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We will be looking at the energy of a graviton, based upon the Stress energy tensor, and from there ascertaining how fluctuations in early universe conditions impact the mass of a graviton. Physically the mass of the graviton would be shrinking right after Planck time and presumably it would be going to its equilibrium value of about 10-62 grams, for its present day value. It, graviton mass, would increase up to the Plank time of about 10-44 seconds. Note that the result that graviton mass shrinks to 10-62 grams for its present day value works only for relic gravitons.

journal of high energy physics, gravitation and cosmology

Gedanken Experiment for Fluctuation of Mass of a Graviton, Based on the Trace of GR Stress Energy Tensor-Pre Planckian Conditions that Lead to Gaining of Graviton Mass, and Planckian Conditions That Lead to Graviton Mass Shrinking to 10&amp;lt;sup&amp;gt;-62&amp;lt;/sup&amp;gt; Grams