Cosmology Flashcards
What is the course about?
Survey of observable Universe-Hubble’s law
Key properties of CMBR
Derivations of the equations that describe cosmic evolution
Distinguish different cosmological models
Describe possible future destiny
The cosmological constant and the accelerating universe
History of the Universe
Big Bang model-success, shortcomings and inflation, (cosmological constant)
The evidence for dark matter
Origin and structures (galaxies and clusters) maybe look into how this relates to temp fluctuations in CMBR.
What is the standard distance measurement in cosmology?
Mpc - 1 million parsecs = 3.26 light years = 9.463 x 10^15m
1 Mpc = 3.086 x 10^22m
How are galaxies treated in cosmology
As point like objects.
What is the mass of a typical galaxy?
10^10 solar masses to 10^11 solar masses.
How many galaxies are there in the observable universe?
10^11 galaxies approx.
What is the typical separation In a galaxy cluster?
1 Mpc.
What is the typical scale of a supercluster of galaxies?
100Mpc.
What is a typical scale of a void between these superclusters?
50-100Mpc.
Over what scale is the universe considered smooth?
> 100 Mpc - structures bigger than this do not seem to observable.
What is the observable universe?
Limited by the finite speed of c and the age of the universe.
Approx 5Gpc~10^26m
What is the apparent hierarchical structure of the universe?
Stars>Galaxies>Clusters>Superclusters>Observable universe.
What is Doppler shift?
Lambda o/ lambda em = 1+v/c
Z (redshift) = v/c = (L obs/ L em) - 1
How do we measure redshift of galaxies?
Compare the emission line Lyman alpha (n=1-n=2) transition of the Hydrogen atom. Rest wavelength of 121.6nm. Far uv.
How did Hubble arrive at his law?
Compared z’s of cepheid variables(standard candles) with distance.
What is Hubble’s law?
v = Ho x d
Or d = cz/Ho-(when v
How is the Ho defined in terms of the Hubble parameter in the standard cosmological model?
Where Ho = 100h km/s/Mpc- the h allows all the uncertainties in Ho to be confined to the h. Where 0.60
What is the current standard value of Ho?
Ho = 72 + - 8km/s/Mpc
How do we know that CMB is not a local phenomena?
The intensity of the radiation would be sensitive to the direction we are observing.
What is a black body radiator?
An object that absorbs all energy incident on it and reflects none.
What are the key characteristics of black body radiation?
The intensity has a peak at a particular small range of wavelengths which is dependent on temperature.
Intensity falls off exponentially with increasing wavelengths
CMB has a characteristic temperature of 2.728 K. -+ 0.004K
What does the black body nature of the CMB implie?
That the when the universe was younger, it was hotter and effectively in a state of near thermal equilibrium. (It is the closest thing to a perfect black body that has ever been observed)
What else is remarkable about the CMB temperature?
That it is very nearly, but not precisely, uniform to 1 part in 10^5
There is also a directional difference of 0.007K in one direction. This corresponds to a Doppler effect of our Galaxies movement as compared to the rest of the universe of about 600km/s.
What is the cosmological principal?
On sufficiently large scales the universe is both isotopic and homogeneous.
What do isotropy and homogeneity mean in the context of the cosmological principal?
That the universe has no preferred direction when viewed from a particular point.
At a given instant the universe appears the same everywhere.
On what scale does the cosmological principal operate.
> 50Mpc
You cannot determine that the universe is homogeneous - but this follows directly from the isotropy at our vantage point.
What is cosmology?
Understand the present state of the universe, thereby shed light on the origin and fate of the universe
Why does isotropy lead to homogeneity of the universe in the cosmological principle?
Consider two points O and G in the universe.
Consider shells around each d1 and d2 around O and d3 around G.
As isotropic then the density of shell d1 and d2 are the same.
If d3 intersects d1and d2 it follows that d1=d2=d3
Since the shells are arbitrary the density of matter throughout he universe must be independent of position. i.e. The universe is homogeneous
Why do we employ the cosmological principal even though it may not apply to our universe?
When invoking the cosmological principal you can make a number of simplifying assumptions when deriving and solving the cosmological equations that determine the evolution of the universe.
As physical quantities are independent of spatial position we can neglect spatial derivatives.
The solutions surprisingly describe the universe we live in.
How does Hubble’s law follow from the cosmological principal?
Consider three evenly separated galaxies, O , A and B respectively.
Consider an observer in A
If O is moving away from A at speed v, applying the isotropic principle, B must also be moving away from A with speed v.
If this is this case from O’s perspective then B is moving away from O with a speed 2v- recession speed is proportional to distance - Hubble’s law!
In view of the observed isotropy of the universe- what does Hubble’s law become?
A vector equation.
V = Ho x r. Where v and r are both vectors.
As we look in the direction r, the recession velocity at distance (mod r) from us is proportional to r.
Taking the modulus of both sides results in the original equation.
What is Newton’s “iron ball” theorem, and how does it apply to the derivation of the Freidmann equation
Material at a greater distance of r exerts no force on the particle.
Material at a distance less than r exerts the same force as if all that material were concentrated at the centre.
As material is all around the sphere then the effects of opposite material effectively cancels out to have zero effect. This means we can simplify the equations to consider the material of an expanding sphere contained within the sphere.
The cosmological principal also allows us to only consider the time varying parts of the equation as the spatial parts disappear.
Derive the Freidmann equation using Newtonian Gravitation.
Take total energy of a particle on the outside of a sphere
U = T + V
Apply cosmological principle and equation for scale factor into T and V
After rearranging and substituting you get.
(a’^2/a^2) = 8piGroe/3 - kc^2/a^2
What is a(t) the scale factor?
a(t) is the time dependent scale factor. It is used in the equation
r = a(t)x
where x is the coordinate distance and this is a constant.
What do the Friedmann and the conservation equation tell us about the universe?
Friedmann’s equation tells us how the expansion of the universe is determined by the density of matter.
The conservation equation tells us how the density of matter changes as the universe expands.
How do we determine how the pressure of the matter is related to density?
Usually by specifying the pressure directly as a function of density.
Thus. P = P(p). Where lower case represents density
If the pressure varies in direct proportion with density, how can we write the equation of state?
P = (gamma-1)p c^2
Why is the c^2 in the continuity equation
From P = roe RT. >. C=sqrt(RT)
>. P = roe c^2. From ideal gas equation
Explain what the acceleration equation shows.
It is the equivalent to F = Ma. For the universe.
What are the implications of the acceleration equation?
If P and p are non- negative then the acceleration of the universe must be negative and that the da/dt must either be - or +- speeding up or slowing down. But Hubble’s constant is + so and a> 0 so the universe must be expanding. Also the fact that the acceleration is negative means that the expansion must be slowing down!
Also if you go back in time da/dt must increase so the plot must concave downwards towards the time axis. As a result there must be a point when the scale factor vanishes- the point of infinite density and zero volume. The Big Bang!
What is the Hubble parameter, and how does it simplify things?
H = (da/dt)/a
Usually refer to da/dt as a dot.
It is useful to simplify the Friedmann, conservation and the acceleration equation.
What other form can you write the Hubble parameter in?
(dlna/dt) evaluated at 0 the current epoch.
