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. 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, (mV/H)2 ∼ O(1)mV/H)∼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.
Nagabhushana Prabhu (Mon,) studied this question.