Induced Gravity in Deconstructed Space at Finite Temperature

We study self-consistent cosmological solutions for an Einstein Universe in a graphbased induced gravity model. The graph-based field theory has been proposed by the present authors to generalize dimensional deconstruction. In this paper, we consider self-consistent Einstein equations for a “graph theory space”. Especially, we demonstrate specific results for cycle graphs. 1 Pre-history 1.1 Induced Gravity Induced Gravity or Emergent Gravity has been studied by many authors. The idea of induced gravity is, “Gravity emerges from the quantum effect of matter fields.” The one-loop effective action can be expressed as the form: − 1 2 ∫ dt t ∑ i Tr exp [ −(−∇ +M i )t ] . (1) In curved D-dimensional spacetime, the trace part including the D-dimensional Laplacian becomes Tr exp [ −(−∇)t ]