Fluctuations from cosmic strings and the microwave background

The spectrum of energy-density perturbations and anisotropies in the microwave background radiation are calculated in models with cosmic strings. The computations are based on a mathematical model of the network of cosmic strings as a combination of a random walk of infinite strings and a distribution of string loops. The energy-density distribution is scale invariant at Hubble radius crossing, but the k dependence of the spectrum is nontrivial and not equal to the result for adiabatic linear perturbations. The anisotropies in the microwave background radiation are smaller than the observational upper bounds on all angular scales for a value μG∼2×${10}^{\mathrm{-}6}$ obtained from independent astrophysical considerations. We include both the effects due to gravitational lensing from long strings and from local gravitational perturbations due to loops (the Sachs-Wolfe effect).