### Is cosmic expansion a mere coordinate effect?

There is a very interesting article about cosmic expansion or rather a claim about the absence of cosmic expansion.

The argument based on the experimental findings of a team of astrophysicists led by Eric Lerner goes as follows. In non-expanding cosmology and also in the space around us (Earth, Solar system, Milky Way), as similar objects go further away, they look fainter and smaller. Their surface brightness remains constant. In Big Bang theory objects actually should appear fainter but bigger. Therefore the surface brightness- total luminosity per area - should decrease with distance. Besides this cosmic redshift would be dimming the light.

Therefore in expanding Universe the most distant galaxies should have hundreds of times dimmer surface brightness since the surface are is larger and total intensity of light emitted more or less the same. Unless of course, the total luminosity increases to compensate this: this would be of course total adhoc connection between dynamics of stars and cosmic expansion rate.

This is not what observations tell. Therefore one could conclude that Universe does not expand and Big Bang theory is wrong.

The conclusion is of course wrong. Big Bang theory certainly explains a log of things. I try to summarize what goes wrong.

- It is essential to make clear what time coordinate one is using. When analyzing motions in Solar System and Milky Way, one uses flat Minkowski coordinates of Special Relativity. In this framework one observes no expansion.

- In cosmology one uses Robertson-Walker coordinates (a,r, θ,φ). a and r a the relevant ones. In TGD inspired cosmology R-W coordinates relate to the spherical variant (t,r
_{M},θ,φ) of Minkowski coordinates by formulas

a

^{2}= t^{2}-r_{M}^{2}, r_{M}= a×r.

The line element of metric is

ds

^{2}= g_{aa}da^{2}-a^{2}[dr^{2}/(1+r^{2})+r^{2}dΩ^{2}]

and at the limit of empty cosmology one has g

_{aa}=1.

In these coordinates the light-cone of empty Minkowski space looks like expanding albeit empty cosmology! a is just the light-cone proper time. The reason is that cosmic time coordinate labels the a=constant hyperboloids (hyperbolic spaces) rather than M^{4}time=constant snapshots. This totally trivial observation is extremely important concerning the interpretation of cosmic expansion. Often however trivial observations are the most difficult ones to make.

- In Zero Energy Ontology (ZEO) - something very specific to TGD - the use of these coordinates is natural since zero energy states are pairs of positive and negative energy states localized about boundaries of causal diamonds (CD), which are intersections of future and past directed light-cones having pieces of light-cone boundary as their boundaries. The geometry of CD suggests strongly the use of R-W coordinates associated with either boundary of CD. The question "Which boundary?" would lead to digression to TGD inspired theory of consciousness. I have talked about this in earlier postings.

- Thus the correct conclusion is that local objects such as stars and galaxies and even large objects do not participate in the expansion when one looks the situation in local Minkowski coordinates - which by the way are uniquely defined in TGD framework since space-time sheets are surfaces in M
^{4}×CP_{2}. In General Relavity the identification of the local Minkowski coordinates could be highly non-trivial challenge.

In TGD framework local systems correspond to their own space-time sheets and Minkowski coordinates are natural for the description of the local physic since space-time sheet is by definition a space-time region allowing a representation as a graph of a map from M^{4}to CP_{2}. The effects caused by the CD inside which the space-time surfaces in question belong to the local physics are negligible. Cosmic expansion is therefore not a mere coordinate effect but directly reflects the underlying ZEO.

- In General Relativity one cannot assume imbeddability of the generic solution of Einstein's equations to M
^{4}× CP_{2}and this argument does not work. The absence of local expansion have been known for a long time and Swiss Cheese cosmology has been proposed as a solution. Non-expanding local objects of constant size would be the holes of Swiss Cheese and the cheese around them would expand. The holes of cheese would correspond to space-time sheets in TGD framework. All space-time sheets can be in principle non-expanding and they have suffered topological condensation to large space-time sheets.

- Einstein-Yang-Mills space-time is obtained from the many-sheeted space-time of TGD by lumping together the sheets and describing it as a region of Minkowski space endowed with an effective metric which is sum of flat Minkowski metric and deviations of the metrics of sheets from Minkowski metric. Same procedure is applied to gauge potentials.

