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Abstract
Starting from the most general scalar-tensor theory with second-order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on Friedmann-Lemaître-Robertson-Walker backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor, and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining nontrivial cosmological solutions.
Highlights
In a little known paper published in 1974, G.W
Starting from the most general scalar-tensor theory with second order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent selftuning mechanism on FLRW backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor and the Gauss-Bonnet combination
Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincare invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem
Summary
For a remotely viable cosmology it should be dynamical in the sense that we can evolve towards H2 + κ/a2 = 0 rather than having it be true at all times This imposes the condition that at least one of the An should be non-vanishing. With Vg′eorge ≡ 0 allowed, if and only if there exist other non-vanishing potentials It follows that the self-tuning version of Horndeski’s theory must take the form. Note the presence of the bare cosmological constant term ρbΛare which can always be absorbed into a renormalisation of the vacuum energy (contained within Sm). This serves as a good consistency check of our derivation. Such a term had to be allowed by the self-tuning theories – if it had not been there it would have amounted to fine tuning the vacuum energy
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