Separating the Universe into real and fake energy densities

摘要: The separate universe technique provides a means of establishing consistency relations between short wavelength observables and the long matter density fluctuations within which they evolve by absorbing latter into cosmological background. We extend it to cases where non-gravitational forces introduce Jeans scale in other species like dynamical dark energy or massive neutrinos. matches synchronous gauge local expansion using acceleration equation accounts for temporal nonlocality dependence response small observables, e.g. nonlinear power spectrum, halo abundance implied bias, $N$-point correlation functions. Above scale, Friedmann relates real densities curvature that is constant comoving coordinates. Below evolves acts fake component. In all cases, evolution on scales correctly modeled as we illustrate scalar field with adiabatic isocurvature initial conditions across set its finite sound speed.