Ghosts in the self-accelerating DGP branch with Gauss–Bonnet effect

The European Physical Journal C, Jun 2015

The Dvali–Gabadadze–Porrati brane-world model provides a possible approach to address the late-time cosmic acceleration. However, it has subsequently been pointed out that a ghost instability will arise on the self-accelerating branch. Here, we carefully investigate whether this ghost problem could be possibly cured by introducing the Gauss–Bonnet term in the five-dimensional bulk action, a natural generalization to the Dvali–Gabadadze–Porrati model. Our analysis is carried out for a background where a de Sitter brane is embedded in an anti–de Sitter bulk. Our result shows that the ghost excitations cannot be avoided even in this modified model.

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Ghosts in the self-accelerating DGP branch with Gauss–Bonnet effect

Eur. Phys. J. C Ghosts in the self-accelerating DGP branch with Gauss-Bonnet effect Yen-Wei Liu 1 2 Keisuke Izumi 2 Mariam Bouhmadi-López 0 4 5 6 Pisin Chen 1 2 3 7 0 Departamento de Física, Universidade da Beira Interior , 6200 Covilhã , Portugal 1 Department of Physics, National Taiwan University , Taipei 10617 , Taiwan 2 Leung Center for Cosmology and Particle Astrophysics, National Taiwan University , Taipei 10617 , Taiwan 3 Graduate Institute of Astrophysics, National Taiwan University , Taipei 10617 , Taiwan 4 IKERBASQUE, Basque Foundation for Science , 48011 Bilbao , Spain 5 Department of Theoretical Physics, University of the Basque Country UPV/EHU , P.O. Box 644, 48080 Bilbao , Spain 6 Centro de Matemática e Aplicações da Universidade da Beira Interior (CMA-UBI) , 6200 Covilhã , Portugal 7 Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University , Stanford, CA 94305 , USA The Dvali-Gabadadze-Porrati brane-world model provides a possible approach to address the latetime cosmic acceleration. However, it has subsequently been pointed out that a ghost instability will arise on the selfaccelerating branch. Here, we carefully investigate whether this ghost problem could be possibly cured by introducing the Gauss-Bonnet term in the five-dimensional bulk action, a natural generalization to the Dvali-GabadadzePorrati model. Our analysis is carried out for a background where a de Sitter brane is embedded in an anti-de Sitter bulk. Our result shows that the ghost excitations cannot be avoided even in this modified model. - In recent years, the late-time cosmic acceleration has been confirmed by several observational pieces of evidence [1–6]. This important discovery leads to one of the great puzzles in cosmology, and various plausible models have been developed to unravel the nature of such a late-time speed-up over the last decade. There have been many attempts at building up reasonable and consistent models by modifying the standard cosmology, which can be roughly categorized into two major directions: one is to introduce a dominant dark energy M. Bouhmadi-López is on leave of absence from UPV and IKERBASQUE. a e-mail: b e-mail: c e-mail: d e-mail: component in the Universe (see, e.g., Ref. [7]), while the other is to modify Einstein’s general relativity at large scales (see, e.g., Refs. [8–10]). An intriguing brane-world scenario proposed by Dvali, Gabadadze, and Porrati (DGP) provides a new mechanism with an induced gravity (IG) term, i.e., a four-dimensional (4D) Ricci scalar, included in the brane action [11]. The IG term is expected to arise as a quantum correction due to the matter field on the brane [12], and it makes possible to reproduce the correct 4D Newtonian gravity at short distances even if the bulk is a five-dimensional (5D) Minkowski space-time with an infinite size [11]. The promising feature of the DGP model is that, when generalized to a Friedmann–Lemaître– Robertson–Walker brane with ordinary matter on it, one of its solutions, called the self-accelerating branch, will become asymptotically de Sitter in the far future, giving rise to a latetime accelerating phase without needing to introduce additional substances on the brane that violates the strong energy condition [13, 14]. Despite this advantage, it was pointed out later on that the self-accelerating branch is plagued with a ghost instability [15–20]. The spin-2 perturbations in this branch, viewed as an effective 4D massive gravity theory on a de Sitter background, are composed of a tower of infinite Kaluza–Klein (KK) massive gravitons. Then the mass of the lowest mode m is within the range 0 < m2 < 2 H 2 if the brane tension is positive, where H is the Hubble parameter, and thus there will be a spin-2 ghost excitation in its helicity-0 component [21].1 On the other hand, if the brane tension is negative, the lowest 1 The instability of the ghost might be suppressed due to the sponta neous breaking of Lorentz symmetry by the helicity-0 ghost [22,23]. mass is larger than the critical scale, i.e., 2H 2 < m2, but the spin-0 perturbation, associated with the brane-bending mode, becomes a ghost instead [17]. In the specific case without brane tension, the lowest mass is equal to the critical scale. Even in this marginal case a detailed analysis shows the existence of a ghost from the mixing between the spin-0 sector and the helicity-0 part of the spin-2 sector [18]. Furthermore, the appearance of ghosts in the DGP self-accelerating branch cannot be eliminated even by invoking a second brane in the bulk with a stabilization mechanism [24]. For more discussions on DGP ghosts, please see Ref. [20] and the references therein. Nonlinear instabilities of the model have also been discussed in Refs. [25–27]. In this paper, we will investigate the possibility of avoiding the ghost in a generalized DGP model. A natural generalization to the DGP gravitational action, base (...truncated)


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Yen-Wei Liu, Keisuke Izumi, Mariam Bouhmadi-López. Ghosts in the self-accelerating DGP branch with Gauss–Bonnet effect, The European Physical Journal C, 2015, pp. 248, Volume 75, Issue 6, DOI: 10.1140/epjc/s10052-015-3463-0