A New Cosmological Scenario in String Theory

TL;DR

This work introduces a cosmological scenario in string theory where space–time is constructed as a quotient of flat space by a boost plus translation, yielding collapsing, intermediate, and expanding phases separated by cosmological horizons. The authors develop a two-dimensional toy model and embed it into string theory as a bosonic orbifold, deriving a modular-invariant one-loop partition function and highlighting the role of winding modes near time-like singularities. They further generalize to higher dimensions with a dilatonic form-field action, deriving region I open-universe behavior and a horizon that links to region II, and discuss the string/M-theory validity and dual descriptions (including a 9–11 flip) that illuminate the singular regime. The proposed framework potentially resolves horizon and singularity problems by horizon boundary conditions and light winding states, offering a novel,/string-inspired route to cosmological evolution with broad theoretical implications for early-universe physics.

Abstract

We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future) horizon. The solutions are naturally embedded in string and M-theory. In the particular case of a two-dimensional cosmology, space-time is flat with an identification under boost and translation transformations. We consider the corresponding string theory orbifold and calculate the modular invariant one-loop partition function. In this case there is a strong parallel with the BTZ black hole. The higher dimensional cosmologies have a time-like curvature singularity in the intermediate region. In some cases the string coupling can be made small throughout all of space-time but string corrections become important at the singularity. This happens where string winding modes become light which could resolve the singularity. The new proposed space-time casual structure could have implications for cosmology, independently of string theory.

Figures (3)

• Figure 1: The different regions in space--time in the light cone coordinates $X^{\pm}=(X\pm T)/\sqrt{2}$. The outer regions $I$ will be interpreted as the cosmological collapsing and expanding phases. In regions $III$ there are closed time--like curves that can be deformed to regions $II$, but always close in region $III$. The surface $|T|=|X|$ acts as a horizon because the closed time--like curves cannot be deformed to enter regions $I$.
• Figure 2: Carter--Penrose diagram for the two--dimensional Kał uża--Klein cosmology. Spatial, future and past infinities are defined with respect to the expanding region $I$. The past (future) horizon of the expanding (collapsing) outer region is a Cauchy surface. The singularity at $t=1/E$ is an artifact of the compactification because this is the surface where $\kappa$ becomes null.
• Figure 3: Carter--Penrose diagrams for open Universe cosmologies. In both diagrams each point represents a $(d-1)$ sphere and $\chi=0$ is a coordinate singularity. The standard diagram in (b) is presented for comparison with our proposal.