Abstract
We study a self-interacting scalar field theory coupled to gravity and are interested in spherically symmetric solutions with a regular origin surrounded by a horizon. For a scalar potential containing a barrier, and using the most general spherically symmetric ansatz, we show that in addition to the known static, oscillating solutions discussed earlier in the literature there exist new classes of solutions which appear in the strong field case. For these solutions the spatial sphere shrinks either beyond the horizon, implying a collapsing universe outside of the cosmological horizon, or it shrinks already inside of the horizon, implying the existence of a black hole surrounding the scalar lump in all directions. Crucial for the existence of all such solutions is the presence of a scalar field potential with a barrier that satisfies the swampland conjectures.
Highlights
We study a self-interacting scalar field theory coupled to gravity and are interested in spherically symmetric solutions with a regular origin surrounded by a horizon
Scalar fields play an important role in modeling and explaining various phenomena in cosmology: for example, they are essential in many models of inflation, ekpyrosis, modified gravity or quintessence, for reviews see, e.g., [1,2,3]
Taking our results from the previous sections we find for a scalar field and a regular origin that just one horizon occurs because fðrÞ develops only one zero leaving us with three distinct cases: (a) Blue region in Figs. 3 and 7: RðrÞ is a monotonic function in r, i.e., θlðrÞ 1⁄4 0 at rH while θnðrÞ ≠ 0 for all r ∈ ð0; ∞Þ
Summary
Scalar fields play an important role in modeling and explaining various phenomena in cosmology: for example, they are essential in many models of inflation, ekpyrosis, modified gravity or quintessence, for reviews see, e.g., [1,2,3]. Experience with Einstein-Yang-Mills solutions with nonzero cosmological constant shows [8] that for some parameter values of the theory Schwarzschild like coordinates cannot be used and one needs to use a different gauge, in which the size of the 2-spheres is a (possibly nonmonotonic) function of the radial coordinate. We find that Schwarzschild like coordinates are applicable only in a small range of the parameter space of the theory and, with a more appropriate gauge, new classes of solutions exist for a vastly increased parameter range. These new solutions have a regular origin, which may be identified as the centre of a scalar lump, and develop a horizon at some radius.
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