6 research outputs found
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
Dynamics with Infinitely Many Derivatives: The Initial Value Problem
Differential equations of infinite order are an increasingly important class
of equations in theoretical physics. Such equations are ubiquitous in string
field theory and have recently attracted considerable interest also from
cosmologists. Though these equations have been studied in the classical
mathematical literature, it appears that the physics community is largely
unaware of the relevant formalism. Of particular importance is the fate of the
initial value problem. Under what circumstances do infinite order differential
equations possess a well-defined initial value problem and how many initial
data are required? In this paper we study the initial value problem for
infinite order differential equations in the mathematical framework of the
formal operator calculus, with analytic initial data. This formalism allows us
to handle simultaneously a wide array of different nonlocal equations within a
single framework and also admits a transparent physical interpretation. We show
that differential equations of infinite order do not generically admit
infinitely many initial data. Rather, each pole of the propagator contributes
two initial data to the final solution. Though it is possible to find
differential equations of infinite order which admit well-defined initial value
problem with only two initial data, neither the dynamical equations of p-adic
string theory nor string field theory seem to belong to this class. However,
both theories can be rendered ghost-free by suitable definition of the action
of the formal pseudo-differential operator. This prescription restricts the
theory to frequencies within some contour in the complex plane and hence may be
thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators
and the implications of restricting the contour of integration. Typos
correcte
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
Bouncing and Accelerating Solutions in Nonlocal Stringy Models
A general class of cosmological models driven by a non-local scalar field
inspired by string field theories is studied. In particular cases the scalar
field is a string dilaton or a string tachyon. A distinguished feature of these
models is a crossing of the phantom divide. We reveal the nature of this
phenomena showing that it is caused by an equivalence of the initial non-local
model to a model with an infinite number of local fields some of which are
ghosts. Deformations of the model that admit exact solutions are constructed.
These deformations contain locking potentials that stabilize solutions.
Bouncing and accelerating solutions are presented.Comment: Minor corrections, references added, published in JHE
Pure Gauge Configurations and Tachyon Solutions to String Field Theories Equations of Motion
In constructions of analytical solutions to open string field theories pure
gauge configurations parameterized by wedge states play an essential role.
These pure gauge configurations are constructed as perturbation expansions and
to guaranty that these configurations are asymptotical solutions to equations
of motions one needs to study convergence of the perturbation expansions. We
demonstrate that for the large parameter of the perturbation expansion these
pure gauge truncated configurations give divergent contributions to the
equation of motion on the subspace of the wedge states. We perform this
demonstration numerically for the pure gauge configurations related to tachyon
solutions for the bosonic and the NS fermionic SFT. By the numerical
calculations we also show that the perturbation expansions are cured by adding
extra terms. These terms are nothing but the terms necessary to make valued the
Sen conjectures.Comment: 30 pages, 9 figures, references added and conclusion extende