http://arxiv.org/abs/1907.02928

We generalise Einstein’s formulation of the traceless Einstein equations to $f(R)$ gravity theories. As in the traceless version of general relativity, we find that in traceless $f(R)$ gravity there is no vacuum energy cosmological constant problem. The cosmological constant is a mere integration constant that is unconnected to any vacuum energy density or constant term in the gravitational lagrangian. We obtain the integrability condition for the cosmological constant to appear as an integration constant without a connection to any vacuum energy density. We show that, in $D$% -dimensional spacetime, traceless higher-order gravity is conformally equivalent to general relativity and a scalar field $\phi $ with a potential given by the scale-invariant form: $V(\phi )=\frac{D-2}{4D}Re^{-\phi }$, where $\phi =[2/(D-2)]\ln f^{\prime }(R)$. Unlike in the conformal equivalent of full general relativity, flat potentials are found to be possible in all spacetime dimensions for polynomial lagrangians of all orders. Hence, we can solve the cosmological constant vacuum energy problem and have accelerated inflationary expansion in the very early universe with a very small cosmological constant at late times for a wide range of traceless theories. Fine-tunings required in traceless general relativity or standard non-traceless $f(R)$ theories of gravity are avoided. We show that the predictions of the scale-invariant conformal potential are completely consistent with microwave background observational data.

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J. Barrow and S. Cotsakis
Mon, 8 Jul 19
15/43

Comments: 17 pages