Inflation and String Theory

Abstract

We review cosmological inflation and its realization in quantum field theory and in string theory. This material is a portion of a book, also entitled "Inflation and String Theory", to be published by Cambridge University Press.

Figures (42)

• Figure 1.1: Spacetime diagram illustrating the horizon problem in comoving coordinates (figure adapted from Lineweaver:2003ie). The dotted vertical lines correspond to the worldlines of comoving objects. We are the central worldline. The current redshifts of the comoving galaxies are labeled on each worldline. All events that we currently observe are on our past light cone. The intersection of our past light cone with the spacelike slice labeled CMB corresponds to two opposite points on the CMB surface of last-scattering. The past light cones of these points, shaded gray, do not overlap, so the points appear never to have been in causal contact.
• Figure 1.2: Inflationary solution to the horizon problem. The comoving Hubble sphere shrinks during inflation and expands during the conventional Big Bang evolution (at least until dark energy takes over). Conformal time during inflation is negative. The spacelike singularity of the standard Big Bang is replaced by the reheating surface: rather than marking the beginning of time, $\tau=0$ now corresponds to the transition from inflation to the standard Big Bang evolution. All points in the CMB have overlapping past light cones and therefore originated from a causally connected region of space.
• Figure 1.3: Time-dependent background fields $\psi_m(t)$ introduce a preferred time slicing of de Sitter space.
• Figure 1.4: The evolution of curvature perturbations during and after inflation: the comoving horizon $(aH)^{-1}$ shrinks during inflation and grows in the subsequent FRW evolution. This implies that comoving scales $(c_s k)^{-1}$ exit the horizon at early times and re-enter the horizon at late times. In physical coordinates, the Hubble radius $H^{-1}$ is constant and the physical wavelength grows exponentially, $\lambda \propto a(t) \propto e^{Ht}$. For adiabatic fluctuations, the curvature perturbations ${\@fontswitch\mathcal{R}}$ do not evolve outside of the horizon, so the power spectrum $P_{\@fontswitch\mathcal{R}}(k)$ at horizon exit during inflation can be related directly to CMB observables at late times.
• Figure 1.5: CMB anisotropies as observed by the Planck satellite. Red (blue) spots are hotter (colder) than the average temperature, reflecting density variations at recombination.