Instabilities of spherical solutions with multiple Galileons andSO(N)symmetry

Abstract

The 4-dimensional effective theory arising from an induced gravity action for a co-dimension greater than one brane consists of multiple galileon fields π I , I = 1, . . . , N , invariant under separate Galilean transformations for each scalar, and under an internal SO(N ) symmetry. We study the viability of such models by examining spherically symmetric solutions. We find that for general, non-derivative couplings to matter invariant under the internal symmetry, such solutions exist and exhibit a Vainshtein screening effect. By studying perturbations about such solutions, we find both an inevitable gradient instability and fluctuations propagating at superluminal speeds. These findings suggest that more general, derivative couplings to matter are required for the viability of SO(N ) galileon theories.

Beyond the cosmological standard model

“…Covariantizing the galileons for such applications is subtle, it requires introducing non-minimal couplings to curvature, which generically destroys the shift symmetry [554][555][556][557][558] (for a construction which couples galileons covariantly to massive gravity while retaining galilean symmetry, see [559][560][561]). Galileons have been generalized in various directions: they have been embedded in supersymmetry and supergravity [562][563][564][565], extended to p-forms [566], extended to multi-galileons [567][568][569][570][571][572] and coupled consistently to gauge fields [573,574]. The shift symmetry itself has even been generalized to a shift by an arbitrary polynomial [219].…”

Stability and superluminality of spherical DBI Galileon solutions

“…Such an analysis was performed for the ordinary galileons in [13], and for multi-galileon theories in [19,20]. In the case of the DGP model [13], it was found that for some choices of parameters, stable solutions exists but always contain superluminal signal propagation.…”

Goldstone’s theorem and Hamiltonian of multi-Galileon modified gravity

“…For example, in the case of SO(N ) fundamental representation, π = (π 1 , π 2 , ..., π N ) can not be linked to π = (π 1 , π 2 , ..., π N ) by an internal SO(N ) transformation. (Note that the SO(N ) invariant coupling P (π 2 )T , P (π 2 ) being a general function of π i π i , has been considered in [16], and the authors found gradient instability as well as superluminal excitations for the spherically symmetric background.) We could argue that from the viewpoint of braneworld scenarios the coupling (3) (instead of, say, π 1 T ) might be what one might expect for symmetric multi-galileon models.…”

“…As ghost instability has been identified on the phenomenologically interesting selfaccelerating branch of the DGP model [6], which can also be easily seen in the local galileon approximation [3,4], attempts have been made to generalize the DGP galileon description to produce a healthy modified gravity theory [5,[7][8][9][10][11][12][13][14][15][16]. In [5], the authors wrote down the most general single galileon Lagrangian.…”

“…One would want to generalize the galileon description to have even more degrees of freedom [11,[14][15][16]. To avoid a proliferation of possible terms in the theory, we can impose internal (global) symmetries within the multiple galileons, so that the multiple galileons form some representation of a group [14], π = (π 1 , ..., π N ).…”