Anisotropic Weyl symmetry and cosmology

Abstract

We construct an anisotropic Weyl invariant theory in the ADMformalism and discuss its cosmological consequences. It extends theoriginal anisotropic Weyl invariance of Hořava-Lifshitz gravityusing an extra scalar field. The action is invariant under theanisotropic transformations of the space and time metric componentswith an arbitrary value of the critical exponent z. One of theinteresting features is that the cosmological constant termmaintains the anisotropic symmetry for z = −3. We also include thecosmological fluid and show that it can preserve the anisotropicWeyl invariance if the equation of state satisfies P = zρ/3.Then, we study cosmology of the Einstein-Hilbert-anisotropic Weyl(EHaW) action including the cosmological fluid, both with or withoutanisotropic Weyl invariance. The correlation of the criticalexponent z and the equation of state parameter ω̄provides a new perspective of the cosmology. It is also shown thatthe EHaW action admits a late time accelerating universe for anarbitrary value of z when the anisotropic conformal invariance isbroken, and the anisotropic conformal scalar field is interpreted asa possible source of dark energy.