On the Cosmological Constant in a Conformally Transformed Einstein Equation

Zeeya Merali

Dor Gabay and Sijo K. Joseph of Tel Aviv University, in Israel, have a new paper (arXiv:1801.00161), currently submitted for peer review, that they would like to discuss with the FQXi Community.

Here is Dr Joseph's introduction:

The value of the cosmological constant obtained using the General Theory of Relativity and the value suggested by Quantum Field Theory disagree greatly, still this is an unresolved problem in Physics called the cosmological constant problem. Einstein's General theory of relativity is purely a geometric theory, while quantum theory is a probabilistic theory. The way to understand quantum theory in a cosmological context is to reformulate it from a probabilistic theory to a geometrical one. Treating Einstein's theory and the quantum theory on an equal geometrical footing, both theories can be merged together with a Lagrange multiplier. Then the resulting theory can give the cosmological constant contribution from a scalar field and the Lagrange multiplier. The key underlying idea is, one should bring quantum theory into a geometric form before merging the theory with General Theory of Relativity, then both theories are consistent and the cosmological constant can be easily evaluated. These results are highly important, since nobody were able to predict the value of the cosmological constant using quantum mechanical arguments. These results also suggest that we need to go beyond Einstein's General Theory of Relativity to Scalar-Tensor theory to incorporate quantum mechanical effects.

Steve Dufourny

Hi Zeeya, All,

It is relevant these results.Thanks for sharing ,

Regards

AlexandreLutun

The cosmological constant problem remains one of the deepest unresolved issues in physics, highlighting the mismatch between Einstein’s geometric theory of relativity and the probabilistic framework of quantum field theory. As the original post suggests, one promising direction is to reformulate quantum theory in a geometrical language before merging it with general relativity.
In this context, my own independent research has led to the development of a unique cosmological framework: the AQ model. AQ behaves as a robust “clone” of ΛCDM in the domains where the standard model excels—namely, BAO and CMB consistency—yet it simultaneously resolves both the Hubble tension (H₀) and the S₈ tension.
Key results
• H₀ tension: AQ bridges the gap between Planck’s 67.4 ± 0.5 km/s/Mpc and local 73.0 ± 1.0 km/s/Mpc, yielding 70.8 ± 0.9 km/s/Mpc.
• S₈ tension: AQ reconciles Planck’s 0.83 ± 0.01 with local lensing ₀.76 ± 0.02, giving 0.78 ± 0.02.
• BAO & CMB robustness: preserved at the same level as ΛCDM.
These results are unusual in the current landscape: most alternative models address one tension at a time, while AQ resolves both simultaneously without sacrificing empirical consistency. This dual achievement suggests that cosmology can move beyond the current divide, uniting robustness with innovation in a falsifiable framework.
Toward partnership
I present these results not only to share scientific progress but to open the way toward a serious partnership. Institutions such as FQXi have a unique role in supporting independent research that bridges robustness with innovation. My work with AQ demonstrates that such support can translate into tangible advances, and I would welcome the opportunity to explore how this collaboration could be developed further.

Crizpher

I find the central premise of this work particularly compelling: before attempting a unification with General Relativity, quantum theory should first be reformulated in a geometric language comparable to that of gravity.

This raises what seems to me a deeper conceptual question. If a geometric formulation turns out to be more natural or more fundamental than the conventional probabilistic description, should we regard this merely as a mathematical convenience, or could it indicate that quantum probability itself is not fundamental?

In other words, is it possible that the wave function does not primarily describe intrinsic randomness, but rather reflects a deeper geometric structure governing the set of physically accessible states?

If so, the cosmological constant problem might represent more than a mismatch between General Relativity and Quantum Field Theory. It could also reflect the fact that we are describing different aspects of reality through different levels of description—one geometric and potentially fundamental, the other probabilistic and perhaps emergent.

From this perspective, the geometrization of quantum theory may have implications extending well beyond the cosmological constant problem itself. It could suggest that probability emerges from a deeper physical structure rather than constituting one of the basic ingredients of nature.

Do the authors view their geometric reformulation as potentially pointing toward such an interpretation, or do they consider it primarily an alternative mathematical representation of standard quantum theory?