2 Propagation of light and horizons
We obtain most of the information about the universe from light. Over the last
century, the development of x-ray, radio and infrared detectors has given us new
windows on the universe. Understanding the propagation of light in an expanding
universe is therefore critical to the interpretation of observations.
Problem 2.1Estimate the total amount of energy received by all optical telescopes
over the course of the last century and compare this energy to that needed to return
this book to your bookshelf.
There is a fundamental limit to how far we can see, since no particles can travel
faster than light. The finite speed of light leads to “horizons” and sets an absolute
constraint on our ability to comprehend the entire universe. The term “horizon”
is used in different contexts in the literature, often without clear definition, and
one of the purposes of this chapter is to carefully delineate the various usages.
We will study in detail conformal diagrams, which are a useful pictorial way of
representing horizons and the causal global structure of spacetime. Finally, we
discuss the basic kinematical tests which aim to measure the distance, angular
size, speed and acceleration of distant objects. Using these tests, one can obtain
information about the expansion rate and deceleration parameter at earlier times,
and thus probe the evolutionary history of the universe.
2.1Lightgeodesics
In Special Relativity, the spacetime interval along the trajectory of a massless
particle propagating with the speed of light is equal to zero:
ds^2 = 0. (2.1)37