Lecture 4: Distance Measures

Question 1

Consider a standard ruler at co-ordinate radius r, the light from which is emitted at co-ordinate time t. The proper length of this standard ruler is

Answer 1

ds where ds^2=a^2(t)r^2 dθ^2

Question 2

We consider a standard candle of luminosity L at co-ordinate radius r1. But we observe

Answer 2

flux Fobs and define dL such that

Fobs=L/4pi dL^2

Question 3

the factor a1^2/a0^2is equivalent to

Answer 3

factor of 1/(1+z)^2 due to the redshifting of the light represented by L=energy/time

Question 4

how to get from RW metric to f(r) as a function of redshift

Answer 4

1. change variables from r to z
2. re-write the Hubble parameter as a function of z
3. note that z=0 and t=t- and using a0=a(t)(1+z)

Question 5

The predicted luminosity distance at a given redshift depends on

Answer 5

the omegas
ie E(z) and H

Question 6

We measure redshifts and estimated luminosity distances (from standard
candles). We then

Answer 6

compare these to the predicted luminosity distances.

Question 7

To make use of cosmic complementarity we combine

Answer 7

multiple different cosmological
probes and / or data spanning different redshift ranges.

Question 8

cosmic complementarity: Overlap between data sets will allow

Answer 8

the values of the parameters to be more tightly constrained.

Question 9

evidence for a flat universe being credible

Answer 9

overlap between different cosmological probes (SNe, CMB, BAO)

the overlap region sits on a boundary between open and closed universes split by k=0