How Inflationary Gravitons Affect the Force of Gravity

Abstract

We employ an unregulated computation the graviton self-energy from gravitons on de Sitter background to infer the renormalized result. This is used to quantum-correct the linearized Einstein equation. We solve this equation for the potentials which represent the gravitational response to static, point mass. We find large spatial and temporal logarithmic corrections to the Newtonian potential and to the gravitational shift. Although suppressed by a minuscule loop-counting parameter, these corrections cause perturbation theory to break down at large distances and late times. Another interesting fact is that gravitons induce up to three large logarithms whereas a loop of massless, minimally coupled scalars produces only a single large logarithm. This is in line with corrections to the graviton mode function: a loop of gravitons induces two large logarithms whereas a scalar loop gives none.

Big Steve and the State of the Universe

“…Weinberg recounted [1] how students poked fun at the erroneous dismissal of loop corrections with the quip, "Just because something is infinite does not mean it is zero!" That story about divergences meant a lot to me when I later encountered skepticism about large logarithmic loop corrections from inflationary gravitons [2][3][4][5][6][7][8] because of the potential for gauge dependence [9][10][11][12]. A procedure for removing gauge dependence is being developed [13,14], and I intend to channel Big Steve when announcing its success: "Just because something is gauge dependent does not mean it is zero!…”

“…This is because their interactions involve derivatives, unlike the ϕ 4 interaction of the scalar model (32). Quantum gravity also involves derivative interactions and its large inflationary logarithms [3][4][5][6][7][8]44] are not completely captured by Starobinsky's stochastic formalism [45]. I suspect that combining Starobinsky's formalism with a variant of the renormalization group will suffice [6], as it did for nonlinear sigma models, but that remains to be proven.…”