Two approaches that prove divergence free nature of non-local gravity

Abstract

This paper is an attempt to study the thermodynamics of the structure formation in the large scale universe in the non local gravity using Boltzmann statistics and the Tsallis statistics. The partition function is obtained in both the approaches and the corresponding thermodynamics properties are evaluated. The important thing about the paper is that we surprisingly get the divergence free integrals and thus stress upon the fact that the nonlocal gravity is the singularity free model of gravity.

Logarithmic corrections to Newtonian gravity and large scale structure

“…However, these divergences can be removed by adding a softening parameter, which accounts for the extended structure of galaxies as reported in [15]. In a recent study it has also been proved that the nonlocal gravity is divergence free [16]. Thermody-namics for systems of galaxies is obtained from the partition function (regularized with a softening parameter), and this can in turn be used to study the clustering properties [17].…”

Modified Yang-Lee theory for nonlocal gravitational potential and their phase transition

“…Under such considerations, nonlocal theories of General Relativity (GR) have recently been studied [5][6][7]. A nonlocal modification of the Einstein-Hilbert action has been studied by Deser and Woodard [8],…”

Study of the Universe populated by Clusters of Galaxies with halo using Newtonian Gravity modified by Tohline.

“…This difficulty can be circumvented by using a combination of 1) the convolution theory of ultrahyperfunctions [5,6,7,8,9] and 2) the Guelfand regularization method [10]. This combination has been used successfully in the references [11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30] 2 Three-dimensional Partition Function…”