Flashcards in D.5 Further Cosmology Deck (21):
What is the universe on a large scale?
Homogenous - uniform in all directions
Isotropic - looks the same in all directions
These two principle comprise the cosmological principle - most models assume this to be true. Additions evidence for the comsooologicsl principle comes form the great degree if isotropy of the CMBR.
What are the variations in temperature of the CMB and density related to?
The density of the universe.
Variations in density are the key to how structure formed in the universe, with perfectly uniform temperature and density int he universe stars and galaxies would not form.
What gives the orbital speed of a mass?
GMm/r^2 = mv^2/r which gives
v = sqr root(GM/r)
What is the dependence of v on r?
Rotation curve of the attracting mass.
What is the first case of the rotation curve?
m moves around a point mass M in this case v = 1/sqr root(r)
What is the second case of the rotation curve?
m moves within a cloud of dust of uniform density p in this case the attracting mass M is the mass enclosed within the sphere of radius r only. Since p = M/V = M/(4pir^3/r) = 3m/4pir^3 we find M = 4pir^3p/3 and so
v = sqr root(G4pir^3p/3r) thus v = r
What is the third case of the rotation curve?
m moves in a cloud of dust of non uniform density whose mass varies with distance from the axis according to M = kr where k is a constant. In this case the density would be
p =M/V = kr/(4pir^3/3) = 3k/4pir^2 so
v = sqr root (GM/r) gives
v = sqr root(Gkr/r) = constant.
What does the rotation curve for the galaxy show?
An initial linear increase suggesting a uniform density near the galactic centre. At larger distances the curve becomes flat consistent with the this rotation curve in which there is substantial mass outside the galactic disk.
What is the matter that affect the galaxy?
Dark matter which is too cold to radiate and so cannot be seen. Estimated 85% of the matter in the universe is dark matter.
What is the evidence for dark matter?
Its gravitational effects on nearby bodies.
What are the two forms of dark matter?
MACHOS (massive compact halo objects) ordinary cold matter that does not radiate eg brown dwarf, black dwarf, small plates.
WIMPS (weakly interacting massive particles) neutrinos fall into this class since they are known to have a small mass although their tiny mass is not enough to account for all non baryonic dark matter.
What formula gives a cosmological interpretation of red shift that is not based on the Doppler effect?
lambda/lambda0 = R/R0
where lamda0 is the emission of a photon of wavelength lamda0 at one time in the history of the universe, and its detection and measurement with a wavelength of lambda at the present time. R0 is the value of the scale factor at the time of the piton's emission and R is its value now. It suggests the galaxies are expanding so wavelengths will expand as well.
What effect does the equation have for the CMB?
It has a direct bearing on the temperature of the CMB that fills the universe. The wavelength lambda0 corresponds to a CMB temperature of T0 so by Wien's law lambda0T0 = constant.
Likewise lambdaT = constant.
Therefore lambda/lambda0 = T0/T so
T0/T = R/R0 or T proportional 1/R.
This shows that as the inverse expands and R gets bigger its temperature drops. The is why the universe is cooling down and why the present temperature of the CMB (2.7K) is so low now.
How do we find the total energy of a cloud of dust of radius r, mass m at the surface of the cloud which moves away from the centre with a speed v that satisfies Hubble's law v = H0r?
The total energy of the mass E = 1/2mv^2 -GMm/r where M is the mass of the cloud, if we call the density of this cloud p then
M = p4/3pir^3 using this together with v=H0r we find E = 1/2mr^2(Ho^2 = 8pipG/3).
This energy is zero if the density is Pc = 3H0^2/8piG = 10^-26kgm-3. This is referred tot he critical density of the universe.
What is important about the critical density?
Plays a crucial role in models for the evolution of the universe. Comparison of the critical density with the sum of the matter and energy density of the universe determine whether the universe has a flat or curved geometry.
What do the solutions of the universe depend on?
Density parameters @m = pm/pcrit and
@^ = p^/pcrit where pm is the actual density of matter in the unversed pcrit is the critical density of the universe and p^ is the density of the vacuum energy.
What happens in the closed model of the universe?
Starts from zero increases to a maximum then decreases to zero again the universe collapses after an initial period of expansion. @m > 1 thus pm>pcrit
What happens in the open model of the universe?
The scale factor increases without limit the universe continue to expand forever.
@m < 1 thus pm < pcrit
What happens in the critical model of the universe?
The universe expand forever but the rate of expansion decreases becoming zero at infinite time. @m = 1. The density of the universe in this case is equal to the critical density pm = pcrit.
What is a flat universe?
@m + @^ = 1 at the present the universe has a flat geometry 32% of its mass energy content is mater and 68% is vacuum energy and it will expand forever at an accelerating rate.