A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
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The galileon as a local modification of gravity
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abstract
In the DGP model, the ``self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar \pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar system tests. Our generalization involves an internal ``galilean'' invariance, under which \pi's gradient shifts by a constant. This symmetry constrains the structure of the \pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts. We show that for such theories in fact there are ``self-accelerating'' deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are also stable against small fluctuations. [Short version for arxiv]
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representative citing papers
Gravitational memory from hairy binary black hole mergers in scalar-Gauss-Bonnet gravity differs from GR by a few percent due to altered nonlinear dynamics, with direct scalar contributions suppressed, and including memory increases GR-sGB mismatch by more than an order of magnitude.
Dynamical dark energy imprints O(1) shifts on black hole quasi-normal modes via cosmological hair, enabling constraints at 10^{-2} (LVK) to 10^{-4} (LISA) precision using the cubic Galileon as example.
Stable black hole solutions with cosmological scalar hair are explicitly derived in the cubic Galileon theory, recovering cosmological behavior at large distances and regular short-range dynamics.
Non-Abelian conformal anomalies are classified via Stora-Zumino descent from the Euler class, placing them on equal footing with perturbative anomalies and enabling WZW terms for anomaly matching.
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
In Ricci-coupled scalar-Gauss-Bonnet gravity, the change in scalar charge during binary black hole mergers generates a scalar memory contribution that modifies the total memory signal on observable timescales.
The boundary of the scalar S-matrix island divides into phases with universal high-energy asymptotics and resonance content, each corresponding to a different UV completion mechanism for gapped scalars.
A master screening equation is derived for luminal Horndeski gravity that recovers Vainshtein and Chameleon mechanisms and introduces Phaedrus screening with screening radius scaling linearly with source mass.
In DHOST theories with Gauss-Bonnet and Weyl operators, gauge symmetry invariance conditions are identical to Hamiltonian constraints eliminating ghosts.
Numerical simulations show ghost-normal scalar systems can remain dynamically bounded for long times when initial data is ultraviolet-dominated and low-amplitude, with some nonlinear potentials creating transient metastable states.
Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.
A review thesis covering Mukhanov parametrization, general scalar-tensor theories, and new slow-roll techniques for canonical and noncanonical inflation observables.
citing papers explorer
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Kontorovich-Lebedev-Fourier Space for de Sitter Correlators
A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
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Gravitational Memory from Hairy Binary Black Hole Mergers
Gravitational memory from hairy binary black hole mergers in scalar-Gauss-Bonnet gravity differs from GR by a few percent due to altered nonlinear dynamics, with direct scalar contributions suppressed, and including memory increases GR-sGB mismatch by more than an order of magnitude.
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Testing Dark Energy with Black Hole Ringdown
Dynamical dark energy imprints O(1) shifts on black hole quasi-normal modes via cosmological hair, enabling constraints at 10^{-2} (LVK) to 10^{-4} (LISA) precision using the cubic Galileon as example.
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Stable black hole solutions with cosmological hair
Stable black hole solutions with cosmological scalar hair are explicitly derived in the cubic Galileon theory, recovering cosmological behavior at large distances and regular short-range dynamics.
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Non-Abelian and Type-A Conformal Anomalies from Euler Descent
Non-Abelian conformal anomalies are classified via Stora-Zumino descent from the Euler class, placing them on equal footing with perturbative anomalies and enabling WZW terms for anomaly matching.
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Degenerate higher-order scalar-tensor theories in metric-affine gravity
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
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Scalar memory from compact binary coalescences
In Ricci-coupled scalar-Gauss-Bonnet gravity, the change in scalar charge during binary black hole mergers generates a scalar memory contribution that modifies the total memory signal on observable timescales.
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The Phases of the Scalar S-Matrix Island
The boundary of the scalar S-matrix island divides into phases with universal high-energy asymptotics and resonance content, each corresponding to a different UV completion mechanism for gapped scalars.
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A Master Equation for Screening in Luminal Horndeski Gravity
A master screening equation is derived for luminal Horndeski gravity that recovers Vainshtein and Chameleon mechanisms and introduces Phaedrus screening with screening radius scaling linearly with source mass.
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AI--Assisted Exploration: DHOST Theories without Quantum Ghosts
In DHOST theories with Gauss-Bonnet and Weyl operators, gauge symmetry invariance conditions are identical to Hamiltonian constraints eliminating ghosts.
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Numerical Investigations of Stable Dynamics in the Presence of Ghosts
Numerical simulations show ghost-normal scalar systems can remain dynamically bounded for long times when initial data is ultraviolet-dominated and low-amplitude, with some nonlinear potentials creating transient metastable states.
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Note on hidden zeros and expansions of tree-level amplitudes
Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.
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The Quintom theory of dark energy after DESI DR2
This review traces the history of dynamical dark energy, presents the no-go theorem against single-field crossing of w = -1, and surveys viable Quintom constructions including multi-field models and modified gravity in light of DESI DR2 hints.
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Noncanonical Approaches To Inflation
A review thesis covering Mukhanov parametrization, general scalar-tensor theories, and new slow-roll techniques for canonical and noncanonical inflation observables.