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 models with the cosmological constants have no contradictions with observation data. At same time the recent analysis of the observation data indicates that the DE with the state parameter w, varying in time and crossing the cosmological constant barrier, gives a better fit than a cosmological constant.
Models with w< -1 violate the null energy condition, have ghosts, and therefore, generally speaking,
are unstable and 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.
A specific model of scalar tachyon field which is derived from the NSR string field theory has been proposed and its cosmological applications has been studied. In the effective field theory approximation the state parameter w< -1 .
We have shown that the late time rolling of the cubic Superstring Field Theory nonlocal tachyon in the FRW Universe leads to a cosmic acceleration with a periodic crossing of the w = -1 barrier. An asymptotic solution for the tachyon and Hubble parameter by linearizing the nonlocal equations of motion is constructed explicitly. For a small Hubble parameter the period of oscillations is a number entirely defined by the parameters of the SFT action.
An influence of the dynamics of the open string tachyon condensation, a non-minimal coupling with closed string massless modes, the graviton and the dilaton has been considered. Coupling of the open string tachyon and the dilaton is motivated by the open String Field Theory in a linear dilaton background and the flat space-time. The influence of the dilaton on the tachyon condensation is essential and provides a significant effect: oscillations of the Hubble parameter and the state parameter become of a cosmological scale. We give an estimation for the period of these oscillations (0.1-1) Gyr and note a good agreement of this period with the observed oscillations with a period (0.15-0.65) Gyr in a distribution of quasar spectra.
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.
Cosmological perturbations in cosmological models with a nonlocal scalar field with quadratic potential have been studied.
We construct equation for the energy density perturbations of the nonlocal scalar field and prove that it is identical to a closed system of local cosmological perturbation equations in a particular model with multiple local free scalar fields.
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.
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. We have found two-parameter set of exact solutions and analysed the crossing of the cosmological constant barrier and
behavior of the state parameter at large time.
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.
We have also studied lump solutions in nonlocal toy models and their cosmological applications.
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 and A.S. Koshelev, Cosmological Signature of Tachyon Condensation, JHEP 0809 (2008) 068; arXiv:0804.3570
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
A.S. Koshelev, Non-local SFT Tachyon and Cosmology,
JHEP 0704 (2007) 029; arXiv:hep-th/0701103
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 and I.V. Volovich, On the null energy condition
and cosmology, Theor. Math. Phys. 155 (2008) 503-511; arXiv:hep-th/0612098
I.Ya. Aref'eva and A.S. Koshelev, Cosmic Acceleration and Crossing of w= -1 barrier
from Cubic Superstring Field Theory, JHEP 0702
(2007) 041; arXiv:hep-th/0605085
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;
I.Ya. Aref'eva and L.V. Joukovskaya,
Time Lumps in Nonlocal Stringy Models and Cosmological
Applications, JHEP 0510 (2005) 087; arXiv:hep-th/0504200
A.S. Koshelev, and S.Yu. Vernov, Exactly Solvable SFT Inspired
Phantom Model, Theor. Math. Phys. 148 (2006) 895-909;
I.Ya. Aref'eva, Nonlocal String Tachyon as
a Model for Cosmological Dark Energy, AIP Conf. Proc. 826,
p-Adic Mathematical Physics, AIP, Melville, NY, 2006, pp. 301-311;