[Paper Review] Horava-Lifshitz gravity and Solar System orbital motions

Lorenzo Iorio, Matteo Luca Ruggiero|arXiv (Cornell University)|Sep 14, 2009

Relativity and Gravitational Theory10 citations

TL;DR

This paper investigates the effects of Horava-Lifshitz gravity on Solar System planetary orbits by analyzing the secular pericentre precession induced by the Kehagias-Sfetsos solution, a weak-field analog of the Schwarzschild black hole. It finds that planetary observations constrain the dimensionless HL parameter 𝜓₀ to 10⁻¹² (Mercury) to 10⁻²⁴ (Pluto), but cannot explain the Pioneer anomaly beyond 20 AU.

ABSTRACT

We focus on Horava-Lifshitz (HL) theory of gravity, and, in particular, on the Kehagias and Sfetsos s solution that is the analog of Schwarzschild black hole of General Relativity. In the weak-field and slow-motion approximation we analytically work out the secular precession of the longitude of the pericentre of a test particle induced by this solution. Its analytical form is different from that of the general relativistic Einstein's pericentre precession. Then, we compare it to the latest determinations of the corrections to the standard Newtonian/ Einsteinian planetary perihelion precessions recently estimated by E.V. Pitjeva with the EPM2008 ephemerides. It turns out that the planets of the solar system, taken singularly one at a time, allow to put lower bounds on the adimensional HL parameter \psi_0 of the order of 10^-12 (Mercury) 10^-24 (Pluto). They are not able to account for the Pioneer anomalous acceleration for r > 20 AU.

Motivation & Objective

• To assess whether Horava-Lifshitz gravity can account for anomalous orbital precessions in the Solar System.
• To compare predictions of the Kehagias-Sfetsos solution in HL gravity with precise planetary ephemerides.
• To derive observational bounds on the dimensionless HL parameter 𝜓₀ using planetary perihelion precession data.
• To test whether HL gravity can explain the Pioneer anomalous acceleration beyond 20 AU.

Proposed method

• Adopting the weak-field and slow-motion approximation of Horava-Lifshitz gravity to derive the orbital precession of a test particle.
• Using the Kehagias-Sfetsos solution as the gravitational background, analogous to the Schwarzschild solution in general relativity.
• Analytically computing the secular precession of the longitude of the pericentre in this HL framework.
• Comparing the theoretical precession rate with the latest EPM2008 ephemerides-based estimates of planetary perihelion corrections.
• Applying observational constraints from individual planets to bound the dimensionless HL parameter 𝜓₀.
• Evaluating the model's compatibility with the Pioneer anomalous acceleration at heliocentric distances r > 20 AU.

Experimental results

Research questions

• RQ1 Does Horava-Lifshitz gravity predict a pericentre precession rate consistent with the latest planetary ephemerides data?
• RQ2 What are the observational bounds on the dimensionless HL parameter 𝜓₀ derived from planetary orbital motions?
• RQ3 Can the Kehagias-Sfetsos solution in HL gravity account for the Pioneer anomalous acceleration at r > 20 AU?
• RQ4 How does the HL-induced precession differ analytically from the Einsteinian perihelion precession in general relativity?
• RQ5 What is the sensitivity of different planets to the HL parameter 𝜓₀, and how do their constraints compare?

Key findings

• The Kehagias-Sfetsos solution in Horava-Lifshitz gravity induces a pericentre precession rate that differs analytically from the general relativistic prediction.
• Mercury provides the tightest constraint on the dimensionless HL parameter 𝜓₀, yielding a bound of approximately 10⁻¹².
• Pluto provides the loosest constraint, yielding a bound of approximately 10⁻²⁴ on the dimensionless HL parameter 𝜓₀.
• The constraints from individual planets are insufficient to explain the Pioneer anomalous acceleration for heliocentric distances r > 20 AU.
• The model does not account for the Pioneer anomaly beyond 20 AU, as the required 𝜓₀ values would be inconsistent with planetary orbital data.