Cosmology Flashcards

Question

On what scale does the cosmological principal operate.

Answer 1

>50Mpc You cannot determine that the universe is homogeneous - but this follows directly from the isotropy at our vantage point.

Answer 2

Understand the present state of the universe, thereby shed light on the origin and fate of the universe

Answer 3

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

Answer 4

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.

Answer 5

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!

Answer 6

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.

Answer 7

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.

Answer 8

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

Answer 9

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.

Answer 10

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.

Answer 11

Usually by specifying the pressure directly as a function of density. Thus. P = P(p). Where lower case represents density

Answer 12

P = (gamma-1)p c^2

Answer 13

From P = roe RT. >. C=sqrt(RT) | >. P = roe c^2. From ideal gas equation

Answer 14

It is the equivalent to F = Ma. For the universe.

Answer 15

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!

Answer 16

H = (da/dt)/a Usually refer to da/dt as a dot. It is useful to simplify the Friedmann, conservation and the acceleration equation.

Answer 17

(dlna/dt) evaluated at 0 the current epoch.