- The motivation is that test particle topologically condenses at all space-time sheets present in given region of M
^{4}and and the effects of the classical fields at these sheets superpose. Thus superposition of fields is replaced with superposition of their effects and linear superposition with set theoretic union of space-time sheets. TGD inspired cosmology*assumes*that the effective metric obtained in this manner allows imbedding as vacuum extremal of Kähler action. The justification of this assumption is that it solves several key problems of

GRT based cosmology.

- The number of field patterns in TGD Universe is extremely small - given by preferred extremals - and the relationship of TGD to GRT and YM theories is like that of atomic physics to condensed matter physics. In the transition to GRT-Yang-Mills picture one gets rid of enormous topological complexity but the extreme simplicity at the level of fields is lost. Only four CP
_{2}coordinates appear in the role of fields in TGD framework and at GRT Yang-Mills limit they are replaced with a large number of classical fields.

## 5 Comments:

/* Big Bang theory certainly explains a log of things. */

Epicycle model explained lotta eclipses and conjunctions, yet it was wrong. Here you can find much more arguments against Big Bang scenario.

To Zephir:

The question of the title was purposefully provocative. I am of course not against Big Bang!

Big Bang is part of TGD and also of reality, as I believe with the reservation that in primordial state one has just a gas of cosmic strings near the boundary of light-cone and mass density goes like 1/a^2 and mass per comoving volume goes to zero. Silent whisper amplitude to quite a big bang would be a more appropriate term. TGD counterpart of inflationary period means transition to a radiation dominated cosmology.

My point is that light-cone proper time which gives cosmological expansion already in empty Minkowski space is physically appropriate in zero energy ontology. In this sense cosmic expansion is coordinate effect. The challenge is to explain why R-W coordinates are appropriate.

These coordinate effects are dangerous concerning interpretation: for instance, the canonical form of inflationary cosmology (de-Sitter space) allows imbedding as completely static cosmology having no Big Bang and this brings in physics.

Causal diamond - in cosmological scales very big one - is intersection of future and past directed light-cones. In Robertson-Walker cosmology the time coordinate ) is light-cone proper time a (or function of it) for its imbedding as space-time surface and thus very natural since R-W can be imbedded inside light-cone and its boundary corresponds to the Big Bang.

R-W cosmology is Lorentz invariant so that energy momentum tensor is extremely simple in these coordinates. In linear Minkowski co-ordinates things would look very complex.

Hence Big Bang is real but looks simple in R-W coordinates made natural by the Lorentz

invariance of the space-time surface characterizing R-W cosmology.

I'm sure you noticed this Matti, but the BICEP2 data on gravitational wave proof of inflationary universe has now been explained as magnetic dust measurement anomaly.

http://www.simonsfoundation.org/quanta/20140921-big-bang-signal-could-all-be-dust-planck-says/

So much for direct (or actually, indirect) proof of inflation.

It's still only a model. Testable, but not proven.

Scratch that (previous note).

I'm not sure anymore that inflation is experimentally falsifiable and as such, a testable hypothesis.

See Paul Steinhardt's argument on this from Princeton String 2014 talks:

https://www.youtube.com/watch?v=_RpwuHOHiB4

To Anynymous:

I commented BICEP2 in the next posting and also in two postings previously. I more or less agree with you.

What is common with TGD and inflation is vanishing curvature of 3-space. In TGD it is correlate for quantum criticality in transition from cosmic string gas phase (cosmic strings as space-time surfaces with 2-D M^4 projection) to radiation dominated cosmology. What is also common is rapidly accelerating expansion.

The energy of inflaton field is replaced with the magnetic energy of flux tubes which decays to particles so that no new primary fields are introduced and also standard model gauge fields reduce to four imbedding space coordidates as field like variables.

TGD model explains also the presence of magnetic fields in cosmological scales: in this respect the model differs from inflation model. Of course it is of course dramatically simpler: four field like like variables instead of gauge fields, Higgs field, inflation field, etc… This is magic of geometry and topology.

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