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We study the cosmological signatures of having extra energy density, $ρ_{ex}$, beyond the $Λ$CDM model that dilutes rapidly, faster than radiation, at a scale factor $a_c$ with a corresponding mode $k_c=a_c H(a_c)$ crossing the horizon at that time. These types of models are motivated by phase transitions of the underlying elementary particles, for example the creation of protons and neutrons from almost massless quarks or the recently proposed Bound Dark Energy model. The rapidly dilution of $ρ_{ex}$ leaves distinctive imprints in the Universe not only in the expansion history with a clear impact on the acoustic scale, $r_s(a_cc)$, and angular distances, $D_A(a)$, but also in the matter and CMB power spectra. The rapidly diluted energy density $ρ_{ex}$, (RDED) generates characteristic signatures that can be observed with current and future precision cosmological data. In particular, we find a bump in the matter power spectrum compared to the standard $Λ$CDM. We identify the amplitude, width, and time scale of the bump to the physical properties of the transition. We study these effects with linear theory, standard perturbation theory, and the correlated impact on cosmological distances, allowing for independent measurements of these extensions of the standard $Λ$CDM model.