Non-local SFT Tachyon and Cosmology

Cosmological scenarios built upon the generalized non-local String Field Theory and $p$-adic tachyons are examined. A general kinetic operator involving an infinite number of derivatives is studied as well as arbitrary parameter $p$. 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 $w>-1$ 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

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

Time Lumps in Nonlocal Stringy Models and Cosmological Applications

We study lump solutions in nonlocal toy models and their cosmological applications. These models are motivated by a description of D-brane decay within string field theory framework. In order to find cosmological solutions we use the simplest local approximation keeping only second derivative terms in nonlocal dynamics. We study a validity of this approximation in flat background where time lump solutions can be written explicitly. We work out the validity of this approximation. We show that our models at large time exhibit the phantom behaviour similar to the case of the string kink.Comment: Latex, 24 pages, 13 figures, Typos corrected, 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

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

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

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

Open Superstring Star as a Continuous Moyal Product

By diagonalizing the three-string vertex and using a special coordinate representation the matter part of the open superstring star is identified with the continuous Moyal product of functions of anti-commuting variables. We show that in this representation the identity and sliver have simple expressions. The relation with the half-string fermionic variables in continuous basis is given.Comment: Latex, 19 pages; more comments added and notations are simplifie

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

A solution to the 4-tachyon off-shell amplitude in cubic string field theory

We derive an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude in cubic string field theory (CSFT). From such a solution we compute the exact coefficient of the quartic effective action relevant for time dependent solutions and we derive the exact coefficient of the quartic tachyon coupling. The rolling tachyon solution expressed as a series of exponentials $e^t$ is studied both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level truncated coefficients are shown to converge to those derived using the exact string amplitude. The agreement with previous work on the subject, both on the quartic tachyon coupling and on the CSFT rolling tachyon, is an excellent test for the accuracy of our off-shell solution.Comment: 26 pages, 5 figure