ABSTRACT
This chapter begins by considering the possible geometry of space as either flat, positively curved, or negatively curved, and explains that the distinction between them relies on the density of matter and energy the Universe. An open universe will expand forever until its eventual heat death, a closed universe will eventually contract ending in a big crunch. A flat universe comprising matter only has a critical density on the boundary between these extremes. Observations of distant type Ia supernovae have revealed that the expansion of the Universe is currently accelerating, pointing to the existence of dark energy. The Universe is most probably geometrically flat but open, comprising 69% dark energy, 26% non-baryonic dark matter (in the form of WIMPs), and 5% baryonic matter, most of which is also dark (in the form of MACHOs and the WHIM). Whether it will end in a heat death or a big rip depends on the equation of state parameter for dark energy or quintessence. An alternative to the Big Bang is presented called the ekpyrotic universe theory, involving cyclic big claps between multi-dimensional branes.
