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Astronomy 182The Origin and Evolution of the

Universe

Lecture 5

Assignment

Today Hand in first 3-page essay summarizing

your understanding of Ferris, Chapter 2, along

with 1 page of questions on issues you do not

understand or feel were not presented clearly in

the book or in class. For next week Read

Chapter 2 of B. Greene, The Elegant

Universe Essay on that chapter due April 16.

Today

Newtonian Cosmology

Alternative cosmologies

Newtonian Cosmology

How does the size (scale factor) a(t) of the

Universe evolve? Consider

a homogenous ball of matter

Kinetic Energy mv2/2

Gravitational

Potential Energy -GMm/d

(Newton) Conservation of Energy Kinetic

Potential Total E constant

mv2/2 - GMm/d E Now

use vHd (Hubble) and M?V(4?/3)?d3 to find

H2 -

(8?/3)G? 2E/md2 -K/a2 where H Hubble

parameter expansion rate (H quantifies

time rate of change of a(t))

M

m

d

density of Universe

Friedmann equation

Satellite Analogy

Conservation of Energy Kinetic Potential

Total E constant

mv2/2 - GMm/d E Same equation

governs orbits of satellites around the Earth

v lt vescape Elt0 bound

elliptical orbit (comm. satellites) v

vescape E0 marginally unbound

(barely escapes) v gt vescape Egt0

unbound orbit, satellite escapes to

infinity (e.g., Voyager)

Elt0

E0

Friedmann Equation

H2 - (8?/3)G? 2E/md2 -K/a2

Define the critical density ?crit

3H02/8?G Subscript

10-29 grams/cm3 0 denotes

present and

the density parameter ?0 ?/?crit

epoch Then ?0 gt 1

implies Elt0 negative Energy, U.

recollapses (closed) ?0 1 implies

E0 Zero Energy, U. marginally expands

forever (open) ?0 lt 1

implies Egt0 positive Energy, U.

expands forever

1 - ?0 -K/a02H02

Empty constant velocities

Accelerating

Size of the Universe

Open

Today

Will the Universe Expand forever or recollapse in

a Big Crunch?

Closed

Gravity of matter slows down expansion

Cosmic Time

Big Bang

Friedmann Equation

1 - ?0 -K/a02H02

In Einsteins General Relativity K curvature

of space ?0 gt 1 implies Kgt0 positive

curvature (3-sphere),

U. recollapses (closed) ?0

1 implies K0 zero curvature (flat

Euclidean space),

U. marginally expands forever ?0

lt 1 implies Klt0 negative curvature

(3-d saddle),

U. expands forever

GEOMETRY IS DESTINY (almost)

Einstein space can be globally curved

Kgt0 K lt 0

K 0 Closed

open

flat

Fate of the Universe Will the

Universe expand forever or recollapse in a Big

Crunch? Is the average density of matter in the

Universe smaller or larger than the

critical density, i.e., is ?0 smaller or larger

than 1? We will study this question later in the

course. Complications We cannot measure the

average density by just inventorying the

masses of all objects we see in the Universe and

dividing by the volume, because we know

there are objects we do NOT see directly

(i.e., which gravitate but do not emit light)

DARK MATTER ?visible matter 0.01

while best current estimate is ?dark matter

0.3 but even this is not the whole story

Dark Energy with ?dark energy 0.7 is

causing the Universe to accelerate

Some have (simplistically) characterized

cosmology as the search for 2 numbers

expansion rate H0

density parameter ?0 In fact, if

Dark Energy exists, then additional number(s)

are needed to characterize the cosmological model

describing our Universe. In particular, Dark

Energy breaks the unique correspondence

between Geometry and Destiny (crunch or

continued expansion). This is due to the fact

that Dark Energy exerts a repulsive

gravitational force that causes the

expansion to accelerate, while the attractive

gravity of ordinary matter causes the

expansion to slow down. We will discuss Dark

Energy later in the course as well.

The Big Bang Singularity at t0 Running

the expansion backward in time, the known laws of

physics break down before one gets back to

the singularity of infinite Temperature and

density. Our basic understanding of Space Time

(spacetime), based upon Einsteins Theory of

General Relativity, must break down when the

Universe was around

tPlanck 10-43 seconds old

TPlanck 1032 degrees At this time, the

classical description of Spacetime (our

notion of space and time) breaks down

quantum fluctuations of spacetime become large.

