By Luca Amendola

Darkish power, the mysterious explanation for the accelerating enlargement of the universe, is among the most vital fields of study in astrophysics and cosmology this present day. Introducing the theoretical rules, observational tools and effects, this textbook is perfect to graduate classes on darkish power, and also will complement complex cosmology classes. delivering a radical creation to this intriguing box, the textbook covers the cosmological consistent, quintessence, k-essence, excellent fluid versions, extra-dimensional versions, and transformed gravity. Observational learn is reviewed, from the cosmic microwave heritage to baryon acoustic oscillations, susceptible lensing and cluster abundances. each bankruptcy ends with difficulties, with complete recommendations supplied, and any calculations are labored via step by step.

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**Example text**

Therefore, the two components completely decouple from each other and evolve independently, and therefore can be treated separately. Since the density perturbation δ is a scalar quantity, only the longitudinal terms, which can be derived from a scalar quantity, couple to the density perturbations. A similar argument holds for the traceless spatial part hij . 9) where the divergences ∂ i hij , ∂ i h⊥ ij (which are vectors) are longitudinal and transverse, respectively, and hTij is transverse, that is ij k ∂i ∂k hij = 0, ∂i ∂j h⊥ ij = 0 , ∂i hTij = 0 .

3): ξ (r) = δ( y + r)δ( y) = 1 V δ( y + r)δ( y)dVy . 22) Therefore, the power spectrum is the Fourier transform of the correlation function (Wiener–Khinchin theorem). The converse property is ξ (r) = (2π )−3 P (k)eik·r d3 k . 23) Notice that here and in the following the Fourier volume factor is not included, as in most literature. e. that the correlation function depends only on the modulus r = |r|, the spectrum depends only on k = |k|: P (k) = π ξ (r) r 2 dr 0 2π e−ikr cos θ sin θ dθ 0 dφ = 4π ξ (r) sin kr 2 r dr .

Let us consider dark energy with an equation of state wDE = PDE /ρDE , satisfying the continuity equation ρ˙DE + 3H (ρDE + PDE ) = 0 . 80) 24 Expansion history of the Universe which can also be written by introducing an average wˆ DE as (0) ρDE = ρDE (a/a0 )−3(1+wˆ DE ) , wˆ DE (z) = 1 ln(1 + z) z 0 wDE (˜z) d˜z . 17) we have K 8π G (ρr + ρm + ρDE ) − 2 . 82) From Eq. 82) we see that the present density parameters defined in Eq. 24) obey the following relation (0) r + (0) m (0) DE + + (0) K = 1.