Graviton Self-Energy from Gravitons in Cosmology. (arXiv:2103.08547v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Tan_L/0/1/0/all/0/1">L. Tan</a> (Florida), <a href="http://arxiv.org/find/gr-qc/1/au:+Tsamis_N/0/1/0/all/0/1">N. C. Tsamis</a> (Crete), <a href="http://arxiv.org/find/gr-qc/1/au:+Woodard_R/0/1/0/all/0/1">R. P. Woodard</a> (Florida)
Although matter contributions to the graviton self-energy
$-i[mbox{}^{munu} Sigma^{rhosigma}](x;x’)$ must be separately conserved
on $x^{mu}$ and ${x’}^{mu}$, graviton contributions obey the weaker
constraint of the Ward identity, which involves a divergence on both
coordinates. On a general homogeneous and isotropic background this leads to
just four structures functions for matter contributions but nine structure
functions for graviton contributions. We propose a convenient parameterization
for these nine structure functions. We also apply the formalism to explicit one
loop computations of $-i[mbox{}^{munu} Sigma^{rhosigma}](x;x’)$ on de
Sitter background, one of the contributions from a massless, minimally coupled
scalar and the other for the contribution from gravitons in the simplest gauge.
We also specialize the linearized, quantum-corrected Einstein equation to the
graviton mode function and to the gravitational response to a point mass.
Although matter contributions to the graviton self-energy
$-i[mbox{}^{munu} Sigma^{rhosigma}](x;x’)$ must be separately conserved
on $x^{mu}$ and ${x’}^{mu}$, graviton contributions obey the weaker
constraint of the Ward identity, which involves a divergence on both
coordinates. On a general homogeneous and isotropic background this leads to
just four structures functions for matter contributions but nine structure
functions for graviton contributions. We propose a convenient parameterization
for these nine structure functions. We also apply the formalism to explicit one
loop computations of $-i[mbox{}^{munu} Sigma^{rhosigma}](x;x’)$ on de
Sitter background, one of the contributions from a massless, minimally coupled
scalar and the other for the contribution from gravitons in the simplest gauge.
We also specialize the linearized, quantum-corrected Einstein equation to the
graviton mode function and to the gravitational response to a point mass.
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