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The cosmological constant problem and the effective potential of a gravity-coupled scalar (2404.12357v2)
Published 18 Apr 2024 in hep-th
Abstract: We consider a quantum scalar field in a classical (Euclidean) De Sitter background, whose radius is fixed dynamically by Einstein's equations. In the case of a free scalar, it has been shown by Becker and Reuter that if one regulates the quantum effective action by putting a cutoff $N$ on the modes of the quantum field, the radius is driven dynamically to infinity when $N$ tends to infinity. We show that this result holds also in the case of a self-interacting scalar, both in the symmetric and broken-symmetry phase. Furthermore, when the gravitational background is put on shell, the quantum corrections to the mass and quartic self-coupling are found to be finite.
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