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Original Hořava Formulation vs Consistent Extension (BPS)

Hořava-Lifshitz Gravity· within family

	Original Hořava Formulation Frontier	Consistent Extension (BPS) Frontier
Proposed	2009	2009 / 2011
Key figures	Petr Hořava	Diego Blas, Oriol Pujolàs, Sergey Sibiryakov
In one sentence	Petr Hořava proposed in 2009 that quantum gravity becomes power-counting renormalizable if the symmetry between space and time is broken at high energies. The theory has anisotropic scaling: time scales as one power and space scales as three powers under a renormalization-group transformation, a so-called z=3 Lifshitz point. The cost is that full Lorentz invariance, foundational to general relativity and the Standard Model, becomes an emergent low-energy property rather than a fundamental symmetry. The paper is widely cited and inaugurated a substantial research program.	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.
Predictions	Lorentz invariance is broken at high energies above the breaking scale; deviations from special relativity should be detectable in principle at sufficiently high-energy probes The theory is power-counting renormalizable in the ultraviolet, so quantum corrections do not produce uncontrolled divergences in the deep UV Anisotropic scaling between space and time produces specific signatures in early-universe physics, including modifications to the spectrum of primordial perturbations Scalar graviton modes are present in addition to the standard tensor modes of general relativity; these modes have specific consequences for gravitational-wave physics and for solar-system tests	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)
Where it breaks	The scalar graviton mode does not decouple at low energies, creating problems for the recovery of general relativity in the infrared The projectable version of the theory (the version where the function setting the pace of time is allowed to vary only across time, not across space) becomes mathematically intractable at everyday energies: the interactions between modes grow so strong that the step-by-step approximation methods physicists rely on stop working, which makes predictions hard to extract Lorentz violation at any energy is strongly constrained by precision experiments; the breaking scale must be very high to evade existing bounds, which limits the theory's phenomenological appeal Most modern work on Hořava-Lifshitz gravity addresses fundamental issues with the original formulation rather than developing the framework as a final theory	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
Key unresolved problem	The extra-mode problem: the original theory carries a spare gravity ripple, the scalar graviton, which does not decouple at everyday energies, so it never quite settles back into ordinary general relativity without bolting on extra pieces.	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.
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Original Hořava Formulation

2009 · Frontier

Consistent Extension (BPS)

2009 / 2011 · Frontier

Proposed

2009

2009 / 2011

Key figures

Petr Hořava

Diego Blas, Oriol Pujolàs, Sergey Sibiryakov

In one sentence

Petr Hořava proposed in 2009 that quantum gravity becomes power-counting renormalizable if the symmetry between space and time is broken at high energies. The theory has anisotropic scaling: time scales as one power and space scales as three powers under a renormalization-group transformation, a so-called z=3 Lifshitz point. The cost is that full Lorentz invariance, foundational to general relativity and the Standard Model, becomes an emergent low-energy property rather than a fundamental symmetry. The paper is widely cited and inaugurated a substantial research program.

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*.

Predictions

Lorentz invariance is broken at high energies above the breaking scale; deviations from special relativity should be detectable in principle at sufficiently high-energy probes
The theory is power-counting renormalizable in the ultraviolet, so quantum corrections do not produce uncontrolled divergences in the deep UV
Anisotropic scaling between space and time produces specific signatures in early-universe physics, including modifications to the spectrum of primordial perturbations
Scalar graviton modes are present in addition to the standard tensor modes of general relativity; these modes have specific consequences for gravitational-wave physics and for solar-system tests

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)

Where it breaks

The scalar graviton mode does not decouple at low energies, creating problems for the recovery of general relativity in the infrared
The projectable version of the theory (the version where the function setting the pace of time is allowed to vary only across time, not across space) becomes mathematically intractable at everyday energies: the interactions between modes grow so strong that the step-by-step approximation methods physicists rely on stop working, which makes predictions hard to extract
Lorentz violation at any energy is strongly constrained by precision experiments; the breaking scale must be very high to evade existing bounds, which limits the theory's phenomenological appeal
Most modern work on Hořava-Lifshitz gravity addresses fundamental issues with the original formulation rather than developing the framework as a final theory

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

Key unresolved problem

The extra-mode problem: the original theory carries a spare gravity ripple, the scalar graviton, which does not decouple at everyday energies, so it never quite settles back into ordinary general relativity without bolting on extra pieces.

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.

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