Intersecting membrane and an anisotropic models of dark energy

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Intersecting membraneandan anisotropic models
of dark energy

• Dmitry G. Orlov (NCU, Taiwan VNIIMS, Russia)

1st June, 2008 NDHU, Taiwan
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• Introduction
• - effective cosmological constant
• - world on brane
• - space like brane
• S - brane intersection
• Anisotropic cosmology
• Conclusions

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Effective cosmological constant
Equation of state
- accelerated expansion of universe
In particularly, this condition must be peformed
for an inflation stage. The matter (energy) which
satisfied this equation is named a dark matter.
Its easy check, that an equation of state for a
cosmological constant is , what provide an
inflationary stage, but until now its still
unclear what is physical meaning of such
quantity and a mechanism which turn it on and
off.
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From another hand, its possible to consider
evolution of field, which on some particular
stage of evolution generate an effective
cosmological constant. The simplest sample for
such field is a scalar field. If for some
interval of time we obtain that a potential
energy of field is positive and greater than
kinetic, that produce a negative pressure and an
accelerated stage in an evolution of
system. The contribution of scalar field
in action for this interval of time may be
consider like effective cosmological constant.
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World on brane
Exterior dimension - a long range
(Randall-Sundrum models) - a compactified
(periodical)
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Space like brane
Chen, Gal'tsov, Gutperle, Phys.Rev. D66 (2002)
024043 Kruczenski, Myers, Peet, JHEP 0205, 039
(2002)
From string theory D-brane is known like
hypersurface which is described by an end of
open string satisfied of Dirichlet boundary
condition. Such object is supported by form field
with RR-charge. If we consider Dirichlet
condition for time-like direction we obtain
space-like hyperbrane or simple s-brane. Exist
also another description of such object like
unstable tachyon condensate, which exist only one
moment and then decay. From begining intesions
of people about s-brane was to construct dS/CFT
correspondence, but when it was found only
avaible for theory II, s-brane was gotten
another application in construction of
cosmological model.
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S-brane intersection
We consider system consists of gravity and
form field coupled with dilaton (scalar field)
We choose follow ansatz for metric
for k-1,0,1 - for cases of hyperbolic, flat and
spherical exterior space. The equations of
motion for this model are invariant under the
discrete S-duality which transform electrical
charged soluion to magnetic one and v.v., so we
restrict our further investigation only to purely
magnetic case.
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The solution is
In previous papers it was consider s-brane
solution for and without a flat
part of exterior space. For every type solution
was obtained an inflationary stage, but without
large enough e-folding (lt70), so we interesting
of result anisotropization and effect of
cylindrical exterior space.
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Anisotropic cosmology
The metric of s-brane for p2 can be represented
in the follow form
now we compatify an axterior dimensions on
q-torus and with
obtain the reducted action in Einstein frame
with a potential of scalar fields and four
dimensions metric
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The completely anisotropic model is decribed by
metric
where and Scale factors and shears Hubble
constant for every direction
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Further investigation of obtained model was done
by numerical method. We has few which solution
is dependent from, vary this parameters we try
to extend maximum amount e-folding. First we
consider the question of flat component of
compactified exterior space, if we have such
part, its only decreasing e-folding, so we
need set qk, exclude flat part. Second
question was a changing in behaviour of system
after introducing anisotropy. For the cases of
flat and spheric exterior space we have change
the property of universe from a tube to a
pancake (or vice versa depending from a sign of
initial parameters) during evolution through
inflation stage. Another property we obtain for
hyperbolic space, in this case initial
anisotropy almost neglect and finally disappear
on a time infinity.
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thick curve - a condition for an expansion, thin
curve - a condition for an acceleration
phase (left picture - anisotropic case, right -
tuned anisotropic)
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Consideration an anisotropic improve e-folding
of solution, but it still not enough for
standart model (60-70 e-folding), so we guess
that resources of this model was over and if we
like better e-folding we have to consider hybryd
models.
Dependence w of equation of state during
inflation stage for hyperbolic exterior space
(isotropic and tuned anisotropic cases).
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Conclusions
1. Considering anisotropic space like brane allow
constract anisotropic cosmological solution
with inflation stage. 2. Flat part of exterior
space only make worse inflation stage and must
be exluded. 3. In the cases of a pure flat and
spherical exterior space the solution has
diverge (or tends to zero) of metric functions on
time infinity, so they dont make agree with
modern theories. 4. The most interesting result
was obtained for case of hyperbolic space. We
have greatest value of e-folding and also an
initial anisotrophy tend to zero after
inflation stage. 5. Although amount of e-folding
in anisotropic model was increase, its still
not enough.