Is Self Creation Cosmology a Viable Alternative to the Standard Model?

[Chronos]

Hi Chronos, good to have your comments!
How? The total energy, rest mass and gravitational binding energy, of a Schwarzschild gravitational field measured at (null) inifinity is simply the Kepler mass M. It does not depend on the distribution of that mass within the spherically symmetric shell.In what frame is this 'global' energy to be measured?Or the other way round? It is GR that does not conserve energy (a frame dependent concept), rather it conserves energy-momentum (a frame independent concept) instead, which only translates into a conservation of energy under very special circumstances.

Garth

An interesting question Garth. But I do not understand your assertion that GR is frame dependent.

 

[Garth]

An interesting question Garth. But I do not understand your assertion that GR is frame dependent.

I didn't mean GR - it is energy in GR that is a frame dependent concept.

In SR two observers moving relative to each other would not agree on the total energy of a third body. Similarly in GR two inertial observers at different altitudes-potentials within a gravitational field would not agree on the total energy of a third body.

Let one inertial observer A be at the Centre of Mass of the Earth - freely falling yet stationary wrt the Earth. Now let a high up brick fall from rest, its rest energy/mass remains constant, yet it builds up speed and therefore its total energy increases as measured by A. Yet to another inertial observer B freely falling close alongside the brick its total energy remains the rest energy!

They would, however, agree on the rest mass, or rest energy, of the brick. This is the body's energy-momentum.

Garth

 

[Chronos]

To introduce a Machian element, neither observer [earth or brick bound] would be able to 'prove' which body was moving in a two-body universe. Of course, introducing a third body changes everything.

 

[Garth]

Yes, motion is relative not absolute - even if there were three or more bodies present.

To make my example more precise, and to correct a false impression I may have created in post #92, if the brick was of negligible mass then its total energy as measured by observer A would be constant, taking A's assessment of the brick's varying time dilation factor into account. This is because there is a Killing Vector field for A's static Earth gravitational field. The two observers would make different assessments of the brick's total energy but both would be constant.

Where two measurements of total energy would differ between the two observers in the sense that one would remain constant and the other vary, is in their determination of the Earth's total energy.

To observer A at the centre of the Earth it would remain constant, however to observer B the Earth's total energy would increase as she accelerated towards the Earth. In B's frame of reference the Earth's field is not static and therefore there is no Killing vector to allow the conservation of energy.

My further point is to emphasise that the frame of reference in which the total energy of the brick is conserved is that frame 'selected by Mach's Principle' - that co-moving with the centre of mass of the system - i.e. A's.

Garth

 

[gptejms]

Garth,

I have a question:-Suppose there are two identical atoms one above the other in a gravitational field(of the Earth say).The atom at lower height(call it A) emits a photon.Say the atom B which is higher is prepared in its de-excited state i.e. it's ready to absorb a photon.The question is:-will it absorb the photon emitted by A?

According to GR the photon is red-shifted,so it does not have enough energy.According to SCC,the photon is not red-shifted but the rest mass of the atom has increased(thereby affecting its energy levels--energy levels obtained from a relativistic equation e.g. the K.G. equation contains the term mc^2,where m is the rest mass).The energy gap in fact widens due to increase in m,so the photon is again not absorbed.

So in both scenarios the photon is not absorbed(though due to different reasons).This may be the true situation but it leaves one a bit uncomfortable--one would expect the photon to be absorbed.What do you have to say?

 

[Garth]

Thank you gptejms for that interesting question.

Note: the expectations of this experiment is the same in GR and SCC.

In SCC there are two conformal frames of measurement, and the SCC Einstein frame in vacuo is canonical GR - so if the expectations were different in this case SCC would have a serious case of internal inconsistency!

The atoms of the absorbing medium would have thermal motion, so if the photons were only red shifted a little then some would still be absorbed.

If the red shift was cosmological then they would not be absorbed by the same transition, but of course they may be by another lesser energy transition. Why does this "leave you uncomfortable?"

Garth

 

[gptejms]

No,there is no thermal motion here--also consider only two level atoms.Anyway,this is not the important point.

Regarding what leaves me uncomfortable:-what one is effectively saying here is that a laser won't operate if the pumping atoms(..don't remember the terminology) are separated from the atoms emitting the coherent light/laser beam in a gravitational field.Could be true---it's worth testing!

 

[Garth]

No,there is no thermal motion here--also consider only two level atoms.Anyway,this is not the important point.

