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Cosmic evolution in DHOST theories with scaling solutions
We study cosmic evolution based on the fixed points in the dynamical analysis
of the Degenerate Higher-Order Scalar-Tensor (DHOST) theories. We consider the
DHOST theories in which the propagation speed of gravitational waves is equal
to the speed of light, the tensor perturbations do not decay to dark energy
perturbations, and the scaling solutions exist. The scaling fixed point
associated with late time acceleration of universe can be either stable or
saddle depending on the parameters of the theory. For some ranges of the
parameters, the accelerated scaling point and the field dominated point can be
simultaneously stable. Cosmic evolution will reach the accelerated scaling
point if the time derivative of the scalar field in the theory is positive
during the matter domination. If the time derivative of the scalar field is
negative during the matter domination, the background universe will evolve
towards the field dominated point. The density parameter of the matter can be
larger than unity before reaching the scaling fixed point if the deviation from
the Einstein theory of gravity is too large and the initial conditions for the
dynamical variables during the matter domination are significantly different
from the accelerated scaling point. The stabilities of MDE fixed point
are similar to the coupled dark energy models. In our consideration, the
universe can only evolve from the MDE to the field dominated point.Comment: 19 pages, 3 figures, 1 tabl