Positivity constraints for pseudolinear massive spin-2 and vector Galileons

Abstract

We derive analyticity constraints on a nonlinear ghost-free effective theory of a massive spin-2 particle known as pseudo-linear massive gravity, and on a generalized theory of a massive spin-1 particle, both of which provide simple IR completions of Galileon theories. For pseudo-linear massive gravity we find that, unlike dRGT massive gravity, there is no window of parameter space which satisfies the analyticity constraints. For massive vectors which reduce to Galileons in the decoupling limit, we find that no two-derivative actions are compatible with positivity, but that higher derivative actions can be made compatible.

Positivity constraints on interacting spin-2 fields

“…The positivity bounds for the case of a single pseudo-linear scalar field were previously studied in [21] where it was argued that the theory was ruled out. In particular, keeping for now the same notation as in [21], the following bounds were obtained on the couplings of the EFT of a single pseudo-linear spin-2 field 1…”

“…Note that the λ i 's in(3.3) are the couplings considered in[21] and not polarization of the ingoing and outgoing states. The couplings are related to those in (2.6) as λ 1 = a 1 , λ 3 =3κ (h) 3 2 , and λ 4 = 6κ (h) 4 , while g * Mp = M 1 .…”

Consistent deformations of free massive field theories in the Stueckelberg formulation

“…The potential vertex proportional to m 2 coincides with the one found in [29,68], and is a particular member of the dRGT class of massive gravity theories (see [58,69] for reviews). In fact, the complete solution (4.18) happens to be special, in that it is the unique massive graviton cubic interaction consistent with positivity constraints of eikonal scattering amplitudes and absence of superluminality [48] (see also [70][71][72][73][74][75][76] for other studies of the S-matrix in massive gravity). It is also interesting that, in D = 4, this vertex corresponds to the unique nonlinear action of a partially massless spin-2 field [29,53,77,78], although as is well known the theory happens to be obstructed at higher orders [79][80][81] (more on this below).…”

Blue-tilted primordial gravitational waves from massive gravity

“…The minimal theory of massive gravity (MTMG) introduced in [20,21] is one of such possibilities and propagates only two physical degrees of freedom in the gravity sector, allowing for self-accelerating, homogeneous and isotropic cosmological solutions without pathologies such as strong coupling and ghosts, that are usually unavoidable in Lorentz-invariant massive gravity [22]. The recently developed positivity bounds that significantly shrink the viable parameter space of the Lorentz-invariant massive gravity theory [23][24][25][26] also do not apply to those Lorentz-violating theories, including MTMG, since those bounds rely on Lorentz invariance at all scales. Moreover, because of the absence of extra degrees of freedom, MTMG completely evades the so called Higuchi bound, which states that the mass of a Lorentz-invariant massive graviton should be greater than the Hubble expansion rate up to a factor of order unity in order to avoid turning extra degrees of freedom into ghosts in cosmological backgrounds [27].…”