In the present work, we analyze the evolution of the scalar and tensorial perturbations and the quantities relevant for the physical description of the Universe, as the density contrast of the scalar perturbations and the gravitational waves energy density during the Bose-Einstein condensation of dark matter. The behavior of these parameters during the Bose-Einstein phase transition of dark matter is analyzed in details. To study the cosmological dynamics and evolution of scalar and tensorial perturbations in a Universe with and without cosmological constant we use both analytical and numerical methods. The Bose-Einstein phase transition modifies the evolution of gravitational waves of cosmological origin, as well as the process of large-scale structure formation.

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We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state p = αρ + kρ 1+1/n . We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin. We also find the equivalent scalar field that could create such an equation of state and calculate the corresponding slow-roll parameters. We calculate the scalar perturbations, the scalar power spectrum, and the spectral index.

Spherical collapse of the Bose-Einstein condensate (BEC) dark matter model is studied in the ThomasFermi approximation. The evolution of the overdensity of the collapsed region and its expansion rate are calculated for two scenarios. We consider the case of a sharp phase transition (which happens when the critical temperature is reached) from the normal dark matter state to the condensate one and the case of a smooth first order phase transition where there is a continuous conversion of "normal" dark matter to the BEC phase. We present numerical results for the physics of the collapse for a wide range of the model's space parameter, i.e. the mass of the scalar particle m χ and the scattering length l s . We show the dependence of the transition redshift on m χ and l s . Since small scales collapse earlier and eventually before the BEC phase transition, the evolution of collapsing halos in this limit is indeed the same in both the CDM and the BEC models. Differences are expected to appear only on the largest astrophysical scales. However, we argue that the BEC model is almost indistinguishable from the usual dark matter scenario concerning the evolution of nonlinear perturbations above typical clusters scales, i.e., 10 14 M . This provides an analytical confirmation for recent results from cosmological numerical simulations (Schive et al., Nat Phys 10:496, 2014).

Abstract. We discuss a universal bound on any excitation of heavy fields during inflation: the ratio of the heavy field's energy density to the one driving inflation must be less than the maximally allowed relative amplitude of oscillations in the power-spectrum (ρ h /ρ I 0.01 according to PLANCK). This bound can be traced back to the sudden change of the equation of state parameter across the excitation event.We employ a sudden transition approximation at the perturbed level, which has been used before in different settings; we check its validity by comparison to the full multi-field result in a concrete case study involving a sudden mass change of an inflaton.