1,503 research outputs found
Exponential-Potential Scalar Field Universes I: The Bianchi I Models
We obtain a general exact solution of the Einstein field equations for the
anisotropic Bianchi type I universes filled with an exponential-potential
scalar field and study their dynamics. It is shown, in agreement with previous
studies, that for a wide range of initial conditions the late-time behaviour of
the models is that of a power-law inflating FRW universe. This property, does
not hold, in contrast, when some degree of inhomogeneity is introduced, as
discussed in our following paper II.Comment: 16 pages, Plain LaTeX, 1 Figure to be sent on request, to appear in
Phys. Rev.
Closed cosmologies with a perfect fluid and a scalar field
Closed, spatially homogeneous cosmological models with a perfect fluid and a
scalar field with exponential potential are investigated, using dynamical
systems methods. First, we consider the closed Friedmann-Robertson-Walker
models, discussing the global dynamics in detail. Next, we investigate
Kantowski-Sachs models, for which the future and past attractors are
determined. The global asymptotic behaviour of both the
Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either
expand from an initial singularity, reach a maximum expansion and thereafter
recollapse to a final singularity (for all values of the potential parameter
kappa), or else they expand forever towards a flat power-law inflationary
solution (when kappa^2<2). As an illustration of the intermediate dynamical
behaviour of the Kantowski-Sachs models, we examine the cases of no barotropic
fluid, and of a massless scalar field in detail. We also briefly discuss
Bianchi type IX models.Comment: 15 pages, 10 figure
Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound
In many cases a nonlinear scalar field with potential can lead to
accelerated expansion in cosmological models. This paper contains mathematical
results on this subject for homogeneous spacetimes. It is shown that, under the
assumption that has a strictly positive minimum, Wald's theorem on
spacetimes with positive cosmological constant can be generalized to a wide
class of potentials. In some cases detailed information on late-time
asymptotics is obtained. Results on the behaviour in the past time direction
are also presented.Comment: 16 page
Intermediate inflation and the slow-roll approximation
It is shown that spatially homogeneous solutions of the Einstein equations
coupled to a nonlinear scalar field and other matter exhibit accelerated
expansion at late times for a wide variety of potentials . These potentials
are strictly positive but tend to zero at infinity. They satisfy restrictions
on and related to the slow-roll approximation. These results
generalize Wald's theorem for spacetimes with positive cosmological constant to
those with accelerated expansion driven by potentials belonging to a large
class.Comment: 19 pages, results unchanged, additional backgroun
Can Gravitational Waves Prevent Inflation?
To investigate the cosmic no hair conjecture, we analyze numerically
1-dimensional plane symmetrical inhomogeneities due to gravitational waves in
vacuum spacetimes with a positive cosmological constant. Assuming periodic
gravitational pulse waves initially, we study the time evolution of those waves
and the nature of their collisions. As measures of inhomogeneity on each
hypersurface, we use the 3-dimensional Riemann invariant and the electric and magnetic parts of
the Weyl tensor. We find a temporal growth of the curvature in the waves'
collision region, but the overall expansion of the universe later overcomes
this effect. No singularity appears and the result is a ``no hair" de Sitter
spacetime. The waves we study have amplitudes between and widths between ,
where , the horizon scale of de Sitter spacetime. This
supports the cosmic no hair conjecture.Comment: LaTeX, 11 pages, 3 figures are available on request <To
[email protected] (Hisa-aki SHINKAI)>, WU-AP/29/9
The stability of cosmological scaling solutions
We study the stability of cosmological scaling solutions within the class of
spatially homogeneous cosmological models with a perfect fluid subject to the
equation of state p_gamma=(gamma-1) rho_gamma (where gamma is a constant
satisfying 0 < gamma < 2) and a scalar field with an exponential potential. The
scaling solutions, which are spatially flat isotropic models in which the
scalar field energy density tracks that of the perfect fluid, are of physical
interest. For example, in these models a significant fraction of the current
energy density of the Universe may be contained in the scalar field whose
dynamical effects mimic cold dark matter. It is known that the scaling
solutions are late-time attractors (i.e., stable) in the subclass of flat
isotropic models. We find that the scaling solutions are stable (to shear and
curvature perturbations) in generic anisotropic Bianchi models when gamma <
2/3. However, when gamma > 2/3, and particularly for realistic matter with
gamma >= 1, the scaling solutions are unstable; essentially they are unstable
to curvature perturbations, although they are stable to shear perturbations. We
briefly discuss the physical consequences of these results.Comment: AMSTeX, 7 pages, re-submitted to Phys Rev Let
Scaling Solutions in Robertson-Walker Spacetimes
We investigate the stability of cosmological scaling solutions describing a
barotropic fluid with and a non-interacting scalar field
with an exponential potential V(\phi)=V_0\e^{-\kappa\phi}. We study
homogeneous and isotropic spacetimes with non-zero spatial curvature and find
three possible asymptotic future attractors in an ever-expanding universe. One
is the zero-curvature power-law inflation solution where
(). Another is the
zero-curvature scaling solution, first identified by Wetterich, where the
energy density of the scalar field is proportional to that of matter with
(). We find that
this matter scaling solution is unstable to curvature perturbations for
. The third possible future asymptotic attractor is a solution with
negative spatial curvature where the scalar field energy density remains
proportional to the curvature with
(). We find that solutions with are
never late-time attractors.Comment: 8 pages, no figures, latex with revte
Energy Density of Non-Minimally Coupled Scalar Field Cosmologies
Scalar fields coupled to gravity via in arbitrary
Friedmann-Robertson-Walker backgrounds can be represented by an effective flat
space field theory. We derive an expression for the scalar energy density where
the effective scalar mass becomes an explicit function of and the scale
factor. The scalar quartic self-coupling gets shifted and can vanish for a
particular choice of . Gravitationally induced symmetry breaking and
de-stabilization are possible in this theory.Comment: 18 pages in standard Late
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