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T H E M A K E U P O F T H E U N I V E R S E

FURTHER COSMOLOGY Book page 675 - 683

© cgrahamphysics.com 2016

COSMOLOGICAL PRINCIPLE

• Is the Universe isotropic or homogeneous?

• There is no place in the Universe that would be

considered as the source of the Big Bang it expanded identical everywhere


ISOTROPY

• Assume Universe

looks the same in every direction

• Not true on small

scale

• Large scale: it looks

the same in all

direction

Imagine:

You are standing

at the edge of the Universe

• Looking outward there

would be a limited number of galaxies sending photons

to us

• Looking inward, there would

be an immense number of

galaxies to send photon


EDGE OF THE UNIVERSE

• The two situations would appear different

• Isotropy says that this isn’t the case


HOMOGENEITY Matter is uniformly spread in space

• Not true on small scale

• On large scale: average density of matter is about the same in all places in the Universe © cgrahamphysics.com 2016

Isotropy and

homogeneity only

considered in scales

of millions of ly


EVIDENCE FOR COSMOLOGICAL PRINCIPLE

• Cosmic microwave background radiation

• CMB is the image of photons emitted from the early

Universe

• Isotropy and homogeneity are seen in its random

appearance

APM Galaxy survey image:

there is no special region or

place that is different from

any other


EINSTEIN AND SPECIAL RELATIVITY

Einstein showed that

• Matter can only distort space time in one of three

ways: 4rth dimension is time

complex to visualize

use impact of 3rd dimension on a flat surface


POSITIVELY CURVED SPACE

• Spherical space of

finite size

• Ω 0 > 1

• By travelling

through the

Universe you could

return to the original

position in space

time


NEGATIVELY CURVED

• Shape of a saddle

of infinite size

• Ω 0 < 1

• You would never

return to the same

point in space time


SURFACE REMAINS FLAT

• Shape remains flat

of infinite size

• Ω 0 = 1

• You would never

return to the same

point in space time


CRITICAL DENSITY 𝜌𝑐

• Critical density is

important

• Needed to determine

what will happen to

the Universe

• It is difficult to

measure density

• We don’t know how

much there is

• Existence of dark

matter


FATE OF THE UNIVERSE

• The critical density is the average density of matter required for the Universe to just halt its expansion, but only after an infinite time

• The Universe could be open, closed or flat


CLOSED UNIVERSE (POSITIVELY CURVED)

• Density of Universe is such that gravity will stop

Universe from expanding

• It will cause Universe to contract

• Leads to big crunch

• Creation process could start again


OPEN UNIVERSE (NEGATIVELY SHAPED SADDLE)

• Gravity is too weak

to stop Universe

from expanding for

ever


FLAT UNIVERSE

• Density is at critical

value

• Universe will only

start to contract

after an infinite

amount of time

Ω 0 = 1


CRITICAL DENSITY

• 𝜌𝑐 - appears to be

no greater than 10

particles per 𝑚3

• Research suggest

that the average

density is very close

to this value

• 𝜌𝑐 for Universe

~ 10−26𝑘𝑔𝑚−3


IMPLICATIONS

• Rate of expansion has been slowing down

• Data from supernova type1a suggests that

Universe may actually be undergoing an

accelerated expansion

caused by dark energy

BUT


FINDING A VALUE FOR 𝜌𝑐

• Imagine a homogeneous sphere of radius r and density 𝜌

• A galaxy of mass M will be moving away with speed v from the center of an imaginative sphere

• Hubble’s Law states the speed of the galaxy as

• 𝑣 = 𝐻0𝑅


TOTAL ENERGY OF GALAXY

• TE=KE+PE

• 𝑇𝐸 =1

2𝑚𝑣2 −

𝐺𝑀𝑚

𝑅

• Mass of sphere

𝜌 =𝑀

𝑉↔ 𝑀 = 𝜌𝑉 =

4

3𝜋𝑅3𝜌

• TE =1

2𝑚(𝐻0𝑅)2−𝐺

𝑚4

3𝜋𝑅3𝜌

𝑅

• TE = 1

2𝑚 𝐻0

2𝑅2 −4

3𝜋𝑚𝐺𝜌𝑅2

• Galaxy will continue to move providing it has enough energy TE becomes positive


LET THE LIMIT OF TE=0

•1

2𝑚 𝐻0

2𝑅2 = 4

3𝜋𝑚𝐺𝜌𝑅2

• 𝐻0 = Hubble constant

• G = Newton’s

gravitational

constant


POSSIBLE DEVELOPMENT OF THE UNIVERSE

• Flat Universe

𝜌 = 𝜌𝑐

• Open Universe

𝜌 < 𝜌𝑐

• Closed Universe

𝜌 > 𝜌𝑐

Accelerating Universe

No gravity, 𝜌 = 0


DENSITY PARAMETER Ω0

• Ratio of actual

matter in

Universe 𝜌 to

critical density 𝜌𝑐

is called the

density

parameter Ω0

• Ω0 = 𝜌

𝜌𝑐

Open Universe

𝜌 < 𝜌𝑐

Closed Universe

𝜌 > 𝜌𝑐

Flat Universe

𝜌 = 𝜌𝑐


4𝑡ℎ POSSIBILITY

• An accelerated Universe might be explained by dark energy

• This is an increasing likely prospect

• Hypothetical dark energy outweighs the gravitational effect of baryonic and dark matter


