Structure formation of ultralight dark matter Sample Clauses

Structure formation of ultralight dark matter. To focus on the effects of an ultralight dilaton field on cosmological observ- xxxxx for use in later detection/exclusion, it is helpful to model its character- istic (local) density anisotropies, and thus its structure formation. Assum- ing the dilaton contributes to the formation of large-scale structure, fluctua- tions of the dilaton field are typically expected to be sourced from inflation (isocurvature) fluctuations. These are assumed to be either carried over into matter perturbations directly through reheating (when the inflaton decayed into the radiation that filled the early universe at the end of inflation) or by falling into potential xxxxx formed by the radiation produced during re- heating. Assuming a LCDM cosmology in what follows (and throughout our work), and using the approximate (WKB) approximation for the dilaton field we may write the dilaton background and perturbation fields more generally in the form + φ φ φ (k;t) = a 3=2(φ cos m t + φ sin m t ) ; (2.11) δφ (k;t) = δφ + (k;t) cos mφ t + xx (k;t) sin mφ t ; (2.12) where (δφ + ; δφ ) depend on wavenumber k and time. Crucially here we have added a spatial dependence. The evolution of perturbations on this (FLRW) background can then be written in the synchronous gauge as [47] δ0 = ku h0 3H c2 δ 9H 2c2 u =k ; (2.13) φ φ 2 s;e f f φ s;e f f φ u0 = H uφ + c2 kδφ + 3c2 H 2uφ ; (2.14) x s;e f f s;e f f ∂x where δφ = δρ φ =ρ φ is the local density perturbation, uφ = ( 1 + ω)vφ is the dimensionless perturbed heat flux with velocity vφ h¯∂δφ =mφ of the dilaton perturbation, H = aH is the Hubble rate in terms of conformal time dτ = dt=a, h is the (gravitational) potential in the synchronous gauge, and the s;e f f s sound speed c2 = hc2i is given by [51] s hc2i = k2=(4m2 a2) φ φ 1 + k2=(4m2 a2) ; (2.15) s calculated using c2 = δP=δρ [52] at late times (mφ H), in a gauge which follows the average (hωφ i = 0). Early time evolution can also be solved for (e.g. Ref. [47]), and for ω = 1 one can show φ 0 = 0 such that adiabatic per- turbations do not grow. Using the Newtonian gauge gravitational potential defined as k2F 2 = 4πa2Gρ δφ ; (2.16) This system can be made into a second-order ODE for the densities [52]: s;e f f
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