Научно-исследовательский институт ядерной физики имени Д.В. Скобельцына
Московского государственного университета имени М.В. Ломоносова

Current cosmological observational data strongly support that the present
Universe exhibits an accelerated expansion providing thereby an evidence
for a dominating dark energy component with the state parameter $w$ is
close to $-1$. So, the present cosmological observations do not exclude a
possibility that the dark energy with $w<-1$ exists.

Inequality $w<-1$ means the violation of the Null Energy Condition (NEC).
Generally speaking models that violate the NEC have ghosts, and
therefore, are unstable and physically unacceptable. However, the
possibility of existence of the dark energy with $w<-1$
as well as the cosmological singularity problem encourage the
investigation of models, which violate the NEC.

It is almost clear that such a possibility can be realized within an
effective theory, while the fundamental theory should be stable and
admit quantization. From this point of view the NEC violation might be a
property of a model that approximates the fundamental theory and describes
some particular features of this theory.

Recently a new class of cosmological models, which is based on the string
field theory and the $p$-adic string theory and obeyed the NEC violation,
has been proposed. Models with a single nonlocal scalar field, originating
from the string field theory description of the rolling tachyon dynamics,
are distinguished by presence of specific nonlocal operators, which
include $\\exp(\\Box)$.