Cosmological singleton gravity theory and dS/LCFT correspondence

Abstract

We study the evolution of cosmological perturbations generated during de Sitter inflation in the singleton gravity theory. This theory is composed of a dipole ghost pair in addition to tensor. We obtain the singleton power spectra which show that the de Sitter/logarithmic conformal field theory (dS/LCFT) correspondence works for computing the power spectra in the superhorizon limit. Also we compute the spectral indices for light singleton which contains a logarithmic correction.Comment: 1+18 pages, no figures, published versio

Einstein-singleton theory and its power spectra in de Sitter inflation

“…µ is just a parameter of connecting φ 2 with φ 1 to get the fourth-order derivative equation for φ 2 from a mixed kinetic term. If one wishes to have a massive singleton, one has to include a potential term of m 2 φ 1 φ 2 [4]: (∇ 2 − m 2 )ϕ 1 = 0, (∇ 2 − m 2 )ϕ 2 = µϕ 1 , (∇ 2 − m 2 ) 2 ϕ 2 = 0.…”

“…It was given by R = −Hδφ/ φ for the single-field inflation in spatially flat gauge, while it takes the form of R S = −H[ϕ 1 / φ1 + ϕ 2 / φ2 ] for the singleton inflation. For example, the power spectrum appeared in dS spacetime with φ1 = φ2 = 0 [3,4] was given by P m ϕ 2 ϕ 2 ∼ z 2w (1 + 2 ln[z]) with w = 3/2 − 9/4 − m 2 /H 2 in the superhorizon limit. However, we remain "cosmological perturbations of the Einstein-singleton theory around the slow-roll inflation" as a future work, worrying about the appearance of the ghost states.…”

“…It seems appropriate to comment that Eqs. ( 14)-( 16) are different from those of a massive singleton in [4]:…”

“…Instead, the authors in [3] have investigated the massive singleton to show the dS/LCFT correspondence in the superhorizon limit of z → 0 as an extension to the dS/CFT correspondence. Recently, two of us have shown that the momentum correlators of LCFT take the same form as the power spectra ×k 3 in the superhorizon limit [4]. This might show that the dS/LCFT correspondence works for obtaining the power spectra in the superhorizon limit.…”

Phase transition for black holes in dilatonic Einstein-Gauss-Bonnet theory of gravitation

“…The HP phase transition has been extensively studied in Refs. [13,14,15,16,17,18,19,20] and with curvature terms in higher dimensions [21,22,23,24,25].…”