Requires a theory of Quantum Gravity (perhaps

provided by Superstring Theory) to go beyond

this point. (See B. Greene, The Elegant

Universe)

Are there plausible Alternative Cosmological

models? Degrees of departure from the

Standard Cosmology 1.

Socialism Models that

incorporate the expansion of the Universe,

but not the Big Bang.

Example Steady State Model

2. Radical anarcho-syndicalist

fringe Models that reject

both expansion and the Big Bang.

Example Tired Light model

Alternatives to the Big Bang?

Steady State Universe conceived in 1949

by Bondi, Gold, and Hoyle in response to

the Age Crisis of the Big Bang (prompted by

Hubbles too-large value for his

constant) Theoretical Motivation Perfect

Cosmological Principle (Universe homogeneous

in time as well as space) Postulates

continuous creation of matter to fill in space

between galaxies, so that the density remains

constant as Universe expands. Universe

infinite in time space, no Big Bang. This

model is expanding but is not evolving.

Problems for Steady State Model

Continuous creation of matter violates

well-established Principle of Conservation of

Energy requires new Physics which has no

other fundamental motivation. Galaxy properties

and the density of galaxies and of Quasars

are now observed to evolve with time. Chief

difficulty origin for the isotropic Cosmic

Microwave Background radiation (which arises

naturally in the Big Bang model) is

unexplained and likely inexplicable. Also,

origin of light element abundances (H, He, Li, D)

unexplained (arise naturally in Big Bang).

Radical alternatives to the expanding Universe

These start from the premise that redshifts are

NOT due to recession velocities, so cannot

infer expansion from Hubbles Law. However,

no alternative explanation for redshift has been

put forward that is physically plausible

consistent with the now very large body of

redshift data (approaching 1 million galaxy

redshifts measured).

Non-cosmological redshifts?

H. Arp observed a number of high-redshift

quasars which appear to be associated with

low-redshift galaxies. He concluded the

redshift cannot be an indicator of distance.

Are these just chance superpositions of objects

on the sky, or real associations? Arp

there are more such associations than can be

explained by chance superposition. Most other

cosmologists 1) need a carefully done survey

to make such a statistical statementArp did

not do this. 2) such superpositions are

expected by gravitational lensing

foreground galaxy makes background objects

brighter, thus more likely to find (looking

for keys under the lamppost).

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Low- Redshift Galaxy

High- Redshift Quasar

Gravitational Lensing

Basically, the same effects that occur in more

familiar optical circumstances magnification

and distortion

Objects farther from the line of sight are

distorted less.

Gravitationally Lensed Quasars

We only find high-redshift objects lensed by

low-redshift galaxies, not the other way around

? redshift IS an indicator of distance

Clusters of Galaxies Size 1025 cm Megaparsec

(Mpc) Mass 1015 Msun Largest

gravitationally bound objects galaxies, gas,

dark matter

Cluster of Galaxies

giant arcs are galaxies behind the cluster,

gravitationally lensed by it

Tired Light Model

Postulates that light loses energy as it travels,

so redshift is not caused by expansion

of the Universe. Objections 1. Requires

an unobserved electromagnetic

interaction to cause light to lose energy this

way. 2. In general, does not predict the

observed linear redshift-distance

relation found by Hubble. 3. Does not

automatically imply that the redshift

is independent of light wavelength, as

observed. 4. Required scattering of

light would smear out appearance

of distant sources, not observed.

Fractal Universe Model

Postulates that the Universe is not homogeneous

over large scales no well-defined mean

density (in contrast to the Cosmological

Principle). i.e., ?(R) M(R) does not

converge as R ? ? 4?R3

3 Inconsistent with observed spatial

clustering of galaxies. No explanation for

Microwave background its isotropy.

Evidence in Favor of Expansion Interpretation of

Redshifts How do we know that redshifts

correspond to distance (rather than to

something else)? Redshifts are observed to be

independent of wavelength, linear with

distance, isotropic, always (except for 10

nearby galaxies) positive (i.e.,

recession). Gravitational lenses high-redshift

(background) objects are lensed by

low-redshift (foreground) objects. CMB

temperature at moderate redshift CN (cyanogen)

molecules as thermometer (rotational vibrations

excited by microwave background photons),

consistent with

TT0(1z) Conclusion NO plausible alternatives

to expansion or Big Bang