# A note on the initial conditions within the effective field theory approach of cosmic acceleration

## TL;DR

This paper examines how initial conditions affect cosmic acceleration models within the effective field theory framework, finding negligible effects from extra scalar fields and small observable differences based on initial setup timing.

## Contribution

It provides a detailed analysis of initial condition impacts in effective field theory models of dark energy, especially regarding scalar perturbations and observable spectra.

## Key findings

- Negligible correction from extra scalar degree of freedom under adiabatic assumption
- No scalar mode in constant and linear models; damped in quadratic models
- Order 1% difference in observable spectra based on initial scalar field setup

## Abstract

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 $\mathcal{O}(0.1\%)$.