Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant

We introduce a new method for establishing the future non-linear stability of perturbations of FLRW solutions to the Einstein–Euler equations with a positive cosmological constant and a linear equation of state of the form p = Kρ. The method is based on a conformal transformation of the Einstein–Euler equations that compactifies the time domain and can handle the equation of state parameter values 0 < K ≤ 1/3 in a uniform manner. It also determines the asymptotic behavior of the perturbed solutions in the far future.