metric, but the separation between the background metric and a perturbed one is not unique. One needs to choose a gauge. A simple choice would be to fix the observer to the unperturbed matter particles, where the observer will detect a velocity of matter field falling under gravity; this is known as the Newtonian or the longitudinal gauge because the observer in the Newtonian gravity limit measures the gravitational potential well where matter is falling in and clumping. The induced metric can be written as where Φ has a complete analogue of Newtonian gravitational potential. In the case when the spatial part of the energy momentum tensor is diagonal, i.e. δT i j = δ i $_{j}$, it follows that Φ = Ψ, [12]. Right at the time of horizon crossing one finds a solution for δφ as where $^{t}$∗ denotes the instance of horizon crossing. Correspondingly, we can also define a power spectrum Note that the phase of δφ$_{k}$ can be arbitrary, and therefore, inflation has generated a Gaussian perturbation. In the limit k → 0, one can find an exact solution for the long wavelength inhomogeneities k ≪ aH [7, 12], which reads: where the dot denotes derivative with respect to physical time. The growing solutions are proportional to c$_{1}$ , the decaying proportional to c$_{2}$ . Concentrating upon the growing solution, it is possible to obtain a leading order term in an expansion with the help of the slow-roll conditions: 16 ds 2 = a $^{2}$( τ ) [ (1 + 2Φ) dτ 2 − (1 − 2Ψ) δ$_{ik}$dx $^{i}$dxk ] , (14) 〈| δφ$_{k}$ | $^{2}$〉 = H ( $^{t}$∗ ) 2 2 k 3 , (15) P $_{φ}$( k ) = k 3 2 π 2 〈| δφ$_{k}$ | $^{2}$〉 = [ H ( $^{t}$∗ ) 2 π ] 2 ≡ [ H 2 π ] 2 ∣ k = aH . (16) δφ$_{k}$ ˙ φ ≈ c$_{1}$ H . (20) Φ$_{k}$ ≈ − c$_{1}$ ˙ H H 2 , (19) Φ$_{k}$ ≈ c$_{1}$ ( 1 a ∫ t 0 $_{a dt}$′ ) · + c$_{2}$ H a , (17) t 0 δφ$_{k}$ ˙ φ = 1 a c$_{1}$ t 0 $_{a dt}$′ − c$_{2}$ ) , (18)