Kavli Affiliate: Misao Sasaki
| First 5 Authors: Atsuhisa Ota, Misao Sasaki, Yi Wang, ,
| Summary:
The radiation-dominated universe is a key ingredient of the standard Big Bang
cosmology. Radiation comprises numerous quantum elementary particles, and the
macroscopic behavior of radiation is described by taking the quantum thermal
average of its constituents. While the interactions between individual
particles and gravitational waves are often neglected in this context, it
raises the question of whether these elementary particles interact with
gravitational waves in the framework of quantum field theory. To address this
question, this paper aims to explore the quantum mechanical aspects of
gravitational waves in a universe dominated by a massless scalar field, whose
averaged energy-momentum tensor plays the role of background radiation. We
establish the equivalence between the classical Einstein equation and the
mean-field approximation of the Heisenberg equation in a local thermal state.
Beyond the mean-field approximation, we analyze the quantum corrections to
gravitational waves, particularly focusing on the thermal radiation loop
corrections. Interestingly, we find the 1-loop correction surpasses the
tree-level spectrum of primordial gravitational waves, which is $O(alpha^2)$
where $alpha=H_{rm inf}/M_{rm pl}$ is the ratio of the inflationary Hubble
parameter to the Planck mass. Then, to see if this result persists even if we
take into account all the higher order loop corrections, the loop expansion is
reorganized in the series expansion in $alpha$. We schematically discuss
two-loop diagrams that may give $O(alpha^2)$ contributions. We leave explicit
computations of these diagrams for future studies. Thus, although we cannot
claim that the whole loop corrections exceed the tree-level spectrum at the
moment, our findings highlight the significance of quantum effects when
studying the interaction between radiation and gravitational waves in the
cosmological context.
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