Exact cosmological solutions of scale-invariant gravity theories

Abstract

We have found new anisotropic vacuum solutions for the scale-invariant gravity theories which generalise Einstein's general relativity to a theory derived from the Lagrangian $R^{1+\delta }$. These solutions are expanding universes of Kasner form with an initial spacetime singularity at $t=0$ and exist for $-1/2<\delta <1/4$ but possess different Kasner index relations to the classic Kasner solution of general relativity to which they reduce when $\delta =0$. These solutions are unperturbed by the introduction of non-comoving perfect-fluid matter motions if $p<\rho$ on approach to the singularity and should not exhibit an infinite sequence of chaotic Mixmaster oscillations when $\delta >0$.

7 pages, 1 figure

References in corpus (2)

• The Power of General Relativity
• Cosmological dynamics of R^n gravity

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