Structure formation in the effective field theory of holographic dark energy

Abstract

Abstract We investigate the structure formation in the effective field theory (EFT) of the holographic dark energy. The equation of motion for the energy contrast δ m of the cold dark matter is the same as the one in the general relativity up to the leading order in the small scale limit, provided the equation of state is quintessence-like. Our EFT breaks down while the equation of state becomes phantom-like. By imposing additional constraints by hand at the Hamiltonian level the unstable scalar graviton can be eliminated solving the instability problem without changing the background evolution. In this case depending on the form of the constraint the effective gravitational constant can be modified and the dust component can obtain a non-vanishing sound speed.