13 research outputs found
Cosmology as Geodesic Motion
For gravity coupled to N scalar fields with arbitrary potential V, it is
shown that all flat (homogeneous and isotropic) cosmologies correspond to
geodesics in an (N+1)-dimensional `augmented' target space of Lorentzian
signature (1,N), timelike if V>0, null if V=0 and spacelike if V<0.
Accelerating cosmologies correspond to timelike geodesics that lie within an
`acceleration subcone' of the `lightcone'. Non-flat (k=-1,+1) cosmologies are
shown to evolve as projections of geodesic motion in a space of dimension
(N+2), of signature (1,N+1) for k=-1 and signature (2,N) for k=+1. This
formalism is illustrated by cosmological solutions of models with an
exponential potential, which are comprehensively analysed; the late-time
behviour for other potentials of current interest is deduced by comparison.Comment: 26 pages, 2 figures, journal version with additional reference
Late-time Cosmic Dynamics from M-theory
We consider the behaviour of the cosmological acceleration for time-dependent
hyperbolic and flux compactifications of M-theory, with an exponential
potential. For flat and closed cosmologies it is seen that a positive
acceleration is always transient for both compactifications. For open
cosmologies, both compactifications can give at late times periods of positive
acceleration. As a function of proper time this acceleration has a power law
decay and can be either positive, negative or oscillatory.Comment: 10 pages, LaTeX, 2 figure
Spinning particles in the vacuum C metric
The motion of a spinning test particle given by the Mathisson-Papapetrou
equations is studied on an exterior vacuum C metric background spacetime
describing the accelerated motion of a spherically symmetric gravitational
source. We consider circular orbits of the particle around the direction of
acceleration of the source. The symmetries of this configuration lead to the
reduction of the differential equations of motion to algebraic relations. The
spin supplementary conditions as well as the coupling between the spin of the
particle and the acceleration of the source are discussed.Comment: IOP macros used, eps figures n.
Accelerating Cosmologies from Exponential Potentials
An exponential potential of the form arising from
the hyperbolic or flux compactification of higher-dimensional theories is of
interest for getting short periods of accelerated cosmological expansions.
Using a similar potential but derived for the combined case of hyperbolic-flux
compactification, we study the four-dimensional flat (and open) FLRW
cosmologies and give analytic (and numerical) solutions with exponential
behavior of scale factors. We show that, for the M-theory motivated potentials,
the cosmic acceleration of the universe can be eternal if the spatial curvature
of the 4d spacetime is negative, while the acceleration is only transient for a
spatially flat universe. We also comment on the size of the internal space and
its associated geometric bounds on massive Kaluza-Klein excitations.Comment: 17 pages, 6 figures; minor typos fixe
Spontaneous decompactification
Positive vacuum energy together with extra dimensions of space imply that our
four-dimensional Universe is unstable, generically to decompactification of the
extra dimensions. Either quantum tunneling or thermal fluctuations carry one
past a barrier into the decompactifying regime. We give an overview of this
process, and examine the subsequent expansion into the higher- dimensional
geometry. This is governed by certain fixed-point solutions of the evolution
equations, which are studied for both positive and negative spatial curvature.
In the case where there is a higher-dimensional cosmological constant, we also
outline a possible mechanism for compactification to a four-dimensional de
Sitter cosmology.Comment: 27 pages, 5 figures, harvmac. v2: refs added, minor notation change
Anisotropic Inflation and the Origin of Four Large Dimensions
In the context of (4+d)-dimensional general relativity, we propose an
inflationary scenario wherein 3 spatial dimensions grow large, while d extra
dimensions remain small. Our model requires that a self-interacting d-form
acquire a vacuum expectation value along the extra dimensions. This causes 3
spatial dimensions to inflate, whilst keeping the size of the extra dimensions
nearly constant. We do not require an additional stabilization mechanism for
the radion, as stable solutions exist for flat, and for negatively curved
compact extra dimensions. From a four-dimensional perspective, the radion does
not couple to the inflaton; and, the small amplitude of the CMB temperature
anisotropies arises from an exponential suppression of fluctuations, due to the
higher-dimensional origin of the inflaton. The mechanism triggering the end of
inflation is responsible, both, for heating the universe, and for avoiding
violations of the equivalence principle due to coupling between the radion and
matter.Comment: 24 pages, 2 figures; uses RevTeX4. v2: Minor changes and added
references. v3: Improved discussion of slow-rol
Phase Space Analysis of Quintessence Cosmologies with a Double Exponential Potential
We use phase space methods to investigate closed, flat, and open
Friedmann-Robertson-Walker cosmologies with a scalar potential given by the sum
of two exponential terms. The form of the potential is motivated by the
dimensional reduction of M-theory with non-trivial four-form flux on a
maximally symmetric internal space. To describe the asymptotic features of
run-away solutions we introduce the concept of a `quasi fixed point.' We give
the complete classification of solutions according to their late-time behavior
(accelerating, decelerating, crunch) and the number of periods of accelerated
expansion.Comment: 46 pages, 5 figures; v2: minor changes, references added; v3: title
changed, refined classification of solutions, 3 references added, version
which appeared in JCA
General Brane Geometries from Scalar Potentials: Gauged Supergravities and Accelerating Universes
We find broad classes of solutions to the field equations for d-dimensional
gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field
with non-vanishing potential. Our construction generates these configurations
from the solution of a single nonlinear ordinary differential equation, whose
form depends on the scalar potential. For an exponential potential we find
solutions corresponding to brane geometries, generalizing the black p-branes
and S-branes known for the case of vanishing potential. These geometries are
singular at the origin with up to two (regular) horizons. Their asymptotic
behaviour depends on the parameters of the model. When the singularity has
negative tension or the cosmological constant is positive we find
time-dependent configurations describing accelerating universes. Special cases
give explicit brane geometries for (compact and non-compact) gauged
supergravities in various dimensions, as well as for massive 10D supergravity,
and we discuss their interrelation. Some examples lift to give new solutions to
10D supergravity. Limiting cases with a domain wall structure preserve part of
the supersymmetries of the vacuum. We also consider more general potentials,
including sums of exponentials. Exact solutions are found for these with up to
three horizons, having potentially interesting cosmological interpretation. We
give several additional examples which illustrate the power of our techniques.Comment: 54 pages, 6 figures. Uses JHEP3. Published versio
Star Models with Dark Energy
We have constructed star models consisting of four parts: (i) a homogeneous
inner core with anisotropic pressure (ii) an infinitesimal thin shell
separating the core and the envelope; (iii) an envelope of inhomogeneous
density and isotropic pressure; (iv) an infinitesimal thin shell matching the
envelope boundary and the exterior Schwarzschild spacetime. We have analyzed
all the energy conditions for the core, envelope and the two thin shells. We
have found that, in order to have static solutions, at least one of the regions
must be constituted by dark energy. The results show that there is no physical
reason to have a superior limit for the mass of these objects but for the ratio
of mass and radius.Comment: 20 pages, 1 figure, references and some comments added, typos
corrected, in press GR