A note on the initial conditions within the effective field theory
  approach of cosmic acceleration
  By using the effective field theory approach, we investigate the role of
initial condition for the dark energy or modified gravity models. In details,
we consider the constant and linear parametrization of the effective Newton
constant models. Firstly, under the adiabatic assumption, the correction from
the extra scalar degree of freedom in the beyond $\Lambda$CDM model is found to
be negligible. The dominant ingredient in this setup is the primordial
curvature perturbation originated from inflation mechanism, and the energy
budget of the matter components is not very crucial. Secondly, the
iso-curvature perturbation sourced by the extra scalar field is studied. For
the constant and linear model of the effective Newton constant, there is no
such kind of scalar mode exist. For the quadratic model, there is a non-trivial
one. However, the amplitude of the scalar field is damped away very fast on all
scales. Consequently, it could not support a reasonable structure formation.
Finally, we study the importance of the setup of the scalar field starting
time. By setting different turn-on time, namely $a=10^{-2} $ and $a=10^{-7} $,
we compare the cosmic microwave background radiation temperature, lensing
deflection angle auto-correlation function as well as the matter power spectrum
in the constant and linear model. We find there is an order of
$\mathcal{O}(1\%)$ difference in the observable spectra for constant model,
while for the linear model, it is smaller than $\mathcal{O}(0.1\%)$.
