Abstract
We reconsider the gravitational wave spectrum induced by scalar perturbations in spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes, focusing on the matter- and $\mathrm{\ensuremath{\Lambda}}$-dominated epochs. During matter domination, subhorizon modes are not free, and a commonly applied approximation for the derivative of the tensor perturbation is flawed. We show analytically that this leads to a significant overestimation of the energy density spectrum. In addition, we demonstrate that gauge-dependent nonoscillating tensor perturbations appear in the presence of a cosmological constant. Complementing the analytical calculations, we compute the according present-day spectrum numerically for a Planck-like $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology, finding that nonoscillating growing modes appear during the transition between matter and $\mathrm{\ensuremath{\Lambda}}$ domination in conformal Newtonian gauge.
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