We derive the first positivity bounds for low-energy Effective Field Theories (EFTs) that are not invariant under Lorentz boosts. "Positivity bounds" are the low-energy manifestation of certain fundamental properties in the UV - to date they have been used to constrain a wide variety of EFTs, however since all of the existing bounds require Lorentz invariance they are not directly applicable when this symmetry is broken, such as for most cosmological and condensed matter systems. From the UV axioms of unitarity, causality and locality, we derive an infinite family of bounds which (derivatives of) the 2→2 EFT scattering amplitude must satisfy even when Lorentz boosts are broken (either spontaneously or explicitly). We apply these bounds to the leading-order EFT of both a superfluid and the scalar fluctuations produced during inflation, comparing in the latter case with the current observational constraints on primordial non-Gaussianity.
Developing our understanding of how correlations evolve during inflation is crucial if we are to extract information about the early Universe from our late-time observables. To that end, we revisit the time evolution of scalar field correlators on de Sitter spacetime in the Schrodinger picture. By direct manipulation of the Schrodinger equation, we write down simple "equations of motion" for the coefficients which determine the wavefunction. Rather than specify a particular interaction Hamiltonian, we assume only very basic properties (unitarity, de Sitter invariance and locality) to derive general consequences for the wavefunction's evolution. In particular, we identify a number of "constants of motion": properties of the initial state which are conserved by any unitary dynamics. We further constrain the time evolution by deriving constraints from the de Sitter isometries and show that these reduce to the familiar conformal Ward identities at late times. Finally, we show how the evolution of a state from the conformal boundary into the bulk can be described via a number of "transfer functions" which are analytic outside the horizon for any local interaction. These objects exhibit divergences for particular values of the scalar mass, and we show how such divergences can be removed by a renormalisation of the boundary wavefunction - this is equivalent to performing a "Boundary Operator Expansion" which expresses the bulk operators in terms of regulated boundary operators. Altogether, this improved understanding of the wavefunction in the bulk of de Sitter complements recent advances from a purely boundary perspective, and reveals new structure in cosmological correlators.
_____ Phys.Rev.D 101 (2020) 2, 021502 [1904.05874] _______________________________________
Positivity in the sky: Constraining dark energy and modified gravity from the UV (Scott Melville and Johannes Noller)
Positivity bounds - the consequences of requiring a unitary, causal, local UV completion - place strong restrictions on theories of dark energy and/or modified gravity. We derive and investigate such bounds for Horndeski scalar-tensor theories and for the first time pair these bounds with a cosmological parameter estimation analysis, using CMB, redshift space distortion, matter power spectrum and BAO measurements from the Planck, SDSS/BOSS and 6dF surveys. Using positivity bounds as theoretical priors, we show that their inclusion in the parameter estimation significantly improves the constraints on dark energy/modified gravity parameters. Considering as an example a specific class of models, which are particularly well-suited to illustrate the constraining power of positivity bounds, we find that these bounds eliminate over 60% of the previously allowed parameter space. We also discuss how combining positivity requirements with additional theoretical priors has the potential to further tighten these constraints: for instance also requiring a subluminal speed of gravitational waves eliminates all but 1% of the previously allowed parameter space.
_____ JCAP 09 (2020) 013 [1910.08831] _______________________________________
Novel Screening with Two Bodies: Summing the ladder in disformal scalar-tensor theories (Anne-Christine Davis and Scott Melville)
When augmenting our cosmological models or gravitational theories with an additional light scalar field, any coupling between matter and this scalar can affect the orbital motion of binary systems. Ordinarily, the new force mediated by the scalar can be naturally the same order of magnitude as the usual gravitational force and therefore is tightly constrained. We show that a disformal coupling between the scalar and matter can lead to a novel screening mechanism in which these fifth forces are suppressed by several orders of magnitude at sufficiently small separations and large relative velocities (such as solar system scales). This is a result of resumming a class of ladder diagrams, which suppresses the propagation of scalar signals between the two bodies. Moreover, we are able to relate potential ambiguities in this resummation to non-perturbative effects (which are invisible to perturbation theory). As a result, solar system tests and future gravitational wave observations can now be used to place meaningful constraints on scalar-tensor theories with disformal couplings. We exemplify this using observational bounds on the precession of planetary orbits.
_____ Phys.Rev.Lett. 121 (2018) 22, 221101 [1806.09417] _______________________________________
Gravitational Rainbows: LIGO and Dark Energy at its Cutoff (Claudia de Rham and Scott Melville)
The recent direct detection of a neutron star merger with optical counterpart has been used to severely constrain models of dark energy that typically predict a modification of the speed of gravitational waves. We point out that the energy scales observed at LIGO, and the particular frequency of the neutron star event, lie very close to the strong coupling scale or cutoff associated with many dark energy models. While it is true that at very low energies one expects gravitational waves to travel at a speed different than light in these models, the same is no longer necessarily true as one reaches energy scales close to the cutoff. We show explicitly how this occurs in a simple model with a known partial UV completion. Within the context of Horndeski, we show how the operators that naturally lie at the cutoff scale can affect the speed of propagation of gravitational waves and bring it back to unity at those scales. We discuss how further missions including LISA and PTAs could play an essential role in testing such models.
_____ JHEP 03 (2018) 011 [1706.02712] _______________________________________
UV complete me: Positivity Bounds for Particles with Spin (Claudia de Rham, Scott Melville, Andrew J. Tolley and Shuang-Yong Zhou)
For a low energy effective theory to admit a standard local, unitary, analytic and Lorentz-invariant UV completion, its scattering amplitudes must satisfy certain inequalities. While these bounds are known in the forward limit for real polarizations, any extension beyond this for particles with nonzero spin is subtle due to their non-trivial crossing relations. Using the transversity formalism (i.e. spin projections orthogonal to the scattering plane), in which the crossing relations become diagonal, these inequalities can be derived for 2-to-2 scattering between any pair of massive particles, for a complete set of polarizations at and away from the forward scattering limit. This provides a set of powerful criteria which can be used to restrict the parameter space of any effective field theory, often considerably more so than its forward limit subset alone.