Abstract
A detailed stability analysis is presented for the de Sitter solution with a homogeneous magnetic field that was recently found in the context of a $U(1)$ gauge theory nonminimally coupled to scalar-tensor gravity. The magnetic field is `stealth' in the sense that the corresponding stress-energy tensor is of the form of an effective cosmological constant and thus is isotropic despite the fact that the magnetic field has a preferred spatial direction. We study the stability of the solution against linear perturbations in the subhorizon and superhorizon limits. We then present some explicit examples that satisfy all stability conditions. The stable de Sitter solution with a homogeneous magnetic field opens up a new possibility for inflationary magnetogenesis, in which magnetic fields in the Universe at all scales may originate from a classical, homogeneous magnetic field sustained during inflation.
Highlights
The origin of magnetic fields in the Universe at various scales is one of the mysteries in modern cosmology
II, we briefly review the model and the solutions studied in Ref. [5], focusing on those without the electric field
We briefly review the model and the de Sitter solution with a homogeneous magnetic field studied in Ref. [5]
Summary
The origin of magnetic fields in the Universe at various scales is one of the mysteries in modern cosmology. In Friedmann-Lemaître-Robertson-Walker (FLRW) backgrounds (including the de Sitter spacetime), w for a homogeneous magnetic field decays as 1=a4, where a is the scale factor, and the only constant value of w that is consistent with the expansion of the Universe is zero For this reason, this simple action does not work. IW 1⁄4 d4xpffi−ffiffiffigffiffifðWÞ; W e2φFμνFμν; ð1:3Þ where φ is a scalar field and it is understood that some kinetic terms for φ are added to the action In this case, the corresponding stress-energy tensor is again proportional to gμν if f0ðWÞ 1⁄4 0. Appendixes A–D show explicit expressions of some matrices and coefficients
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