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.
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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)