Scalar field theories in curved space

Details Scalar field theories in curved space Scalar field theories in curved space

Oct 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..32.1949h&link_type=abstract

Physical Review D (Particles and Fields), Volume 32, Issue 8, 15 October 1985, pp.1949-1953

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46

Lagrangian And Hamiltonian Approach, Other Special Classical Field Theories, Other Topics In General Relativity And Gravitation

Scientific paper

We investigate the behavior of scalar fields (φ) in curved space which have a potential V[φ]=V0+(1/2)m2φ2+(1 /3!)ηφ3+(1/4!)λφ4 and a general coupling to gravity (1/2)ξRφ2. The back-reaction of gravity strongly affects the stability of scalar fields. By examining the scalar field equations and the Einstein equations, we clarify conditions for the system to have an absolutely stable ground state in which φ is constant and a metric is either Minkowski, or de Sitter, or anti-de Sitter. We find that (i) cubic interactions cause instability, unless ξ=0, (ii) Higgs scalar fields in the standard model must have ξeq(1/6), (iii) negative quartic interaction couplings (λ<0) can make sense, and (iv) a free scalar field with a tiny mass can reduce the bare large vacuum energy density V0 to an extremely small value (~m2G-1ξ-1). Based on the last observation, the vanishing-cosmological-constant problem is viewed not as a problem of how to reduce the bare vacuum energy density, but as that of how to get a large gravitational constant (G>>||m2V0||).

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