Catch-Me-If-You-Can: The Overshoot Problem and the Weak/Inflation Hierarchy

TL;DR

This paper investigates the overshoot problem in LVS string cosmology, showing that a large hierarchy between inflationary and weak scales naturally leads to a stable vacuum, favoring high inflation scales and possibly involving a primordial string network.

Contribution

It demonstrates that the overshoot problem can be resolved in LVS cosmology through attractor solutions, linking the hierarchy of scales to initial conditions and the presence of a string network.

Findings

Overshoot problem is solvable via attractor tracker solutions in LVS.

A large inflation/weak hierarchy favors ending in a stable vacuum.

A primordial string network may produce a gravitational wave-dominated early universe.

Abstract

We study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). LVS cosmology features a long kination epoch as the volume modulus rolls down the exponential slope towards the final minimum, with an energy density that scales as $m_s^4$. This roll admits attractor tracker solutions, and if these are located the overshoot problem is solved. We show that, provided a sufficiently large hierarchy exists between the inflationary scale and the weak scale, this will always occur in LVS as initial seed radiation grows into the tracker solution. The consistency requirement of ending in a stable vacuum containing the weak hierarchy therefore gives a preference for high inflationary scales -- an anthropic argument, if one likes, for a large inflation/weak hierarchy. We discuss various origins, both universal and model-dependent, of the initial seed radiation (or matter). One particularly interesting case is that of a fundamental string network arising from brane inflation -- this may lead to an early epoch in which the universe energy density principally consists of gravitational waves, while an LVS fundamental string network survives into the present universe.