Cosmo Exam Requires Writing Flashcards
Prove hubbles law
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Show that the black body temperature is proportional to (1+z)
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Find the formula for the age of the universe in terms of z
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Show the expression for the angular diameter distance of an object at a certain redshift
What is interesting about this
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The angular diameter distance actually turns over, objects start getting bigger as they get further away. (Due to the dimming of the surface brightness they become harder to see.)
derive the redshift formula
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Derive the Saha equation
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Derive the minimum number of e foldings of inflation required to resolve the flatness problem
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Derive expressions for the parameters Ω_r, Ω_m, Ω_k and Ω_Λ in terms of ρ_crit, Ho, a_o, k and Λ
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Derive the dependence of the scale factor a on time r in a flat radiation dominated universe, using the fluid equation and the Friedman velocity equation
t^1/2
Show that including only a cosmological constant and no fluid component is equivalent to adopting a fluid with an equation of state parameter w= -1 without any cosmological constant
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Sketch the comoving number density of a non-degenerate particle species in thermal equilibrium as a function of mc^2/kT. Indicate which part of the plot corresponds to a relativistic regime and which part to the non relativistic regime
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Derive the acceleration equation and the Friedman equation using Newtonian dynamics. State the corollaries you use. Also derive the fluid equation.
The corollaries : no gravitational field inside a spherical shell of matter, can treat the gravitational attraction of a sphere as if it were concentrated at the centre.
Assume the sphere is expanding homogeneously
Derive the time dependence of a for a flat universe for both the radiation dominated and matter dominated case
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Use thermodynamics to derive the fluid equation
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Derive the radiation dominated density dependence on a
a^-4
Derive the matter dominated density dependence on a
a^-3
Find the equation for critical density
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Sketch the evolution of the density of RD MD CD and ΛD against log a
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Derive the time dependence of a for a for a flat matter dominated universe
t^2/3
Derive the value of a in a closed universe such that there is no expansion
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(The full solution of a(t) is symmetric around this point. It climbs from a=0 to a max and then falls back to 0 at 2tmax)
Derive the time dependence for a for a flat radiation dominated universe
t^1/2
Show that the universe grows exponentially at late times
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Find the age of the universe for a flat, matter dominated universe
Is this consistent?
Hoto = 2/3
We have found objects in the universe which we believe are older than this. Hence we require the universe to be dominated by a form of matter which gives a larger value. This will have the effect of an accelerating scale factor.
Draw a diagram of horizons in the expanding universe
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Find an expression for the proper distance to the horizon as a function of z
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Find the expression for the luminosity distance at a certain redshift
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Derive an expression for the surface brightness.
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Draw diagrams of the angular diameter distance and the luminosity distance against redshift
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Derive the dependence of density on a for an arbitrary w
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Derive the redshift of radiation matter equality
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Show that the effect of redshifting upon a black body is the black body at a new temp T = (1+z) To
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Find the ratio of baryons per photons
What relevance does this have on the matter antimatter asymmetry
For every billion photons there is roughly one baryon, roughly one electron. So when the universe was hot enough that electrons and positrons were considered radiation, they would have been in equilibrium with roughly equal number densities. If there is just one electron extra for every 10^9 positrons the electron would be left over when the electrons and positrons annihilated. Hence the complete present day asymmetry between matter and antimatter is due to only a one in a billion asymmetry at earlier times.
Find the average number of interactions experienced by a particle after time t
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Find the equation which relates the density to the equilibrium density and interaction rate
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Find an expression for the neutrino density parameter and hence place a limit on the sum of the neutrino mass
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What is a wimp
Weakly interacting massive particle, which might be dark matter
Write the equation for hydrogen recombination
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Write the equation for Thomson scattering
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Show that hydrogen recombination must have frozen out
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Calculate the freeze out neutron - proton ratio
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Write the crucial weak interactions
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Write the chain reactions forming deutrium and beyond
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Calculate the mass fraction of a helium nucleus
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What is the tritium path
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Show Ωk is an increasing function with z for both matter and radiation domination
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Derive the density parameter for monopoles today and show it overcloses the universe
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Draw the dependence of the scale factor and the temperature with time
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Show that inflation requires negative pressure in the early universe
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Calculate the number of N folds required to solve the horizon problem
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Calculate the number of N folds required to solve the flatness problem
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Calculate how many N folds are required to solve the monopole problem
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Derive the equation governing the scalar field
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Sketch and explain the the shape of the potential for the inflation scalar field
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Derive the expression for the particle horizon
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Calculate a numerical value for the mass fraction of helium formed by Big Bang nucelosynthesis. State any assumptions made
Assume all of the neutrons go into He nuclei, so the number density of helium is about half of the number density of neutrons
Calculate the number of e foldings required for inflation to solve the monopole problem
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Draw the equilibrium ionisation fraction X as a function of redshift
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