Abstract
We examine cosmic energy equation for extended galaxy structures on the basis of different models of universe. We also extend the power spectrum and density fluctuations for extended structure by introducing softening parameter both for linear and non-linear regimes. The results are compared with earlier results of point mass structures. It is found that softening parameters introduced in the theory influence the thermodynamic fluctuation theory. Results obtained with spectrum analysis are also compared with Riemannian geometric approach (Ruppeiner in Rev. Mod. Phys. 67:605, 1995) to the galaxy clustering. The singular solutions of thermodynamic fluctuation results can be interpreted on the basis of power spectrum analysis in terms of power index law of two point correlation function.
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