNe Ia]

Recent Discovery:The Expansion of the Universe Seems to be Accelerating

Type I supernovae: from ones in nearby galaxies, know luminosity. In distant galaxies, determine apparent brightness. Thus determine distance. Works for more than 3000 Mpc. From redshifts, they arenot expanding as quickly from eachother as galaxies are now.

The gravity of matter should retard the expansion. But a new distance indicator shows that the expansion rate was slower in the past!

H0 wassmaller inpast (i.e.for distantgalaxies)

Taking this into account, best age estimate of Universe is 13.8 Gyrs.

Red

shift

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hift

in

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of sp

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l lin

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Note, 2011 Nobel Prize in Physics was awarded for this discovery

Source: E. Wright, UCLA

What can explain the acceleration?Current theory: “Dark Energy”

Einstein in 1917 introduced a special mathematical term, Lambda (“L”) as part of General Relativity.

He thought it was needed to balance gravitational attraction and create a static Universe (turned out to be wrong!).

But, we can think of L as repulsive force that exists even in a vacuum.

The accelerating universe indicates there is (something akin to) a L.

More generally called "dark energy". We have little idea of its physical nature.

The measured amount of acceleration implies that there is actually more “dark energy” than the energy contained in matter !

Supported by –CMBR measurements Statistical studies ofSupernovae Ia measurements Galaxy Clusters

Current Theories : Universe is 70% + “Dark Energy” !!

Will this change? Stay tuned!

• Astronomers and physicists are seeking advanced methods to study the early universe to try and understand “Dark Energy”• One leading candidate – a new space telescope, “WFIRST”

Successes of the Big Bang Theory

1) It explains the expansion of the universe.

2) It predicted the cosmic microwave background radiation, its uniformity, its current temperature, and its black-body spectrum.

3) It predicted the correct helium abundance (and lack of other primordial elements).

Misconceptions about the Big Bang

1. “The universe was once small.” The observable universe, which isfinite, was once small. The nature of the entire universe at early timesis not yet understood. It is consistent with being infinite now (or hasenormous radius of curvature).

2. “The Big Bang happened at some point in space.” The CMBRshowed that it happened everywhere in the universe.

3. “The universe must be expanding into something.” It is not expanding into “empty space”. That would imply the Big Bang happened at some location in space.

It is a stretching of space itself.

4. “There must have been something before the Big Bang.”

The Big Bang was a singularity in space and time (like the center of a black hole). Our laws of physics say the observable universe had infinitesimally small size, and infinite temperature and density. Such “infinities” indicate a breakdown of our theories.

In these conditions, we don’t have a physics theory to describe the nature of space and time. At the Big Bang, time took on the meaning that we know it to have.

"Before" is only a relevant concept given our everyday understanding of time. We must await a better understanding of the nature of space and time. Such theories are in their infancy.Why did Big Bang occur? We don’t know.

Shouldn’t be surprising that these concepts are hard to grasp.So was the heliocentric Solar System 400 years ago.