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defined as 

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with n$_{s}$ − 1 being referred to as the tilt of the spectrum. For constant spectral index, P $_{ζ}$( k ) ∝ k n$_{s}$ − $^{1}$. P ζ is scale invariant for n$_{s}$ = 1. In general, n$_{s}$ = n$_{s}$ ( k ), with cosmic inflation predicting n$_{s}$ close but not exactly equal to unity, so that the spectrum is approximately (but not quite) scale invariant. The Planck spacecraft made measurements of the spectrum at what is known as the pivot scale , which is k$_{0}$ ≡ 0 . 002 Mpc − $^{1}$. When combined with other data, the data obtained from the Planck spacecraft [40] yields values for the spectrum and spectral index of 

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