| Nearly every attempt to unify the fundamental forces incorporates the idea of compact extra dimensions. The notion was introduced by Kaluza and Klein in the 1920s and is an essential part of contemporary string theory and M-theory. In most treatments the extra dimensions are static. We consider the consequences of extra dimensions with time-varying radii. The radii are modeled by light scalar fields. These may have unusual properties which produce observable effects, such as non-canonical kinetic energies, couplings to matter and radiation, and non-minimal coupling to gravity.; Extra dimensions may be responsible for dark energy in the late universe. The simplest model of dark energy is characterized by its equation of state. We show that constraints placed on realistic models by the universality of free fall, variation of fundamental constants and metric tests of gravity are often stricter than bounds on the equation of state. Testing the equivalence principle maybe an effective way of distinguishing some quintessence models from a cosmological constant.; In certain dark energy models the speed of sound is much less than the speed of light. We calculate how this affects the cosmic microwave background and show that the speed of sound may be measurable, provided dark energy is sufficiently dense at decoupling. This is another possible signature of quintessence.; Dynamical extra dimensions may have consequences for the early universe. In the cyclic model, the universe is described in terms of a series of contractions and expansions of an extra dimension. The big bang is preceded by a big crunch and quantum fluctuations of the scalar field produce structure in universe. We consider how the fluctuations evolve and build over many cycles and show that there are no observable instabilities or adverse effects.; In the cyclic model extra dimensions act as both dark energy and as an agent to cause contraction and a big crunch. Previous theorems suggested that contraction necessarily leads to chaotic behavior and unacceptable inhomogeneity. We show that homogeneous contraction is possible if the pressure-to-density ratio of the scalar field is sufficiently large. |
