Static Solitons in an Expanding Universe
Abstract
We show, analytically, that a static sine-Gordon soliton cannot exist in 1 + 1 non-dynamical de Sitter spacetime if α:= (m/H)2 < 2, where m is the mass parameter of the sine-Gordon theory and H is the Hubble constant. Conversely, we also show that static sine-Gordon solitons exist in 1 + 1 non-dynamical de Sitter spacetime if α> 2. The above threshold is explained---qualitatively and to within an O(1) factor---using a heuristic argument involving the interplay of tensile force in the Lorentzian sine-Gordon soliton and the tidal force in de Sitter spacetime. A similar heuristic argument, which remains to be confirmed analytically, also suggests the existence of a threshold, $ (m_V/H)^2 \sim O(1)$, below which the tidal forces are too strong to permit the existence of a static `t Hooft--Polyakov monopole in non-dynamical 3 + 1 de Sitter spacetime; mV is the mass of the vector boson. Linde has suggested that new inflation could have triggered secondary inflation at the core of a GUT (Grand Unified Theory) monopole even if the Hubble constant at or after the GUT phase transition was significantly smaller than the mass of the X boson. We present a heuristic argument, which suggests that the SO(3) `t Hooft--Polyakov monopole does not allow secondary inflation at its core when the inflationary background is weak. Based on the above, as yet analytically unconfirmed, heuristic argument for the SO(3) `t Hooft--Polyakov monopole, we conjecture that secondary inflation at the core of a GUT monopole is infeasible.
Versions
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BibTeX
@misc{prabhu2026static,
title = {{Static Solitons in an Expanding Universe}},
author = {Nagabhushana Prabhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28540},
eprint = {2609.28540},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28540},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Static Solitons in an Expanding Universe
AU - Nagabhushana Prabhu
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.28540
UR - https://arxiv.org/abs/2609.28540
AB - We show, analytically, that a static sine-Gordon soliton cannot exist in 1 + 1 non-dynamical de Sitter spacetime if α:= (m/H)^2 < 2, where m is the mass parameter of the sine-Gordon theory and H is the Hubble constant. Conversely, we also show that static sine-Gordon solitons exist in 1 + 1 non-dynamical de Sitter spacetime if α> 2. The above threshold is explained---qualitatively and to within an O(1) factor---using a heuristic argument involving the interplay of tensile force in the Lorentzian sine-Gordon soliton and the tidal force in de Sitter spacetime. A similar heuristic argument, which remains to be confirmed analytically, also suggests the existence of a threshold, $ (m_V/H)^2 \sim O(1)$, below which the tidal forces are too strong to permit the existence of a static `t Hooft--Polyakov monopole in non-dynamical 3 + 1 de Sitter spacetime; m_V is the mass of the vector boson. Linde has suggested that new inflation could have triggered secondary inflation at the core of a GUT (Grand Unified Theory) monopole even if the Hubble constant at or after the GUT phase transition was significantly smaller than the mass of the X boson. We present a heuristic argument, which suggests that the SO(3) `t Hooft--Polyakov monopole does not allow secondary inflation at its core when the inflationary background is weak. Based on the above, as yet analytically unconfirmed, heuristic argument for the SO(3) `t Hooft--Polyakov monopole, we conjecture that secondary inflation at the core of a GUT monopole is infeasible.
ER -