98 research outputs found
Quantization of the Riemann Zeta-Function and Cosmology
Quantization of the Riemann zeta-function is proposed. We treat the Riemann
zeta-function as a symbol of a pseudodifferential operator and study the
corresponding classical and quantum field theories. This approach is motivated
by the theory of p-adic strings and by recent works on stringy cosmological
models. We show that the Lagrangian for the zeta-function field is equivalent
to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of
the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and
the Langlands program is indicated. The Beilinson conjectures on the values of
L-functions of motives are interpreted as dealing with the cosmological
constant problem. Possible cosmological applications of the zeta-function field
theory are discussed.Comment: 14 pages, corrected typos, references and comments adde
Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric
A general class of cosmological models driven by a nonlocal scalar field
inspired by the string field theory is studied. Using the fact that the
considering linear nonlocal model is equivalent to an infinite number of local
models we have found an exact special solution of the nonlocal Friedmann
equations. This solution describes a monotonically increasing Universe with the
phantom dark energy.Comment: 18 pages, 3 figures, a few misprints in Section 5 have been correcte
Non-local SFT Tachyon and Cosmology
Cosmological scenarios built upon the generalized non-local String Field
Theory and -adic tachyons are examined. A general kinetic operator involving
an infinite number of derivatives is studied as well as arbitrary parameter
. The late time dynamics of just the tachyon around the non-perturbative
vacuum is shown to leave the cosmology trivial. A late time behavior of the
tachyon and the scale factor of the FRW metric in the presence of the
cosmological constant or a perfect fluid with is constructed explicitly
and a possibility of non-vanishing oscillations of the total effective state
parameter around the phantom divide is proven.Comment: 17 pages, LaTeX; v2: JHEP3 class is used, references adde
Cosmological tachyon from cubic string field theory
The classical dynamics of the tachyon scalar field of cubic string field
theory is considered on a cosmological background. Starting from a nonlocal
action with arbitrary tachyon potential, which encodes the bosonic and several
supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi
formalism and with a generalized Friedmann equation, appliable in braneworld or
modified gravity models. The cases of cubic (bosonic) and quartic
(supersymmetric) tachyon potential in general relativity are automatically
included. We comment the validity of the slow-roll approximation, the stability
of the cosmological perturbations, and the relation between this tachyon and
the Dirac-Born-Infeld one.Comment: 20 pages JHEP style, 1 figure; v4: misprints corrected, matches the
published versio
Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation
We derive equations of motion for the tachyon field living on an unstable
non-BPS D-brane in the level truncated open cubic superstring field theory in
the first non-trivial approximation. We construct a special time dependent
solution to this equation which describes the rolling tachyon. It starts from
the perturbative vacuum and approaches one of stable vacua in infinite time. We
investigate conserved energy functional and show that its different parts
dominate in different stages of the evolution. We show that the pressure for
this solution has its minimum at zero time and goes to minus energy at infinite
time.Comment: 16 pages, 5 figures; minor correction
Non-extremal Localised Branes and Vacuum Solutions in M-Theory
Non-extremal overlapping p-brane supergravity solutions localised in their
relative transverse coordinates are constructed. The construction uses an
algebraic method of solving the bosonic equations of motion. It is shown that
these non-extremal solutions can be obtained from the extremal solutions by
means of the superposition of two deformation functions defined by vacuum
solutions of M-theory. Vacuum solutions of M-theory including irrational powers
of harmonic functions are discussed.Comment: LaTeX, 16 pages, no figures, typos correcte
Time Machine at the LHC
Recently, black hole and brane production at CERN's Large Hadron Collider
(LHC) has been widely discussed. We suggest that there is a possibility to test
causality at the LHC. We argue that if the scale of quantum gravity is of the
order of few TeVs, proton-proton collisions at the LHC could lead to the
formation of time machines (spacetime regions with closed timelike curves)
which violate causality. One model for the time machine is a traversable
wormhole. We argue that the traversable wormhole production cross section at
the LHC is of the same order as the cross section for the black hole
production. Traversable wormholes assume violation of the null energy condition
(NEC) and an exotic matter similar to the dark energy is required. Decay of the
wormholes/time machines and signatures of time machine events at the LHC are
discussed.Comment: 12 pages, LATEX, comments and references adde
Dynamics with Infinitely Many Time Derivatives in Friedmann-Robertson-Walker Background and Rolling Tachyon
Open string field theory in the level truncation approximation is considered.
It is shown that the energy conservation law determines existence of rolling
tachyon solution. The coupling of the open string field theory action to a
Friedmann-Robertson-Walker metric is considered which leads to a new time
dependent rolling tachyon solution is presented and possible cosmological
consequences are discussed.Comment: 18 pages, 8 figure
Sigma-model for Generalized Composite p-branes
A multidimensional gravitational model containing several dilatonic scalar
fields and antisymmetric forms is considered. The manifold is chosen in the
form M = M_0 x M_1 x ... x M_n, where M_i are Einstein spaces (i > 0). The
block-diagonal metric is chosen and all fields and scale factors of the metric
are functions on M_0. For the forms composite (electro-magnetic) p-brane ansatz
is adopted. The model is reduced to gravitating self-interacting sigma-model
with certain constraints. In pure electric and magnetic cases the number of
these constraints is m(m - 1)/2 where m is number of 1-dimensional manifolds
among M_i. In the "electro-magnetic" case for dim M_0 = 1, 3 additional m
constraints appear. A family of "Majumdar-Papapetrou type" solutions governed
by a set of harmonic functions is obtained, when all factor-spaces M_k are
Ricci-flat. These solutions are generalized to the case of non-Ricci-flat M_0
when also some additional "internal" Einstein spaces of non-zero curvature are
added to M. As an example exact solutions for D = 11 supergravity and related
12-dimensional theory are presented.Comment: 33 pages, Latex. Some corrections and rearrangements are mad
Analysis of scalar perturbations in cosmological models with a non-local scalar field
We develop the cosmological perturbations formalism in models with a single
non-local scalar field originating from the string field theory description of
the rolling tachyon dynamics. We construct the equation for the energy density
perturbations of the non-local scalar field in the presence of the arbitrary
potential and formulate the local system of equations for perturbations in the
linearized model when both simple and double roots of the characteristic
equation are present. We carry out the general analysis related to the
curvature and entropy perturbations and consider the most specific example of
perturbations when important quantities in the model become complex.Comment: LaTeX, 25 pages, 1 figure, v2: Subsection 3.2 and Section 5 added,
references added, accepted for publication in Class. Quant. Grav. arXiv admin
note: text overlap with arXiv:0903.517
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