### 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.

- The perturbations to the Robertson-Walker metric contain only two local scalings parameterized as dτ
^{2}→ (1+2Ψ)dτ^{2}and dx^{i}dx_{i}→ (1-2Φ)dx^{i}dx_{i}. Vector perturbations and tensor perturbations (gravitational radiation classically) are neglected. - 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.
- 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.

- 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.
- 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?

- 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! - 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 haveΛg

^{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.

- 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.
- 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).
- 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?
- 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".

## 10 Comments:

Matti, I am glad that you also predicted the value 1/3 on Lubos' blog. Of course, I got called a crackpot for saying this.

I really miss my home in Oxford, because I never felt like I had a home before. Oh, well. I guess we can only soldier on.

The recipe for Lubos relies on single ingredients: take a lot of intellect, a lot of ego, but very little love. Holger Nielsen about whom I told in your blog was baked using different recipe: take a lot of intellect, a lot of love, and forget ego completely.

My very few visits to institutes outbroad have not lasted more than week. I really enjoyed my time in Freiburg near the border of Italy (27 years ago I think!).

I really love to work alone free of all social pressures. Web makes possible communications without this usual fight about who talks and who is forced to only listen.

I work much better when I have people to talk to, and many seminars to stimulate me. Unfortunately, it is not to be.

A very good short explanation of the paper. I am busy doing some work in matlab (university practices) and had not time to read it Your post has given me the ingredients to properly understand what was being discussed in cosmic variance and reference frame.

Thank you Javier! I agree;-).

Finally GR has failed a test. To me GR and Newton's gravity theory failed decades before when the flat rotation curves and comic acceleration were discovered.

The Tully-Fisher Relation, the Mass-Luminosity Relation and my experiments suggest that is not MASS that attracts other mass but the RADIATION leaving it that attracts mass. See http://vixra.org/abs/0907.0018

Peter Fred

Dear Peter,

I did not actually say that GR fails the test, only the assumption that gravitational perturbations can be assigned to cold dark matter fails.

If one assumes that the perturbations of the metric can be assigned to what is identified as dark energy rather than to dark matter, then one can understand eta=1/3.

In also proposed TGD based identification of dark energy explaining the negative pressure in terms of negative string tension of string like objects of astrophysical and cosmological scale.

Concerning your experiment. The claimed 22 per cent increase of gravitational mass due to heating by Delta T of order 100 C is so gigantic effect that it should have made itself visible in every day technology long time ago.

As far as I understood, you did your experiment in non-vacuum. Heating induces fluid flows and these could explain your results. Maybe you could vary the weight of the test body and find how the effect depends on its weight.

Matti said

"...heating by Delta T of order 100 C is so gigantic effect that it should have made itself visible in every day technology"

The effect will go away if the heat does not flow through the test mass in one direction. It is very hard to get a substantial amount of heat to flow through an object on the surface of the earth other than upwards. An essential part of the experiment is the ice placed above the test mass that is housed in a copper container. This enables a lot of heat to move vertically through the test mass quickly.

Just like the test mass, everybody object on the surface of the earth normally has a good deal of heat moving upward through it from the center of the earth to the outer atmosphere.

My tests suggests that this one-directional heat transfer is the reason for the downward center directed force experienced by all objects on the surface of the earth. Can you tell me just how the mass of the earth is able produce an attractive force on every surface object? I can go on and on how the heat transferring though a body produces the gravitational force. Can you further interpret why mass mediates the gravitational force. To me this 300 year old idea of "mass attracting mass" smacks of being a

sterile ad hoc formalism.Maybe a vacuum will kill the radiometer effect. But the gravity that we all observe and feel does not occur in a vacuum. Most planets, the stars, galaxies and clusters have some sort atmospheres where gravity can be observed.

By the way all the above gravitationally bound systems have a heat source at the center and a cold source in their outer parts.

Newton's constant has been tested and variations which are present are very small (Cavendish experiments). These tests have certainly used vacuum in order to eliminate hydrodynamic flows so that the hypothesis that thermal flux or IR radiation is responsible for gravitational force is definitely excluded.

If Newton's law of gravitation were just an ad hoc formalism, it would be very difficult to understand how we have managed to travel to moon.

The general relativistic view is that mass does not mediate gravitational force but makes surrounding space-time curved. This is extremely beautiful and economical description applying at long length scales. Einstein's equations describe what happens in fantastic accuracy and predict new confirmed effects.

The best manner to test your hypothesis is to repeat the experiment in vacuum: if heat radiation is responsible for the effect the use of vacuum should produce same effect. You could also lower the temperature of objects so that it is very low: gravitation should become very low or disappear totally. The experimenters have certainly studied gravitation at low temperatures and should have long ago detected such a dramatic effect.

Matti said

"You could also lower the temperature of objects so that it is very low: gravitation should become very low or disappear totally"

I done this and found the lower the applied power hence the lower the temperature of the heat source, the lower the weight increase. You can see this in the graph's. Just when the power is turned on the observed change of weight is slight. All the graph's rise until the maximum heat output of the heat element is reached. The force graph will quit rising, if the heat cannot move upwards through the test mass.

Matti said "If Newton's law of gravitation were just an ad hoc formalism, it would be very difficult to understand how we have managed to travel to moon."

Ptolemaic geocentric motion can be thought of as a sterile ad hoc formalism. However in the 20th century ships and airplanes were still using geocentric coordinates to navigate the globe. Its an artifact due to the rotation of the earth.

I contend the notion of gravity based on the attractive powers of mass is an artifact due to the fact that if mass has temperature it puts out radiation. You can have a vacuum and the objects inside that vacuum will still have a temperature and hence they will put out radiation. Liquid helium will climb the walls of the container. This could be interpreted as an indication that gravity does not work too well at very low temperatures.

Podkletnov found that when his test mass hovered over a vat of liquid helium and the superconducting disc inside that vat rotated, the test mass hovering above lost weight by 3%.

As Fig 3 shows in my paper when the ~1000 gm hollow copper sphere hovers over the copper container filled with ice, it looses 4.9% of its weight or 54 gm of gravitational mass.

I can come up with arguments that my experiments violate the principle of equivalence--but I am not sure. I am more confident that they go against Einstein's interpretation of what E=mc^2 means. He wrote

"Now we can reverse the relation that an increase of E in the amount of energy must be accompanied by an increase of E/c^2 in the mass. I can easily supply to the mass—for instance, if I heat it by 10 degrees. So why not measure the mass increase, or weight increase, connected with this change? The trouble here is that in the mass increase the enormous factor of c^2 occurs in the denominator of the fraction. In such a case the increase is too small to be measured directly; even with the most sensitive balance."

Instead of dismissing my experiments as being impossible with the prospect of the them being a violation of the principle of equivalence and Einstein's idea of the equivalency of mass and energy, with the latest failure of GR, with the 16 years plus failure to detect the dark matter in the laboratory and with the failure of GR to give a plausible explanation for cosmic acceleration, if I were you I would to begin to think just how beautiful GR is.

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