3,705 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
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
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
Paragrassmann Algebras with Many Variables
This is a brief review of our recent work attempted at a generalization of
the Grassmann algebra to the paragrassmann ones. The main aim is constructing
an algebraic basis for representing `fractional' symmetries appearing in
integrable models and also introduced earlier as a natural generalization of
supersymmetries. We have shown that these algebras are naturally related to
quantum groups with . By now we have a general
construction of the paragrassmann calculus with one variable and preliminary
results on deriving a natural generalization of the Neveu--Schwarz--Ramond
algebra. The main emphasis of this report is on a new general construction of
paragrassmann algebras with any number of variables, N. It is shown that for
the nilpotency indices the algebras are almost as simple as
the Grassmann algebra (for which ). A general algorithm for
deriving algebras with arbitrary p and N is also given. However, it is shown
that this algorithm does not exhaust all possible algebras, and the simplest
example of an `exceptional' algebra is presented for .Comment: 12 page
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
Two-Dimensional Dilaton Gravity and Toda - Liouville Integrable Models
General properties of a class of two-dimensional dilaton gravity (DG)
theories with multi-exponential potentials are studied and a subclass of these
theories, in which the equations of motion reduce to Toda and Liouville
equations, is treated in detail. A combination of parameters of the equations
should satisfy a certain constraint that is identified and solved for the
general multi-exponential model. From the constraint it follows that in DG
theories the integrable Toda equations, generally, cannot appear without
accompanying Liouville equations.
We also show how the wave-like solutions of the general Toda-Liouville
systems can be simply derived. In the dilaton gravity theory, these solutions
describe nonlinear waves coupled to gravity as well as static states and
cosmologies. A special attention is paid to making the analytic structure of
the solutions of the Toda equations as simple and transparent as possible, with
the aim to gain a better understanding of realistic theories reduced to
dimensions 1+1 and 1+0 or 0+1.Comment: 14 pages. To be published in Proceedings of `QUARKS-2008', Sergiev
Posad, 23-29 May, 200
Global Properties of Exact Solutions in Integrable Dilaton-Gravity Models
Global canonical transformations to free chiral fields are constructed for DG
models minimally coupled to scalar fields. The boundary terms for such
canonical transformations are shown to vanish in asymptotically static
coordinates if there is no scalar field.Comment: 5 pages, LaTeX, Conf. Report, Dubna, July 13-17, 199
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