Energy’s and amplitudes’ positivity

By Alberto Nicolis, R. Rattazzi, E. Trincherini. 2009

213 citations recorded by the source corpus.

In QFT, the null energy condition (NEC) for a classical field configuration is usually associated with that configuration’s stability against small perturbations, and with the sub-luminality of these. Here, we exhibit an effective field theory that allows for stable NEC-violating solutions with exactly luminal excitations only. The model is the recently introduced ‘galileon’, or more precisely its conformally invariant version. We show that the theory’s low-energy S-matrix obeys standard positivity as implied by dispersion relations. However we also show that if the relevant NEC-violating solution is inside the effective theory, then other (generic) solutions allow for superluminal signal propagation. While the usual association between sub-luminality and positivity is not obeyed by our example, that between NEC and sub-luminality is, albeit in a less direct way than usual.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/903215037da2a67198b73034c3ccd4164dbc6d7e

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Citations in the corpus

A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “Implications of the UV completion: Even if the UV completion of a theory is not known, one can infer important properties of the low energy effective field theory based on the unitarity and analyticity requirements of the scattering amplitudes [106, 107, 108, 109, 110].”
G-bounce (2011, background): “7 It is the presence of higher derivatives in the action and the corresponding kinetic mixing between the scalar and the metric which allows for a stable violation of the NEC [72, 73].”
Proof of the weak gravity conjecture from black hole entropy (2018, result): “It would be interesting to draw a direct connection between our results and previous discussions of unitarity and analyticity [11,27].”
Imperfect Dark Energy from Kinetic Gravity Braiding (2010, background): “See also Refs.”
Horndeski theory and beyond: a review (2019, background): “nditions, (42), (43), (49) and (50), are not correlated with the sign of H˙ . Therefore, one can construct NEC-violating stages that are nevertheless stable within the Galileon and Horndeski theories [97] (see, however, [98]). This opens up Pandora’s box of nonsingular bouncing cosmology [99, 100, 1”
Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity (2014, background): “This general class of actions includes essentially all universally coupled models of dark energy with one scalar degree of freedom: quintessence [1, 2], Brans-Dicke models [44], kessence [45, 46], kinetic gravity braiding [47–49], galileons [50, 51].”
Quantum Gravity Constraints from Unitarity and Analyticity (2015, background): “Note that taking t strictly to zero is not required to derive a positivity bound [29] and positivity holds for any non-negative t below μ(2) [30].”
Positive moments for scattering amplitudes (2020, unknown): “11 Since the amplitude is analytic also for 0 ≤ t ≤ 4m2 [26], ImM̂(ŝ, t) = ∑ n ∂ n t ImM(s, t)|t=0t/n! > 0 is positive there [6, 7], so that the constraints of section I apply up to replacing an(ŝ) → an(ŝ, t) for 0 ≤ t ≤ 4m2.”
Beyond the Cosmological Standard Model (2014, unknown): “This constraint derives from demanding that the retarded propagator has support only on the future light cone, which is satisfied provided that the index of refraction n(ω) defined through k = n(ω)ω , (D-XXII) is analytic in the upper complex plane and that its limit is n(ω) → 1 as ω → ∞ [571, 976, ”
Effective field theory of dark energy: A review (2019, background): “The latter arise from requiring basic principles such as a unitary, causal, local UV completion [216, 217, 218, 219].”
Positive signs in massive gravity (2016, background): “The last is also known in the literature as the Galileon [5, 6, 10, 11].”
The imperfect fluid behind kinetic gravity braiding (2011, background): “A galilean-symmetric generalisation of this scalar field theory was introduced in [21, 22].”
The EFT-hedron (2020, methodology): “Such extended positivity away from the forward limit was suggested long ago in [19], and utilized as consistency conditions for EFT in [20], deriving bounds in [21].”
New positivity bounds from full crossing symmetry (2020, background): “Thanks to the analyticity in the complex t plane [11], the positivity bounds can also be extended away from the forward limit [9] (see [3, 12–15] for earlier work).”
Galilean Genesis: An Alternative to inflation (2010, methodology): “In Section 6, we will discuss this issue and its implications applying to our case the general discussion of [2].”