Scaling cosmologies, geodesic motion and pseudo-susy

Abstract

One-parameter solutions in supergravity carried by scalars and a metric trace out curves on the scalar manifold. In ungauged supergravity these curves describe a geodesic motion. It is known that a geodesic motion sometimes occurs in the presence of a scalar potential and for time-dependent solutions this can happen for scaling cosmologies. This note contains a further study of such solutions in the context of pseudo-supersymmetry for multi-field systems whose first-order equations we derive using a Bogomol'nyi-like method. In particular we show that scaling solutions that are pseudo-BPS must describe geodesic curves. Furthermore, we clarify how to solve the geodesic equations of motion when the scalar manifold is a maximally non-compact coset such as occurs in maximal supergravity. This relies upon a parametrization of the coset in the Borel gauge. We then illustrate this with the cosmological solutions of higher-dimensional gravity compactified on a $n$-torus.

14 pages, slight change in title, references added, typos corrected. Version accepted for publication in Class. Quantum Grav

References in corpus (24)

• Dynamics of dark energy
• Exponential potentials and cosmological scaling solutions
• Assisted inflation
• Gravitational Stability and Renormalization-Group Flow
• Fake Supergravity and Domain Wall Stability
• Generalized Assisted Inflation
• Hidden supersymmetry of domain walls and cosmologies
• Dynamics of Assisted Inflation
• De Sitter Space in Supergravity and M Theory
• Correspondence between kinematical backreaction and scalar field cosmologies - the `morphon field'
• First-order formalism and dark energy
• R--R Scalars, U--Duality and Solvable Lie Algebras
• On the fakeness of fake supergravity
• States and Curves of Five-Dimensional Gauged Supergravity
• Scale-invariance in expanding and contracting universes from two-field models
• Pseudo-supersymmetry and a Tale of Alternate Realities
• Recurrent Acceleration in Dilaton-Axion Cosmology
• Cosmological backgrounds of superstring theory and Solvable Algebras: Oxidation and Branes
• Dynamics of Generalized Assisted Inflation
• Integrability of Supergravity Billiards and the generalized Toda lattice equation
• Gauging CSO groups in N=4 Supergravity
• Tits-Satake projections of homogeneous special geometries
• Scaling Cosmologies of N=8 Gauged Supergravity
• Scaling solutions and geodesics in moduli space

Cited by in corpus (19)

• Braneworld Models of Scalar Fields with Generalized Dynamics
• Generating Geodesic Flows and Supergravity Solutions
• First-order flow equations for extremal and non-extremal black holes
• Pseudo-supersymmetry and a Tale of Alternate Realities
• Black holes in supergravity and integrability
• Domain-wall/Cosmology correspondence in adS/dS supergravity
• First-order framework and domain-wall/brane-cosmology correspondence
• A first-order formalism for timelike and spacelike brane solutions
• Fake supersymmetry versus Hamilton-Jacobi
• CMB constraints on $\beta$-exponential inflationary models
• First-order formalism for dark energy and dust
• Braneworld solutions from scalar field in bimetric theory
• Black holes as generalised Toda molecules
• Cosmological Model of Interacting Tachyon Field
• Cosmological twinlike models with multi scalar fields
• 4D gravity on a non-BPS bent dilatonic brane
• Comments on fake supersymmetry
• Duality linking standard and tachyon scalar field cosmologies
• Brane structure from a scalar field in general covariant Horava-Lifshitz gravity