Closed String Tachyon Condensation and Worldsheet Inflation

TL;DR

This work studies how closed string tachyon condensation on the string worldsheet, encoded in Liouville gravity coupled to matter, can reproduce inflationary cosmologies in two dimensions. By analyzing both homogeneous and inhomogeneous tachyon condensates, it demonstrates slow-roll and topological inflation, exact solvable cases, and the role of domain-wall seeds, with the Liouville field acting as the worldsheet scale factor. It then explores quantum aspects—stress-tensor backreaction, minisuperspace wavefunctions, string production, and 2D de Sitter thermodynamics—before arguing that localized tachyon condensates provide a controlled late-time relaxing endpoint and proposing an alternative mechanism in which universal pair production yields inflationary 2D universes. The framework relies on the conformal anomaly constraint c_{ m tot} = 1 + 3Q^2 + c_{ m matter} - 26 = 0 with Q = 2/ obreak rac{rac}{rac}{rac}{} and Q = 2/ obreak rac{rac}{rac}{rac}{}; together these structures illuminate how worldsheet dynamics can generate and eventually relax an inflationary phase, offering a two-dimensional testing ground for inflationary scenarios and cosmological constant relaxation.

Abstract

Closed string tachyon condensation in spacetime generates potentials on the worldsheet that model two-dimensional inflationary cosmology. These models illustrate and elucidate a variety of aspects of inflation, in particular the generation of quantum fluctuations and their back-reaction on geometry. We exhibit a class of Liouville gravity models coupled to matter that can exhibit, for example: (a) pure de Sitter gravity; (b) slow-roll inflation; (c) topological inflation; and (d) graceful exit into an FRW phase. The models also provide a quantitative testing ground for ideas about the origin of inflation, such as the various `no-boundary/tunnelling' proposals, and the `eternal/chaotic' inflationary scenario. We suggest an alternative mechanism for quantum creation of cosmological spacetimes which, in the context of the model, provides a natural explanation for why the typical FRW cosmology at large scales underwent a period of inflation at small scale.

Figures (5)

• Figure 1: The three classes of solution of de Sitter Liouville theory, corresponding to positive, zero, and negative energy (relative to the Casimir energy on the cylinder $-{{1\over 8}} Q^2$). Large positive $\phi$ corresponds to large scale factor. The positive energy solution describes gravity coupled to matter energy density; it has an FRW-like 'big bang' in the past and dS asymptotics in the far future. The zero energy solution describes de Sitter geometry in flat coordinates, while the negative energy solution describes the 'bounce' geometry of global de Sitter space.
• Figure 2: Domains of the de Sitter conformal diagram covered by the metrics (\ref{['milneds']}), (\ref{['flatds']}), (\ref{['globalds']}), respectively. For simplicity, only half of the conformal diagram is shown in each case ( i.e. the zero-dimensional 'angular sphere' consists of two points).
• Figure 3: The boundary of a test open string propagating in an open string tachyon background is 'repelled from the future'. The ends of the string find each other and annihilate, leaving a free closed string whose propagation to the future is unhindered.
• Figure 4: Plots of the scale factor $\phi$ and matter field $X$ during topological inflation. At early and late worldsheet time $\tau$, the matter field $X$ has one unit of winding. The spacetime picture, however, consists of a pair of oppositely wound strings annihilating and leaving behind an unwound string perched at a maximum of the cosine matter potential.
• Figure 5: The fractal structure of the eternally/chaotically inflating universe. The shaded domains represent the ordinary FRW cosmological regions that arise when the chaotic inflaton sporadically falls out of the inflationary regime. In a two-dimensional model, such configurations represent violent UV fluctutations of the Liouville mode, which might not have physical significance.