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Consistent Extension (BPS) vs Foundational Analysis (Sotiriou-Visser-Weinfurtner)

Hořava-Lifshitz Gravity· within family

	Consistent Extension (BPS) Frontier	Foundational Analysis (Sotiriou-Visser-Weinfurtner) Frontier
Proposed	2009 / 2011	2009
Key figures	Diego Blas, Oriol Pujolàs, Sergey Sibiryakov	Thomas P. Sotiriou, Matt Visser, Silke Weinfurtner
In one sentence	Blas, Pujolàs, and Sibiryakov proposed in 2009 a non-projectable extension of Hořava-Lifshitz gravity that addresses the scalar-graviton pathologies of the original formulation. By allowing the lapse function to depend on space as well as time, the theory gains an additional symmetry-breaking pattern that decouples the problematic scalar mode at low energies. The 2009 paper, Consistent Extension of Horava Gravity, is the most-cited Hořava extension at roughly 628 INSPIRE citations; the colloquial 'healthy extension' name originates in their 2011 follow-up Models of non-relativistic quantum gravity: The Good, the bad and the healthy.	Sotiriou, Visser, and Weinfurtner published in 2009 a systematic theoretical analysis of Hořava-Lifshitz gravity that identified which formulations are phenomenologically viable Lorentz-violating quantum gravity candidates. Their paper Phenomenologically viable Lorentz-violating quantum gravity mapped the parameter space of allowed extensions, classified the constraints from solar-system tests and astrophysical observations, and established the framework for subsequent technical work in the field. The paper has 294 INSPIRE citations and represents the canonical early systematic analysis.
Predictions	Non-projectable Hořava gravity has a scalar graviton mode with a mass that depends on the parameters of the extension; the mode decouples from low-energy physics The theory recovers something close to general relativity in the infrared limit, modulo Lorentz-violating corrections that vanish at sufficiently low energies Modified gravitational-wave dispersion relations arise from the Lorentz-violating structure and are in principle testable by binary-inspiral gravitational-wave observations Specific cosmological signatures arise in early-universe physics (modifications to the primordial perturbation spectrum that depend on the parameters of the extension)	Phenomenologically viable Hořava-Lifshitz gravity requires non-projectable formulations that decouple the scalar graviton mode at low energies Specific parameter constraints from solar-system tests (perihelion shifts, light bending) place upper bounds on Lorentz-violating couplings Gravitational-wave dispersion relations differ from standard [[general relativity]] at high frequencies; binary-inspiral observations constrain the deviation Pulsar timing constraints on Lorentz-violating gravity (Will and others, in the broader test-of-gravity literature) bound the SVW framework's parameter space
Where it breaks	The non-projectable extension introduces additional free parameters; the theory's predictive power is correspondingly reduced Lorentz violation remains the foundational feature, and the empirical constraints on Lorentz violation from precision experiments continue to push the breaking scale higher The 2011 'healthy' classification is technical and the boundary between healthy and unhealthy extensions depends on parameter choices that may not have natural priors The framework still does not produce a complete UV completion of gravity; it addresses the IR pathologies but the high-energy physics remains the same as the original Hořava theory	The SVW analysis addresses theoretical viability and phenomenological constraints but does not address the deeper UV-completion question; the framework inherits the same UV physics as the original Hořava 2009 formulation Some authors have argued that SVW does not capture all the subtleties of the modern BPS-type non-projectable extensions; the 2009 framework predates the 2011 BPS Good, the bad, healthy classification Phenomenological constraints continue to push the Lorentz-violating couplings into corners of parameter space where the theory is hard to distinguish from general relativity; whether this is a robustness feature or a sign of being constrained out is debated The framework does not produce distinctive observational signatures that would unambiguously favor Hořava-Lifshitz over Asymptotic Safety, Causal Dynamical Triangulation, or other quantum-gravity candidates
Key unresolved problem	The too-many-knobs problem, the repaired non-projectable version adds free parameters with no natural values to guess, weakening its predictions, while experiments testing Lorentz invariance keep squeezing where any symmetry-breaking could hide.	The no-fingerprint problem: the framework offers no distinctive observational signature, no clean fingerprint, that would tell Hořava-Lifshitz gravity apart from plain general relativity or from rival quantum-gravity candidates.
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Consistent Extension (BPS)

