2.1 Perturbation Modeling in Cosmology

Smoot’s Nobel-winning work analyzed tiny fluctuations in the CMB — minute variations in temperature that encoded the seeds of galaxies and cosmic structure. These perturbations can be represented mathematically as:

$$\delta T(\theta, \phi) = \sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell} a_{\ell m} Y_{\ell m}(\theta, \phi)$$

Where:

• $$\delta T(\theta, \phi)$$

  = CMB temperature anisotropy,

• $$a_{\ell m}$$

  = coefficients encoding fluctuation amplitudes,

• $$Y_{\ell m}$$

  = spherical harmonics describing angular modes.

These perturbations are not noise — they are the fingerprints of the universe’s birth, revealing the structure of space-time and the distribution of matter.