3,701 research outputs found
Affine generalizations of gravity in the light of modern cosmology
We discuss new models of an `affine' theory of gravity in multidimensional
space-times with symmetric connections. We use and develop ideas of Weyl,
Eddington, and Einstein, in particular, Einstein's proposal to specify the
space - time geometry by use of the Hamilton principle. More specifically, the
connection coefficients are determined using a `geometric' Lagrangian that is
an arbitrary function of the generalized (non-symmetric) Ricci curvature tensor
(and, possibly, of other fundamental tensors) expressed in terms of the
connection coefficients regarded as independent variables. Such a theory
supplements the standard Einstein gravity with dark energy (the cosmological
constant, in the first approximation), a neutral massive (or tachyonic) vector
field (vecton), and massive (or tachyonic) scalar fields. These fields couple
only to gravity and can generate dark matter and/or inflation. The new field
masses (real or imaginary) have a geometric origin and must appear in any
concrete model. The concrete choice of the geometric Lagrangian determines
further details of the theory, for example, the nature of the vector and scalar
fields that can describe massive particles, tachyons, or even `phantoms'. In
`natural' geometric theories, which are discussed here, dark energy must also
arise. We mainly focus on intricate relations between geometry and dynamics
while only very briefly considering approximate cosmological models inspired by
the geometric approach.Comment: 12 pages; several typos, eq.(37), and references [24] and [26]
correcte
Constructing and solving cosmologies of early universes with dark energy and matter. I
The main purpose of this paper is to advance a unified theory of dark matter,
dark energy, and inflation first formulated in 2008. Our minimal affine
extension of the GR has geodesics coinciding with the pseudo Riemannian ones,
up to parameterizations. It predicts a `sterile' massive vecton and depends on
two new dimensional constants, which can be measured in the limit of small
vecton velocity. In a special gauge, this velocity has an upper limit near
which it grows to infinity. The linearized vecton theory is similar to the
scalar models of inflation except the fact of internal anisotropy of the
vecton. For this reason we study general solutions of scalar analogs of the
vecton theory without restricting the curvature parameter and anisotropy by
using previously derived exact solutions as functions of the metric. It is
shown that the effects of curvature and anisotropy fast decrease in expanding
universes. Our approach can be applied to anisotropic universes, which is
demonstrated on an exactly solvable strongly anisotropic cosmology. To
characterize different cosmological scenarios in detail we introduce three
characteristic functions, two of which are small and almost equal during
inflation and grow near the exit. Instead of the potential it is possible to
use one of the two characteristic functions. This allows to approximately
derive flat isotropic universes with `prescribed' scenarios, which is the
essence of our constructive cosmology of early universes. The most natural
application of our approach is in analytically constructing characteristic
functions of inflationary models with natural exits. However, the general
construction can be applied to other problems, e.g., to evolution of
contracting universes.Comment: 25 pages, mostly `cosmetic' corrections on pages 1-5, 7, 16-17, 21-2
Integrals of equations for cosmological and static reductions in generalized theories of gravity
We consider the dilaton gravity models derived by reductions of generalized
theories of gravity and study one-dimensional dynamical systems simultaneously
describing cosmological and static states in any gauge. Our approach is fully
applicable to studying static and cosmological solutions in multidimensional
theories and also in general one-dimensional dilaton - scalaron gravity models.
We here focus on general and global properties of the models, on seeking
integrals, and on analyzing the structure of the solution space. We propose
some new ideas in this direction and derive new classes of integrals and new
integrable models.Comment: 15 pages. arXiv admin note: substantial text overlap with
arXiv:1302.637
Unified description of cosmological and static solutions in affine generalized theories of gravity: vecton - scalaron duality and its applications
We briefly describe the simplest class of affine theories of gravity in
multidimensional space-times with symmetric connections and their reductions to
two-dimensional dilaton - vecton gravity field theories (DVG). The distinctive
feature of these theories is the presence of an absolutely neutral massive (or
tachyonic) vector field (vecton) with essentially nonlinear coupling to the
dilaton gravity (DG). We show that in DVG the vecton field can be consistently
replaced by an effectively massive scalar field (scalaron) with an unusual
coupling to dilaton gravity. With this vecton - scalaron duality, one can use
methods and results of the standard DG coupled to usual scalars (DGS) in more
complex dilaton - scalaron gravity theories (DSG) equivalent to DVG. We present
the DVG models derived by reductions of multidimensional affine theories and
obtain one-dimensional dynamical systems simultaneously describing cosmological
and static states in any gauge. Our approach is fully applicable to studying
static and cosmological solutions in multidimensional theories as well as in
general one-dimensional DGS models. We focus on global properties of the
models, look for integrals and analyze the structure of the solution spaces. In
integrable cases, it can be usefully visualized by drawing a `topological
portrait' resembling phase portraits of dynamical systems and simply exposing
global properties of static and cosmological solutions, including horizons,
singularities, etc. For analytic approximations we also propose an integral
equation well suited for iterations.Comment: 22 pages. arXiv admin note: substantial text overlap with
arXiv:1112.3023. The previous version is essentially edited. Many side
remarks removed and misprints correcte
On Einstein - Weyl unified model of dark energy and dark matter
Here we give a more detailed account of the part of the conference report
that was devoted to reinterpreting the Einstein `unified models of gravity and
electromagnetism' (1923) as the unified theory of dark energy (cosmological
constant) and dark matter (neutral massive vector particle having only
