General relativity and quantum field theory are the cornerstones of our understanding of physical processes, from subatomic to cosmic scales. While both theories work remarkably well in their tested domains, they show minimal overlap. However, our research challenges this separation by revealing that non-perturbative effects bridge these distinct domains. We introduce a novel mechanism wherein, at linear order, spin-2 fields around an arbitrary background acquire effective mass due to the spontaneous symmetry breaking (SSB) of either global or local symmetry of complex scalar field minimally coupled to gravity. The action of the spin-2 field is identical to the extended Fierz-Pauli (FP) action, corresponding to the mass deformation parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3367_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha = 1/2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. We show that this occurs due to the effect of SSB on the variation of the energy-momentum tensor of the matter field, which has a dominant effect during SSB. The extended FP action has a salient feature, compared to the standard FP action: the action has 6 degrees of freedom with no ghosts. For local U(1) SSB, we establish that the effective mass of spin-2 fields is related to the mass of the gauge boson and the electric charge of the complex scalar field. Interestingly, our results indicate that the millicharged dark matter scalar fields, generating dark photons, can produce a mass of spin-2 fields of the same order as the Hubble constant <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3367_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">$(H_0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Hence, we argue that the dark sector offers a natural explanation for the acceleration of the current Universe.

Generation of effective massive Spin-2 fields through spontaneous symmetry breaking of scalar field

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发表日期：

2025年2月5日

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Susobhan Mandal,
S. Shankaranarayanan

摘要

General relativity and quantum field theory are the cornerstones of our understanding of physical processes, from subatomic to cosmic scales. While both theories work remarkably well in their tested domains, they show minimal overlap. However, our research challenges this separation by revealing that non-perturbative effects bridge these distinct domains. We introduce a novel mechanism wherein, at linear order, spin-2 fields around an arbitrary background acquire effective mass due to the spontaneous symmetry breaking (SSB) of either global or local symmetry of complex scalar field minimally coupled to gravity. The action of the spin-2 field is identical to the extended Fierz-Pauli (FP) action, corresponding to the mass deformation parameter $\alpha = 1/2$ $α = 1 / 2$ . We show that this occurs due to the effect of SSB on the variation of the energy-momentum tensor of the matter field, which has a dominant effect during SSB. The extended FP action has a salient feature, compared to the standard FP action: the action has 6 degrees of freedom with no ghosts. For local U(1) SSB, we establish that the effective mass of spin-2 fields is related to the mass of the gauge boson and the electric charge of the complex scalar field. Interestingly, our results indicate that the millicharged dark matter scalar fields, generating dark photons, can produce a mass of spin-2 fields of the same order as the Hubble constant $(H_0)$ $(H_{0})$ . Hence, we argue that the dark sector offers a natural explanation for the acceleration of the current Universe.