Regarding what leaves me uncomfortable:-what one is effectively saying here is that a laser won't operate if the pumping atoms(..don't remember the terminology) are separated from the atoms emitting the coherent light/laser beam in a gravitational field.Could be true---it's worth testing!

Yes it might be worth testing, somebody with expertise in that field will have to give a more definitive answer.

But certainly unless the emitting and absorbing apparatus are at absolute zero there will be thermal motion of the atoms concerned.

Garth

 

[gptejms]

But certainly unless the emitting and absorbing apparatus are at absolute zero there will be thermal motion of the atoms concerned.

Yes,of course.What I meant in my original question was that in the ideal case(where a delta function is emitted and absorbed by atoms)one would not see one atom absorbing what the other emitted if they were in a gravitational field.

 

[gptejms]

Another question I wanted to ask you(something I didn't understand):-how does increase in rest mass of atoms translate to apparent red-shift of photons(which otherwise have the same energy in scc).You don't seem to be taking recourse to energy levels in your argument as I do.

 

[Garth]

Another question I wanted to ask you(something I didn't understand):-how does increase in rest mass of atoms translate to apparent red-shift of photons(which otherwise have the same energy in scc).You don't seem to be taking recourse to energy levels in your argument as I do.

There are two conformal frames of measurement in SCC.

In the Einstein conformal frame (GR with scalar field) the masses of fundamental particles remain constant and in vacuo the theory reduces to canonical GR. There is a conformal equivalence between SCC abd GR. The scalar field is decoupled from matter and space-time and exists as a 'ghost field'.

Energy-momentum is conserved wrt covariant differentiation, but not, in general, energy. Photons suffer gravitational and cosmological red shift, although as in GR there is no satisfactory explanation of where that energy goes to - it is simply not conserved.

In the Jordan conformal frame the scalar field is not decoupled and affects both space-time (as in BD) and the motion of particles through space-time. A scalar field force perturbs particles, but not photons, from their geodesic paths.

A consequence of the theory in vacuo is the scalar field force exactly compensates for the scalar field perturbation of space-time, so although particles do not follow geodesics of the SCC space-time they do follow geodesics of GR space-time.

It is this exact compensation in vacuo which results in the conformal equivalence between SCC and GR. Energy-momentum is not conserved but energy is locally conserved in general.

As a consequence in the Jordan frame photons do not suffer red shift. They do not lose or gain energy The energy of the photon does not change, after all why should it? It has traversed curved space-time with no forces acting on it along a null-geodesic. No work has been done on, or by, the photon so why should its energy change? (Remember gravitation in GR - and SCC - is explained as the effect of the curvature of space-time, not as a real Newtonian force.)

As I said in an earlier post above in the Jordan Frame, in which energy is locally conserved, gravitational red shift is interpreted not as a loss of potential energy by the photon but rather as a gain of potential energy, which increases atoms' rest mass in the apparatus measuring it.

Whereas no work has been done on or by the photon between the two levels, work has to be done on the apparatus to lift it from the lower to the higher level!

This increase in fundamental particles' rest mass changes the atoms' energy levels and it is this change that is measured as gravitational or cosmological red shift.

Garth

 

[gptejms]

Whereas no work has been done on or by the photon between the two levels, work has to be done on the apparatus to lift it from the lower to the higher level!

This increase in fundamental particles' rest mass changes the atoms' energy levels and it is this change that is measured as gravitational or cosmological red shift.

You didn't mention the energy levels anywhere in your work.I think you took it in the sense of ratio of photon's energy to the rest mass(which goes down as the atomic clock goes up)--right?!--anyway,this way of looking at it is also fine,though the energy level approach is a better one.

There are two conformal frames of measurement in SCC.

In the Einstein conformal frame (GR with scalar field) the masses of fundamental particles remain constant and in vacuo the theory reduces to canonical GR. There is a conformal equivalence between SCC abd GR. The scalar field is decoupled from matter and space-time and exists as a 'ghost field'.

Energy-momentum is conserved wrt covariant differentiation, but not, in general, energy. Photons suffer gravitational and cosmological red shift, although as in GR there is no satisfactory explanation of where that energy goes to - it is simply not conserved.

In the Jordan conformal frame the scalar field is not decoupled and affects both space-time (as in BD) and the motion of particles through space-time. A scalar field force perturbs particles, but not photons, from their geodesic paths.

A consequence of the theory in vacuo is the scalar field force exactly compensates for the scalar field perturbation of space-time, so although particles do not follow geodesics of the SCC space-time they do follow geodesics of GR space-time.

It is this exact compensation in vacuo which results in the conformal equivalence between SCC and GR. Energy-momentum is not conserved but energy is locally conserved in general.

