Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Cosmic Acceleration from M Theory on Twisted Spaces

Ishwaree P. Neupane, David L. Wiltshire

TL;DR

This work demonstrates that acceleration in four dimensions can arise from time-dependent compactifications of pure gravity on twisted product spaces, circumventing former no-go results. By deriving the 4D effective action with multiple canonically normalized scalars and a multi-exponential potential generated by twists and curvature, the authors construct exact cosmological solutions exhibiting transient or eternal acceleration, depending on the internal geometry and twist structure. They show that geometric twists can create a local de Sitter minimum in the scalar potential, enabling periods of accelerated expansion even with Ricci-flat internal spaces, and they explore two-, three-, and higher-scalar cases with explicit solutions and acceleration criteria. The results highlight a framework in which higher-dimensional gravity and internal geometry directly shape late-time cosmology, with potential connections to quintessence, moduli stabilization, and multi-stage inflation, while outlining avenues for incorporating fluxes and more general compactifications. $V(oldsymbol{ extvarphi})$ features cross-coupled exponential terms that drive acceleration, and the work provides concrete examples and analytic expressions for the evolution of the scale factor and moduli across diverse internal-space configurations.

Abstract

In a recent paper [I.P. Neupane and D.L. Wiltshire, Phys. Lett. B 619, 201 (2005).] we have found a new class of accelerating cosmologies arising from a time--dependent compactification of classical supergravity on product spaces that include one or more geometric twists along with non-trivial curved internal spaces. With such effects, a scalar potential can have a local minimum with positive vacuum energy. The existence of such a minimum generically predicts a period of accelerated expansion in the four-dimensional Einstein-conformal frame. Here we extend our knowledge of these cosmological solutions by presenting new examples and discuss the properties of the solutions in a more general setting. We also relate the known (asymptotic) solutions for multi-scalar fields with exponential potentials to the accelerating solutions arising from simple (or twisted) product spaces for internal manifolds.

Cosmic Acceleration from M Theory on Twisted Spaces

TL;DR

This work demonstrates that acceleration in four dimensions can arise from time-dependent compactifications of pure gravity on twisted product spaces, circumventing former no-go results. By deriving the 4D effective action with multiple canonically normalized scalars and a multi-exponential potential generated by twists and curvature, the authors construct exact cosmological solutions exhibiting transient or eternal acceleration, depending on the internal geometry and twist structure. They show that geometric twists can create a local de Sitter minimum in the scalar potential, enabling periods of accelerated expansion even with Ricci-flat internal spaces, and they explore two-, three-, and higher-scalar cases with explicit solutions and acceleration criteria. The results highlight a framework in which higher-dimensional gravity and internal geometry directly shape late-time cosmology, with potential connections to quintessence, moduli stabilization, and multi-stage inflation, while outlining avenues for incorporating fluxes and more general compactifications. features cross-coupled exponential terms that drive acceleration, and the work provides concrete examples and analytic expressions for the evolution of the scale factor and moduli across diverse internal-space configurations.

Abstract

In a recent paper [I.P. Neupane and D.L. Wiltshire, Phys. Lett. B 619, 201 (2005).] we have found a new class of accelerating cosmologies arising from a time--dependent compactification of classical supergravity on product spaces that include one or more geometric twists along with non-trivial curved internal spaces. With such effects, a scalar potential can have a local minimum with positive vacuum energy. The existence of such a minimum generically predicts a period of accelerated expansion in the four-dimensional Einstein-conformal frame. Here we extend our knowledge of these cosmological solutions by presenting new examples and discuss the properties of the solutions in a more general setting. We also relate the known (asymptotic) solutions for multi-scalar fields with exponential potentials to the accelerating solutions arising from simple (or twisted) product spaces for internal manifolds.

Paper Structure

This paper contains 21 sections, 126 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Product space compactification: Basic Equations
  3. Compactification on symmetric spaces
  4. The solution with a non-zero twist
  5. Solutions with flat and hyperbolic extra dimensions
  6. The field equations in $\delta=0$ gauge
  7. M-theory phantom cosmology
  8. Multiple scalars and cosmology in four-dimensions
  9. The two scalar case
  10. Accelerating solutions
  11. The three scalar case
  12. de Sitter vacuum and cosmic acceleration
  13. Exponential potentials with more than one scalar
  14. A model of eternal acceleration
  15. More than one geometric twist
  16. ...and 6 more sections

Figures (3)

  • Figure 1: The number of e--folds during acceleration epoch (case I) as a function of the parameter $\alpha\equiv c_{\hbox{$2$}}/c$, $\beta\equiv c_{\hbox{$3$}}/c$, for $p=17$, $q=2$, ($d=26$). $N_e$ is maximum around $(\alpha,\beta)=0$.
  • Figure 2: The number of e--folds during acceleration epoch (case II) as a function of the parameter $\alpha\equiv c_{\hbox{$1$}}/c$, $\beta\equiv c_{\hbox{$3$}}/c$, for $p=2$, $q=2$, ($d=11$). $N_e$ is maximum around $(\alpha,\beta)=0$.
  • Figure 3: The number of e--folds $N$ vs scalar field $\varphi_2$, for the potential (\ref{['varphi1=0']}).