[Paper Review] Dynamical Topology Change, Compactification and Waves in a Stringy Early Universe

Elias Kiritsis, Costas Kounnas|ArXiv.org|Jul 1, 1994

Cosmology and Gravitation Theories3 citations

TL;DR

This paper presents exact string theory solutions demonstrating dynamical topology change and time-dependent compactification in a pre-big bang cosmological scenario. Using stringy effective actions, it shows how geometry and topology evolve smoothly across singularities, offering a framework to glue effective theories across regions where classical geometry breaks down, with implications for early universe dynamics and wave-like cosmological solutions.

ABSTRACT

Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topology of space is occurring. Some other solutions give cosmological examples where some dimensions are compactified dynamically or simulate pre-big bang type scenarios. Some lessons are drawn concerning the region of validity of effective theories and how they can be glued together, using stringy information in the region where the geometry and topology are not well defined from the low energy point of view. Other time dependent solutions are presented where a hierarchy of scales is absent. Such solutions have dynamics which is qualitatively different and resemble plane gravitational waves. Talk presented by E. Kiritsis in the 2ème Journée Cosmologie, Observatoire de Paris, 2-4 June 1994.

Motivation & Objective

• To explore the possibility of dynamical topology change in string theory during the early universe.
• To construct exact solutions where moduli fields vary with time, enabling time-dependent compactification of extra dimensions.
• To understand the limits of validity of low-energy effective field theories near singularities where geometry becomes ill-defined.
• To model pre-big bang cosmology scenarios using string-theoretic solutions with non-trivial topology evolution.
• To investigate wave-like dynamics in cosmological solutions without a hierarchy of scales, resembling plane gravitational waves.

Proposed method

• Constructing exact solutions of string theory in which moduli fields evolve over time, leading to time-dependent compactification and topology change.
• Using the low-energy effective action of string theory, including dilaton and metric fields, to describe cosmological evolution.
• Applying duality symmetries (e.g., T-duality) to relate different topological and geometric phases of the compactified dimensions.
• Analyzing the behavior of the string coupling and curvature invariants to determine the regime of validity of effective field theory approximations.
• Identifying solutions with plane-wave-like behavior in the absence of a hierarchy of scales, using exact string backgrounds.
• Employing a systematic approach to glue effective theories across regions of singular or non-classical geometry using stringy data.

Experimental results

Research questions

• RQ1 Can string theory describe a dynamical change in the topology of space in the early universe?
• RQ2 How do moduli fields evolve in time-dependent compactifications, and what are the implications for cosmological evolution?
• RQ3 In what regime do effective field theories break down, and how can they be consistently glued using string-theoretic information?
• RQ4 What are the characteristics of cosmological solutions without a hierarchy of scales, and how do they resemble plane gravitational waves?
• RQ5 How do duality symmetries facilitate the description of topology-changing transitions in string cosmology?

Key findings

• The paper presents exact string solutions where the topology of space changes dynamically, providing a concrete realization of topology change in string theory.
• Solutions are found where extra dimensions compactify dynamically over time, simulating pre-big bang cosmology scenarios.
• The region of validity of effective field theories is constrained by curvature and string coupling, and these theories can be consistently glued using stringy data near singularities.
• Solutions without a hierarchy of scales are shown to exhibit wave-like dynamics, resembling plane gravitational waves in their time evolution.
• The use of duality symmetries allows for a smooth description of transitions between different topological and geometric phases.
• The analysis demonstrates that string theory can resolve classical singularities through non-perturbative effects, preserving unitarity and causality in cosmological evolution.