The stability of the de-Sitter universe in nonlocal gravity

We constructed the ghost-free condition for nonlocal gravity using de-Sitter background field expansion and identified the structure of the nontrivial form factors. Our analysis shows that the particle spectrum of this model is nearly equivalent to general relativity(GR), with the potential addition of a scalar particle with positive mass m. Additionally, by employing recursion relations, we established the equivalence between nonlocal gravity and higher-derivative gravity. Moreover, we provided a comprehensive proof of the stability of de-Sitter solution within the nonlocal framework.