String Field Theory Inspired Cosmological Models
The cosmological acceleration suggests that the present day
Universe is dominated by a smoothly distributed slowly varying
cosmic fluid with negative pressure, the so-called dark energy (DE). The observable DE state parameter w is close to -1.
The well-known LambdaCDM model, where dark energy comes from the effective cosmological constant, fits quite well the observational data. Nevertheless, possibility that the recent analysis of the observation data indicates that the varying in time dark energy with the state parameter w varies in time and crosses the cosmological constant barrier w= -1 gives a better fit than a cosmological constant is widely discussed.
Models with w< -1 violate the null energy condition, have ghosts, and therefore,
are unstable and, generally speaking, physically unacceptable. However, the possibility of the existence of dark energy with w< -1
on the one hand and the cosmological singularity problem on the
other hand encourage the investigation of models with w< -1 .
Recently a wide class of nonlocal cosmological models based on the string field theory
and the p-adic string theory attracts a lot of attention and are actively developed. Due to the presence of
phantom excitations nonlocal models are of interest to describe the present observation data in cosmology.
In the dark energy model (I.Ya. Aref'eva, arXiv:astro-ph/0410443) it is implied that the Universe is a slowly decaying D3-brane, whose dynamics is described by an open string tachyon mode. According to the Sen conjugation, the tachyon motion from an unstable vacuum to the stable vacuum describes the D-brane transition to the true vacuum.
The interest in cosmological models related to open string field theory is inspired by the possibility of obtaining solutions describing transitions from a perturbed vacuum to the true vacuum (rolling solutions).
A standard property of nonlocal cosmological models is the null energy condition violation and arising of phantom
fields. The standard quantization of models with high order derivatives leads to instability. If the theory with $w< -1$ can be interpreted as an approximation in the framework of the fundamental theory, then instability can be considered an artefact of the approximation.
Maybe there exists such choice of effective theory parameters that the instability turns
out to be essential only at times that are not described in the framework of the effective theory approximation. It means that terms with high order derivatives can be treated as corrections essential
only at small energies below the physical cutoff. This approach allows to consider these effective theories physically acceptable with the presumption that an effective theory is an approximation of a fundamental theory.
With the lack of quantum gravity, we can just trust string theory or deal with an effective theory admitting the UV completion.
An exact solution to the Friedmann equations with a string inspired phantom scalar matter field has been constructed. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the string field theory framework. The notable features of the concerned model are a ghost sign of the kinetic term and a special polynomial form of the effective tachyon potential. The constructed solution is stable with respect to small fluctuations of the initial conditions in FRW and Bianchi I metrics, special deviations of the form of the potential, and with respect to small fluctuations of the initial value of the CDM energy density.
We have considered the Universe as a slowly decaying D3-brane. The D3-brane dynamics is approximately described by a nonlocal string tachyon interaction and a back reaction of gravity is incorporated in the closed string tachyon dynamics. In a local effective approximation this dark energy model contains one phantom component and one usual field with a simple polynomial interaction. To understand cosmological properties of this system we study toy models with the same scalar fields but with modified interactions. These modifications admit polynomial superpotentials. We have constructed such string inspired potential that some exact solutions correspond to the state parameter w > -1 at large time, whereas other ones correspond to w < -1 at large time. We have demonstrated that the superpotential method is very effective to seek new exact solutions.
A general class of cosmological models driven by a nonlocal scalar field inspired by string field theories has been 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 nonlocal model to a model with an infinite number of local fields some of which are ghosts. We have found exact special solutions of the nonlocal Friedmann equations, which describe a monotonically increasing Universe with the phantom dark energy. Exact solutions for the nonlocal Einstein equation in the Bianchi I
metric has been found as well
Nonlocal cosmological models with linear and quadratic potentials has been considered. We study the action with an arbitrary analytic function F of box operator. The way of localization of nonlocal Einstein equations, which
allows to find particular solutions for nonlocal Einstein equations has been proposed for an arbitrary analytic function F with simple and double roots. One and the same functions solve the initial nonlocal Einstein equations and the obtained local Einstein equations.
The stability of isotropic cosmological solutions in the Bianchi I model has been considered. We proved that the conditions sufficient for the Lyapunov stability in the Friedmann-Robertson-Walker metric provide the stability with respect to anisotropic perturbations in the Bianchi I metric and with respect to the cold dark matter energy density fluctuations. Sufficient conditions for the Lyapunov stability of the isotropic fixed points of the system of the Einstein equations are found. This result is applied to one field and two field cosmological models inspired by string field theory, which violate the null energy condition. We also analyse the stability of solutions in the k-essence model.
A method for the search of exact solutions for equation of a nonlocal scalar field in nonflat metric has been considered. In the Friedmann-Robertson-Walker metric the proposed method can be used in the case of an arbitrary potential, with the exception of linear and quadratic potentials, and allows to get in quadratures solutions, which depend on two arbitrary parameters. Exact solutions have been found for an arbitrary cubic potential, which consideration is motivated by the string field theory, as well as for exponential, logarithmic and power potentials.
S.Yu. Vernov, Exact Solutions for Nonlocal Nonlinear Field Equations in Cosmology arXiv:1005.5007
I.Ya. Aref'eva, N.V. Bulatov, and S.Yu. Vernov, Stable Exact Solutions in Cosmological Models with Two Scalar Fields, Theor. Math. Phys. 163 (2010) to be published;
S.Yu. Vernov, Localization of nonlocal cosmological models
with quadratic potentials in the case of double roots, Class. Quant.
Grav. 27 (2010) 035006; arXiv:0907.0468
I.Ya. Aref'eva, N.V. Bulatov, L.V. Joukovskaya, and S.Yu. Vernov,
Null Energy Condition Violation and Classical Stability in the Bianchi I Metric,
Phys. Rev. D 80 (2009) 083532; arXiv:0903.5264
A.S. Koshelev and S.Yu. Vernov, Cosmological perturbations in
SFT inspired nonlocal scalar field models, 2009, arXiv:0903.5176
I.Ya. Aref'eva, L.V. Joukovskaya, and S.Yu. Vernov,
Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric,
J. Phys. A: Math. Theor. 41 (2008) 304003;
I.Ya. Aref'eva, L.V. Joukovskaya, and S.Yu. Vernov,
Bouncing and accelerating solutions in nonlocal stringy models,
JHEP 0707 (2007) 087; arXiv:hep-th/0701184
Construction of Exact Solutions in Two-Fields Models and the
Crossing of the Cosmological Constant Barrier,
Theor. Math. Phys. 155 (2008) 544-556; arXiv:astro-ph/0612487
I.Ya. Aref'eva, A.S. Koshelev, and S.Yu. Vernov, Crossing the w= -1 barrier
in the D3-brane dark energy model, Phys. Rev. D 72 (2005)
A.S. Koshelev, and S.Yu. Vernov, Stringy Dark Energy Model with
Cold Dark Matter, Phys. Lett. B 628 (2005) 1-10;
A.S. Koshelev, and S.Yu. Vernov, Exactly Solvable SFT Inspired
Phantom Model, Theor. Math. Phys. 148 (2006) 895-909;