An Intuitive Approach to Cosmic Horizons

Abstract

How far, in space, can we see? And can we see an object whose Hubble recessional velocity exceeds the speed of light? Maybe you’ve thought about these questions before, or perhaps you’ve seen them discussed in the literature or mentioned in the media. With the recent popularity of inflation and Big Bang cosmology, they’re hard to avoid. The discussion that follows is an attempt to resolve some common misconceptions—often seen in the popular literature—concerning the above two questions, and to do so in a way that appeals to kinematical intuition. A simple thought experiment will be used to initiate the discussion and to answer the question, “Can we see objects with faster-than-light recessional velocity?” Hubble’s law, along with a simple assumption about the kinematics of light in expanding space, will be used to derive expressions, customarily derived in a general relativistic context, that allow cosmologists to determine our observational limits and define our cosmological horizons. Some of the results may surprise you. Before we delve into the topic fully, though, let’s first lay some theoretical groundwork.