Red Tilt in CMB | Explaining Inflation & Measurement

[skydivephil]

Can anyone give a good explnanation of red tilt in comsology? why inflation predicts this and how its measured in the CMb? Many thanks.

 

[bapowell]

A 'red tilt' refers to the shape of the spectrum of density perturbations. The primordial density perturbations are what give rise to the temperature anisotropies measured in the CMB. We can therefore use the CMB to constrain this spectrum. A simple ansatz for the shape of the primordial power spectrum is

$$P(k) \propto k^{n - 1}$$

where $k$ is the wavenumber of the perturbation (this power spectrum is the Fourier transform of the spatial correlation function, and so small $k$ corresponds to large-scale perturbations.) For $n < 1$, one sees that there is more power on large scales -- in the infrared. This is called a red spectrum, or a 'red tilt'. Conversely, if $n > 1$, there is more power on small scales and the spectrum is said to be blue tilted. In the CMB, a red spectrum would indicate itself by giving larger anisotropy on large scales (low CMB multipoles).

Inflation does not exclusively predict a red spectrum -- it can predict both blue and red. It just so happens that the more popular models, like chaotic and 'new' inflation, predict red spectra. However, simple models of hybrid inflation give blue spectra, for example.