Since λ∞𝑅

COSMIC SCALE FACTOR R

• Wavelength of emitted radiation will always be in

accordance with the cosmic scale factor R

• 𝑍 =∆λ

λ=

𝑅

𝑅0− 1 where z is the ratio b/w λ and

• R = cosmic scale factor, which would have

changed from 𝑅0 𝑡𝑜 𝑅

• Assuming Black Body

retains its shape

during expansion

• 𝑇∞1

𝑅 and 𝑇∞

1

λ

Cosmological Redshift

λ of the emitted radiation is

lengthened due to the

expansion of the Universe © cgrahamphysics.com 2016

EVIDENCE FOR DARK MATTER

• fg


SUPPOSE…

• …a star of mass m is near the center of a spiral galaxy of total mass M

• The average density of the galaxy is 𝜌

• Star moves in circular orbit with orbital velocity v and radius R

𝑣2 =𝐺𝑀

𝑅


CENTRAL BULB

• Assume the central

bulb is spherical

• 𝑣2 =𝐺𝑀

𝑅= 𝐺

4

3𝜋𝑅3𝜌

𝑅

• 𝑣2 =4

3𝐺𝜌𝜋𝑅2

• 𝑣 =4

3𝐺𝜌𝜋 × 𝑅

• Hence

• 𝑣 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑅


ASSUME STAR IN ARMS OF GALAXY

• If the star is in the less populated areas of the arms of a galaxy, the galaxy would behave as if the total mass was concentrated at its center

• Stars would be free to move with nothing impede their orbits

• 𝑣2 =𝐺𝑀

𝑅 𝑎𝑛𝑑 𝑣∞

1

𝑅


SPEED OF STARS IN ARM: 𝑣∞1

𝑅

• When plotting

rotational velocity against the distance from center of galaxy, we would expect to see rapidly increasing line that changes to decaying at the edge of the hub


EXPECTATION VS OBSERVATION

• By increasing speed from redshifts a different, much higher curve is observed

• Stars far out into the region beyond the arms move at same speeds as stars inside the galaxy


EXPLANATION

• Dark matter forms a halo around the outer

rim of a galaxy

• Matter is not luminous or baryonic and

emits no radiation


DARK MATTER HALO

• When the halo with dark matter is added

to the curve, it almost fits the observed

data


OTHER EVIDENCE

• Velocity of galaxies

orbiting each other

in clusters

• They emit far less

light than

suggested by their

velocities WRT their

mass


GRAVITATIONAL LENSING

• Radiation passing

through a cluster of

galaxies becomes

much more

distorted than

expected due to

the luminous mass

of the cluster

• This is observable

from Quasars


X-RAY IMAGES

• X-ray images of elliptical galaxies show halos of hot gas extending well outside the galaxy

• To be bound to the galaxy, galaxy must have mass far greater than observed

Up to 90% of galaxies is assumed to

be dark matter


WHAT IS DARK MATTER?

Nobody knows


CANDIDATES FOR DARK MATTER

MACHO’s

• Massive compact halo

objects

- black holes

- neutron stars

- small stars such as

brown dwarfs

• Compact stars at the end of their lives with high density

• Detected by gravitational lensing

• Not sufficient to provide amount of dark matter in Universe


WIMP’S

• Weakly interacting massive particles

• They are subatomic particles

- non baryonic

- they pass through baryonic

matter with very little effect

- massive does not mean big,

but rather they have mass,

also very small mass

• To make up dark matter, there

would need to be an unimaginable amount of them © cgrahamphysics.com 2016

MORE WIMP’S

• 1998 neutrinos with very little mass were discovered

• other hypothetical particles are called axions and neutralinos

• They have not been discovered experimentally

Dark matter research in CERN


DARK ENERGY

• Unknown force

causing galaxies to

move further apart

and stretching the

fabric of space

faster


ESA’S PLANCK MISSION

• 68% of the Universe

consists of dark energy

• 26.8% is dark matter

• 4.9% is ordinary matter


DATA FROM SUPERNOVA

• Supernova dimmer than expected

• They are further away than expected

• They must be speeding up rather than slowing down

• Suggested explanation:

• Dark energy is a property of space

• As universe expands so does dark energy

• Dark energy comes into existence with more space


ANISTROPIES IN CMB

According to Big Bang Theory

• First ~300000years of Universe atoms

could not exist

• Matter distributed as ionized plasma

• Photons trapped in fog that hid early times of Universe’s

history

Universe expanded

• Density and temperature

dropped

• Nucleus and electrons

could combine to form

atoms

• Epoch of recombination

• Now photon could

escape

• CMB is the record of

these at the moment of

their escape © cgrahamphysics.com 2016

BLACK BODY SPECTRUM

Multiple scattering of photons resulted in BB spectrum

• Had temperature

~ 3000K

• They were undergoing

cosmological redshift to

longer λ during their

~ 13 billion journey

• Now detected in

microwave region at

temperature of 2.725K

• In agreement with Big

Bang prediction © cgrahamphysics.com 2016

DEFINITION ANISOTROPY

• Although radiation

is almost perfectly

isotropic,

observations show

slightly variations in

temperature

• Temperature

fluctuations with

direction are

called anisotropies


FLUCTUATIONS…..

• Fluctuations in temperature

correspond to regions of

slightly different densities

• Slightly shorter λ in direction

of constellation Leo (hotter)

• In opposite direction

radiation is slightly cooler

• Fluctuations in density

developed later into

galaxies and galaxy clusters


EVIDENCE FROM CMB ANISOTROPIES…

….. may require to rethink the theory

• Lack of symmetry in

average temperatures

in opposite

hemispheres in sky

suggest Universe may

not be isotropic

• There is also a cold spot

extending over a patch

of sky


HUBBLE CONSTANT

• The Hubble constant is

now ~ 67.15km𝑠−1𝑀𝑝𝑐−1

• Significantly less

• Age of Universe 13.82

billion of years

• New orbiting

telescopes will

provide new

additional data

NASA/ESA Euclid mission James Webb space telescope


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