Multiple inflation, cosmic string networks and the string landscape

Motivated by the string landscape we examine scenarios for which inflation isa two-step process, with a comparatively short inflationary epoch near thestring scale and a longer period at a much lower energy (like the TeV scale).We quantify the number of $e$-foldings of inflation which are required to yieldsuccessful inflation within this picture. The constraints are very sensitive tothe equation of state during the epoch between the two inflationary periods, asthe extra-horizon modes can come back inside the horizon and becomereprocessed. We find that the number of $e$-foldings during the firstinflationary epoch can be as small as 12, but only if the inter-inflationaryperiod is dominated by a network of cosmic strings (such as might be producedif the initial inflationary period is due to the brane-antibrane mechanism). Inthis case a further 20 $e$-foldings of inflation would be required at lowerenergies to solve the late universe's flatness and horizon problems.Comment: 27 pages, 6 figures; v2: refences adde