Statistical mechanics of the cosmological many-body problem. II. Results of higher order contribution

We calculate the irreducible triplet contribution to galaxy clustering in the cosmological many-body problem. These triplets generally represent short-lived configurations in which three close objects interact with pairwise gravitational forces. From the resulting grand canonical partition function, we obtain higher order analytical expressions for thermodynamic quantities such as specific heats, isothermal compressibility, and thermal expansion in the system. Compared with previous analyses, which included reducible but not irreducible triplets, the additional terms are usually small, especially in the limit of large N. This confirms the thermodynamic results. We also derive the modified spatial distribution functions and show that they agree with recent observational results. The inclusion of triplet and higher order irreducible clusters does not significantly modify the results of the reducible terms in the partition function or of its thermodynamic consequences such as the distribution function.