Cosmological perturbations in Horava-Lifshitz gravity

Journal Article · Thu Apr 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.083508· OSTI ID:21409565

Xian, Gao; Yi, Wang ^[1]; Brandenberger, R ^[2]; Riotto, A ^[3]

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1. Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, No. 55, Zhong-Guan-Cun East Road, Hai-Dian District, Beijing 100080 (China)
2. Department of Physics, McGill University, Montreal, QC, H3A 2T8 (Canada)
3. Theory Division, CERN, CH-1211 Geneve 23 (Switzerland)

We study cosmological perturbations in Horava-Lifshitz Gravity, a recently proposed potentially ultraviolet-complete quantum theory of gravity. We consider scalar metric fluctuations about a homogeneous and isotropic space-time. Starting from the most general metric, we work out the complete second order action for the perturbations. We then make use of the residual gauge invariance and of the constraint equations to reduce the number of dynamical degrees of freedom. At first glance, it appears that there is an extra scalar metric degree of freedom. However, introducing the Sasaki-Mukhanov variable, the combination of spatial metric fluctuation and matter inhomogeneity for which the action in general relativity has canonical form, we find that this variable has the standard time derivative term in the second order action, and that the extra degree of freedom is nondynamical. The limit {lambda}{yields}1 is well behaved, unlike what is obtained when expanding about Minkowski space-time. Thus, there is no strong coupling problem for Horava-Lifshitz gravity when considering cosmological solutions. We also compute the spectrum of cosmological perturbations. If the potential in the action is taken to be of 'detailed balance' form, we find a cancellation of the highest derivative terms in the action for the curvature fluctuations. As a consequence, the initial spectrum of perturbations will not be scale-invariant in a general space-time background, in contrast to what happens when considering Horava-Lifshitz matter leaving the gravitational sector unperturbed. However, if we break the detailed balance condition, then the initial spectrum of curvature fluctuations is indeed scale-invariant on ultraviolet scales. As an application, we consider fluctuations in an inflationary background and draw connections with the 'trans-Planckian problem' for cosmological perturbations. In the special case in which the potential term in the action is of detailed balance form and in which {lambda}=1, the equation of motion for cosmological perturbations in the far UV takes the same form as in general relativity. However, in general the equation of motion is characterized by a modified dispersion relation.

• OSTI ID: 21409565
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DEGREES OF FREEDOM
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
DISTURBANCES
ELECTROMAGNETIC RADIATION
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FLUCTUATIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
METRICS
MINKOWSKI SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM GRAVITY
RADIATIONS
RELATIVITY THEORY
SPACE
SPACE-TIME
SPECTRA
STRONG-COUPLING MODEL
ULTRAVIOLET RADIATION
VARIATIONS