gravitational interactions). After summarizing Einstein's work and related
earlier work of Weyl and Eddington, we present an approach to finding
spherically symmetric solutions of the simplest variant of the Einstein models
that was earlier mentioned in Weyl's work as an example of his generalization
of general relativity. The spherically symmetric static solutions and
homogeneous cosmological models are considered in some detail. As the theory is
not integrable we study approximate solutions. In the static case, we show that
there may exist two horizons and derive solutions near the horizons. In
cosmology, we propose to study the corresponding expansions of possible
solutions near the origin and derive these expansions in a simplified model
neglecting anisotropy. The structure of the solutions seems to hint at a
possibility of an inflation mechanism that does not require adding scalar
fields.Comment: Report to conference `Selected problems of modern theoretical
physics' Dubna, Russia, June 23-27, 2008; 18 pages LaTex; sections 2.3.1 and
2.3.3, comments to Discussion added; Appendix II removed; 2 references
removed, several references added for section 2.3. In version 3, typos
corrected, the paragraph with equations (33), (34) somewhat extended and
clarifie
A fresh view of cosmological models describing very early Universe: general solution of the dynamical equations
The dynamics of any spherical cosmology with a scalar field (`scalaron')
coupling to gravity is described by the nonlinear second-order differential
equations for two metric functions and the scalaron depending on the `time'
parameter. The equations depend on the scalaron potential and on the arbitrary
gauge function that describes time parameterizations. This dynamical system can
be integrated for flat, isotropic models with very special potentials. But,
somewhat unexpectedly, replacing the `time' variable by one of the metric
functions allows us to completely integrate the general spherical theory in any
gauge and with apparently arbitrary potentials. The main restrictions on the
potential arise from positivity of the derived analytic expressions for the
solutions, which are essentially the squared canonical momenta. An interesting
consequence is emerging of classically forbidden regions for these analytic
solutions. It is also shown that in this rather general model the inflationary
solutions can be identified, explicitly derived, and compared to the standard
approximate expressions. This approach can be applied to intrinsically
anisotropic models with a massive vector field (`vecton') as well as to some
non-inflationary models.Comment: 10 pages; added 2 pages (Sec. 5); significantly edited: Sec.4 (p.7),
Abstract, Sec.1; corrected misprint
Integrable Models of Horizons and Cosmologies
A new class of integrable theories of 0+1 and 1+1 dimensional dilaton gravity
coupled to any number of scalar fields is introduced. These models are
reducible to systems of independent Liouville equations whose solutions must
satisfy the energy and momentum constraints. The constraints are solved thus
giving the explicit analytic solution of the theory in terms of arbitrary
chiral fields. In particular, these integrable theories describe spherically
symmetric black holes and branes of higher dimensional supergravity theories as
well as superstring motivated cosmological models.Comment: 15 page
On solving dynamical equations in general homogeneous isotropic cosmologies with scalaron
We study general dynamical equations describing homogeneous isotropic
cosmologies coupled to a scalaron . For flat cosmologies (), we
analyze in detail the gauge-independent equation describing the differential,
, of the map of the metric to
the scalaron field , which is the main mathematical characteristic
locally defining a `portrait' of a cosmology in `-version'. In the
`-version', a similar equation for the differential of the inverse map,
, can be solved asymptotically or for
some `integrable' scalaron potentials . In the flat case,
and satisfy the first-order differential
equations depending only on the logarithmic derivative of the potential. Once
we know a general analytic solution for one of these -functions, we can
explicitly derive all characteristics of the cosmological model. In the
-version, the whole dynamical system is integrable for and
with any `-potential', ,
replacing . There is no a priori relation between the two potentials
before deriving or , which implicitly depend on the
potential itself, but relations between the two pictures can be found by
asymptotic expansions or by inflationary perturbation theory. Explicit
applications of the results to a more rigorous treatment of the chaotic
inflation models and to their comparison with the ekpyrotic-bouncing ones are
outlined in the frame of our `-formulation' of isotropic scalaron
cosmologies. In particular, we establish an inflationary perturbation expansion
for . When all the conditions for inflation are satisfied and
obeys a certain boundary (initial) condition, we get the standard inflationary
parameters, with higher-order corrections.Comment: New version: 33 pages instead 32; revised and extended Abstract,
Sections 4.3, 5; edited Section 1, changed a few titles; corrected misprint
Integrable Low Dimensional Models for Black Holes and Cosmologies from High Dimensional Theories
We describe a class of integrable models of 1+1 and 1-dimensional dilaton
gravity coupled to scalar fields. The models can be derived from high
dimensional supergravity theories by dimensional reductions. The equations of
motion of these models reduce to systems of the Liouville equations endowed
with energy and momentum constraints. We construct the general solution of the
1+1 dimensional problem in terms of chiral moduli fields and establish its
simple reduction to static black holes (dimension 0+1), and cosmological models
(dimension 1+0). We also discuss some general problems of dimensional reduction
and relations between static and cosmological solutions.Comment: 27 page
A New Class of Integrable Models of 1+1 Dimensional Dilaton Gravity Coupled to Scalar Matter
Integrable models of 1+1 dimensional gravity coupled to scalar and vector
fields are briefly reviewed. A new class of integrable models with nonminimal
coupling to scalar fields is constructed and discussed.Comment: LaTeX, 8 pages, no figures. Talk given at the VIII International
Conference on Symmetry Methods in Physics (Dubna 1997), to be published at
Phys. of At. Nucl. 1998, vol. 61, #1
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