Cosmological perturbations in conformal gravity II

Abstract

In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a flat background. For this construction to hold it is not necessary that the perturbative geometry associated with the fluctuations itself be conformal to flat. Using this construction we show that in a conformal Robertson-Walker cosmology early universe fluctuations grow as $t^4$. We present the scalar, vector, tensor decomposition of the fluctuations in the conformal theory, and compare and contrast our work with the analogous treatment of fluctuations in the standard Einstein gravity theory.

arXiv comment39 pages, expanded version. Final version, to appear in Phys. Rev. D

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• Gauging scale symmetry and inflation: Weyl versus Palatini gravity
• Conformal gravity does not predict flat galaxy rotation curves
• Exact solution to perturbative conformal cosmology in the recombination era
• Three-dimensional and four-dimensional scalar, vector, tensor cosmological fluctuations and the cosmological decomposition theorem
• Critique of the use of geodesics in astrophysics and cosmology
• Cosmological Fluctuations on the Light Cone
• Exact solution to perturbative conformal cosmology from recombination until the current era
• Imprint of galactic rotation curves and metric fluctuations on the recombination era anisotropy