Further Cosmology - WordPress.com PRINCIPLE •Is the Universe isotropic or homogeneous? •There is...
Transcript of Further Cosmology - WordPress.com PRINCIPLE •Is the Universe isotropic or homogeneous? •There is...
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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
EDGE OF THE UNIVERSE
• The two situations would appear different
• Isotropy says that this isn’t the case
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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
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
© cgrahamphysics.com 2016
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
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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
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NEGATIVELY CURVED
• Shape of a saddle
of infinite size
• Ω 0 < 1
• You would never
return to the same
point in space time
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SURFACE REMAINS FLAT
• Shape remains flat
of infinite size
• Ω 0 = 1
• You would never
return to the same
point in space time
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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
© cgrahamphysics.com 2016
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
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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
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OPEN UNIVERSE (NEGATIVELY SHAPED SADDLE)
• Gravity is too weak
to stop Universe
from expanding for
ever
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FLAT UNIVERSE
• Density is at critical
value
• Universe will only
start to contract
after an infinite
amount of time
Ω 0 = 1
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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
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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
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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
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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
© cgrahamphysics.com 2016
LET THE LIMIT OF TE=0
•1
2𝑚 𝐻0
2𝑅2 = 4
3𝜋𝑚𝐺𝜌𝑅2
• 𝐻0 = Hubble constant
• G = Newton’s
gravitational
constant
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POSSIBLE DEVELOPMENT OF THE UNIVERSE
• Flat Universe
𝜌 = 𝜌𝑐
• Open Universe
𝜌 < 𝜌𝑐
• Closed Universe
𝜌 > 𝜌𝑐
Accelerating Universe
No gravity, 𝜌 = 0
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
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
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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
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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
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
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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
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EXPLANATION
• Dark matter forms a halo around the outer
rim of a galaxy
• Matter is not luminous or baryonic and
emits no radiation
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DARK MATTER HALO
• When the halo with dark matter is added
to the curve, it almost fits the observed
data
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OTHER EVIDENCE
• Velocity of galaxies
orbiting each other
in clusters
• They emit far less
light than
suggested by their
velocities WRT their
mass
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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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
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
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DARK ENERGY
• Unknown force
causing galaxies to
move further apart
and stretching the
fabric of space
faster
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ESA’S PLANCK MISSION
• 68% of the Universe
consists of dark energy
• 26.8% is dark matter
• 4.9% is ordinary matter
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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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016
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
© cgrahamphysics.com 2016