A new cosmological finding challenging General Relativity

I learned this morning about highly interesting new results challenging general relativity based cosmology. Sean Carroll and Lubos Motl commented the article A weak lensing detection of a deviation from General Relativity on cosmic scales by Rachel Bean. The article Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges by Chung-Pei Ma and Edmund Bertschinger allows to understand the mathematics related to the cosmological perturbation theory necessary for a deeper understanding of the article of Bean.

The message of the article is that under reasonable assumptions General Relativity leads to a wrong prediction for cosmic density perturbations in the scenario involving cold dark matter and cosmological constant to explain accelerated expansion. The following represents my first impressions after reading the article of Rachel Bean and the paper about cosmological perturation theory.

1. Assumptions

"Reasonable" means at least following assumptions about the perturbation of the metric and of energy momentum tensor.

1. The perturbations to the Robertson-Walker metric contain only two local scalings parameterized as dτ²→ (1+2Ψ)dτ² and dxⁱdx_i→ (1-2Φ)dxⁱdx_i. Vector perturbations and tensor perturbations (gravitational radiation classically) are neglected.

2. The traceless part (in 3-D sense) of the perturbation of energy momentum tensor vanishes. Geometrically this means that the perturbation does not contain a term for which the contribution to 3-curvature would vanish. In hydrodynamical picture the vanishing of this term would mean that the mass current for the perturbation contains only a term representing incompressible flow. During the period when matter and radiation were coupled this assumption makes sense. The non-vanishing of this term would mean the presence of a flow component - say radiation of some kind- which couples only very weakly to the background matter. Neutrinos would represent one particular example of this kind of contribution.

3. The model of cosmology used is so called ΛCDM (cosmological constant and cold dark matter).

These assumptions boil down to a simple equation

η= Φ/Ψ=1.

2. The results

The prediction can be tested and Rachel Bean indeed did it.

1. Ψ makes itself visible in the motion of massive objects such as galaxies since they couple to Newton's potential. This motion in turn makes itself visible as detected modifications of the microwave background from ideal. The so called Integrated Sachs-Wolfe effect is due to the redshift of microwave photons between last surface of scattering and Earth and caused by the gravitational fields of massive objects. Ordinary matter does not contribute to this effect but dark energy does.

2. Φ makes itself visible in the motion of light. The so called Weak lensing effect distorts the images of the distant objects: apparent size is larger than the real one and there is also distortion of the shape of the object.

From these two data sources Rachel Bean deduces that η differs significantly from the GRT value and concentrates around η=1/3 meaning that the scaling of the time component of the metric perturbation is roughly 3 times larger than for spatial scaling.

3. What could be the interpretation of the discrepancy?

What η=1/3 could mean physically and mathematically?

1. From Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges one learns that for neutrinos causing shear stress one has Φ= (1+2R_ν/5)Ψ, where R_ν is mass fraction of neutrinos: hence η should increase rather than decrease! If this formula generalizes, a negative mass fraction R= -5/3 would be present! Something goes badly wrong if one tries to interpret the result in terms of the perturbations of the density of matter - irrespective of whether it is visible or dark!

2. What about the perturbations of the density of dark energy? Geometrically η=1/3 would mean that the trace of the metric tensor defined in terms of the background metric is not affected. This means conservation of the metric determinant for the deformations so that small four-volumes are not affected. As a consequence, the interaction term T^αβ δg_αβ receives a contribution from G^αβ but not from the cosmological term Λg^αβ. This would suggest that the perturbation is not that of matter but of the vacuum energy density for which one would have

   Λg^αβ δ g_αβ=0 .

The result would not challenge General Relativity (if one accepts the notion of dark energy) but only the assumption about the character of the density perturbation. Instead of matter it would be the density of dark energy which is perturbed.

4. TGD point of view

What TGD could say about this.

1. In TGD framework one has many-sheeted space-time, dark matter hierarchy represented by the book like structure of the generalized imbedding space, and dark energy is replaced with dark matter at pages of the book with gigantic Planck constant so that the Compton lengths of ordinary particles are gigantic and the density of matter is constant in long scales so that one can speak about cosmological constant in General Relativity framework. The periods with vanishing 3-curvature are replaced by phase transitions changing the value of Planck constant at some space-time sheets and inducing lengthening of quantum scales: the cosmology during this kind of periods is fixed apart from the parameter telling the maximal duration of the period. Also early inflationary period would correspond to his kind of phase transition. Obviously, many new elements are involved so that it is difficult to say anything quantitative.

2. Quantum criticality means the existence of deformations of space-time surface for which the second variation of Kähler action vanishes. The first guess would be that cosmic perturbations correspond to this kind of deformations. In principle this would allow a quantitative modeling in TGD framework. Robertson-Walker metrics correspond to vacuum extremals of Kähler action with infinite spectrum of this kind of deformations (this is expected to hold true quite generally although deformations disappear as one deforms more and more the vacuum extremal).

3. Why the four-volumes defined by the Robertson-Walker metric should remain invariant under these perturbations as η=1/3 would suggest? Are the critical perturbations of the energy momentum tensor indeed those for the dominating part of dark matter with gigantic values of Planck constant and having an effective representation in terms of cosmological constant in GRT so that the above mentioned equations implying conservation of four-volume result as a consequence?

4. The most natural interpretation for the space-time sheets mediating gravitation is as magnetic flux tubes connecting gravitationally interacting objects and thus string like objects of astrophysical size. For this kind of objects the effectively 2-dimensional energy momentum tensor is proportional to the induced metric. Could this mean -as I proposed many years ago when I still took seriously the notion of the cosmological constant as something fundamental in TGD framework- that in the GRT description based on the replacement string like objects with energy momentum tensor the resulting energy momentum tensor is proportional to the induced metric? String tension would explain the negative pressure preventing the identification of dark energy in terms of ordinary particles.

For a background see the chapters TGD and Cosmology and Cosmic Strings of the book "Physics in Many-Sheeted Space-time".