2009 / 2011 · Frontier

Foundational Analysis (Sotiriou-Visser-Weinfurtner)

2009 · Frontier

Proposed

2009 / 2011

2009

Key figures

Diego Blas, Oriol Pujolàs, Sergey Sibiryakov

Thomas P. Sotiriou, Matt Visser, Silke Weinfurtner

In one sentence

Blas, Pujolàs, and Sibiryakov proposed in 2009 a non-projectable extension of Hořava-Lifshitz gravity that addresses the scalar-graviton pathologies of the original formulation. By allowing the lapse function to depend on space as well as time, the theory gains an additional symmetry-breaking pattern that decouples the problematic scalar mode at low energies. The 2009 paper, *Consistent Extension of Horava Gravity*, is the most-cited Hořava extension at roughly 628 INSPIRE citations; the colloquial 'healthy extension' name originates in their 2011 follow-up *Models of non-relativistic quantum gravity: The Good, the bad and the healthy*.

Sotiriou, Visser, and Weinfurtner published in 2009 a systematic theoretical analysis of Hořava-Lifshitz gravity that identified which formulations are phenomenologically viable Lorentz-violating quantum gravity candidates. Their paper *Phenomenologically viable Lorentz-violating quantum gravity* mapped the parameter space of allowed extensions, classified the constraints from solar-system tests and astrophysical observations, and established the framework for subsequent technical work in the field. The paper has 294 INSPIRE citations and represents the canonical early systematic analysis.

Predictions

Non-projectable Hořava gravity has a scalar graviton mode with a mass that depends on the parameters of the extension; the mode decouples from low-energy physics
The theory recovers something close to general relativity in the infrared limit, modulo Lorentz-violating corrections that vanish at sufficiently low energies
Modified gravitational-wave dispersion relations arise from the Lorentz-violating structure and are in principle testable by binary-inspiral gravitational-wave observations
Specific cosmological signatures arise in early-universe physics (modifications to the primordial perturbation spectrum that depend on the parameters of the extension)

Phenomenologically viable Hořava-Lifshitz gravity requires non-projectable formulations that decouple the scalar graviton mode at low energies
Specific parameter constraints from solar-system tests (perihelion shifts, light bending) place upper bounds on Lorentz-violating couplings
Gravitational-wave dispersion relations differ from standard [[general relativity]] at high frequencies; binary-inspiral observations constrain the deviation
Pulsar timing constraints on Lorentz-violating gravity (Will and others, in the broader test-of-gravity literature) bound the SVW framework's parameter space

Where it breaks

The non-projectable extension introduces additional free parameters; the theory's predictive power is correspondingly reduced
Lorentz violation remains the foundational feature, and the empirical constraints on Lorentz violation from precision experiments continue to push the breaking scale higher
The 2011 'healthy' classification is technical and the boundary between healthy and unhealthy extensions depends on parameter choices that may not have natural priors
The framework still does not produce a complete UV completion of gravity; it addresses the IR pathologies but the high-energy physics remains the same as the original Hořava theory

The SVW analysis addresses theoretical viability and phenomenological constraints but does not address the deeper UV-completion question; the framework inherits the same UV physics as the original Hořava 2009 formulation
Some authors have argued that SVW does not capture all the subtleties of the modern BPS-type non-projectable extensions; the 2009 framework predates the 2011 BPS *Good, the bad, healthy* classification
Phenomenological constraints continue to push the Lorentz-violating couplings into corners of parameter space where the theory is hard to distinguish from general relativity; whether this is a robustness feature or a sign of being constrained out is debated
The framework does not produce distinctive observational signatures that would unambiguously favor Hořava-Lifshitz over Asymptotic Safety, Causal Dynamical Triangulation, or other quantum-gravity candidates

Key unresolved problem

The too-many-knobs problem, the repaired non-projectable version adds free parameters with no natural values to guess, weakening its predictions, while experiments testing Lorentz invariance keep squeezing where any symmetry-breaking could hide.

The no-fingerprint problem: the framework offers no distinctive observational signature, no clean fingerprint, that would tell Hořava-Lifshitz gravity apart from plain general relativity or from rival quantum-gravity candidates.

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