As a consequence in the Jordan frame photons do not suffer red shift. They do not lose or gain energy The energy of the photon does not change, after all why should it? It has traversed curved space-time with no forces acting on it along a null-geodesic. No work has been done on, or by, the photon so why should its energy change? (Remember gravitation in GR - and SCC - is explained as the effect of the curvature of space-time, not as a real Newtonian force.)

As I said in an earlier post above in the Jordan Frame, in which energy is locally conserved, gravitational red shift is interpreted not as a loss of potential energy by the photon but rather as a gain of potential energy, which increases atoms' rest mass in the apparatus measuring it.


Garth

I have questions on this part too.Are you saying that both in Einstein and Jordan frames,SCC in vacuo is equivalent to GR?In Einstein frame,the scalar field exists as a ghost field(in vacuo) whereas in JF,the scalar field affects both space-time and particles--the two effects cancel out in vacuo--is this what you are saying?

Now regarding vacuo--aren't you in vacuo all(or most of)the time?--you don't discuss what's happening in the Earth's interior in GR.

 

[Garth]

You didn't mention the energy levels anywhere in your work.I think you took it in the sense of ratio of photon's energy to the rest mass(which goes down as the atomic clock goes up)--right?!--anyway,this way of looking at it is also fine,though the energy level approach is a better one.

Agreed.

I have questions on this part too.Are you saying that both in Einstein and Jordan frames,SCC in vacuo is equivalent to GR?In Einstein frame,the scalar field exists as a ghost field(in vacuo) whereas in JF,the scalar field affects both space-time and particles--the two effects cancel out in vacuo--is this what you are saying?

That is what I said

Now regarding vacuo--aren't you in vacuo all(or most of)the time?--you don't discuss what's happening in the Earth's interior in GR.

Yes we are, which is why so far there has been a degeneracy in the tests, they have not differentiated between GR and SCC, so that tests that verify the one theory have verified the other also.

I have identified three tests that resolve this degeneracy:The GP-B geodetic precession, the locally measured bending of a light path towards a gravitating body such as the Sun or Earth (not the standard deflection test) and a bottoming out of the Casimir force in weak gravitational fields.

The first is being evaluated at present, the second produces a transverse bending of the LIGO 8 km laser light path of about 10^-12m towards the Sun, which is too small to be detected as yet, and the third should be detectable away from the Sun's gravitational field somewhere between the orbits of Jupiter and Saturn with present experimental sensitivities.

The principle of equivalence is also broken and different matierials, e.g. gold and aluminium, should fall towards the Earth at different rates, but only at the one part in 10¹⁷ level three orders of magnitude smaller than present experimental sensitivity.

Garth

 

[gptejms]

According to your theory,a particle moving at a constant velocity v has a rest mass different from the the one at rest.This is because in order to attain the constant velocity v, starting from rest, the particle has to accelerate and when the particle accelerates(it's as if it's in a gravit. field so) its rest mass changes.So do you mean SR needs to be modified(at least in the JF frame)?

J.Singh

 

[Garth]

According to your theory,a particle moving at a constant velocity v has a rest mass different from the the one at rest.This is because in order to attain the constant velocity v, starting from rest, the particle has to accelerate and when the particle accelerates(it's as if it's in a gravit. field so) its rest mass changes.So do you mean SR needs to be modified(at least in the JF frame)?

J.Singh

The fact that the mass of an object moving relative to an observer is observed to have a greater 'relativistic mass' or total energy because the object's kinetic energy is allowed for, as measured in the observer's frame.

SR does not need to be changed, in fact in its JF SCC is consistent with this SR 'energy principle' by also including gravitational potential energy in the rest mass.

Garth

 

[gptejms]

Garth,

The increase in rest mass is not quite the same as a greater relativistic mass.In your case the rest mass may increase or decrease depending on whether the atom accelerates towards me(an observer at \infty)or away from me.This directional dependence,however,is a desirable feature!

This is because it explains the doppler effect in terms of energy levels of the source of light.If the source moves towards me,its rest mass increases thereby widening the gap between the energy levels--the reverse happens if the source moves away from me.So,it explains the relativistic doppler effect in terms of energy levels!You can't give such an explanation in SR,because relativistic mass does not depend on the direction of velocity.

 

[gptejms]

Photo-Doppler problem

I'll give you some background to my last post.A friend and class-fellow of mine came up with the following interesting problem(during the starting days of our M.Sc.):-There's a photocell and a (monochromatic)source of light at a certain distance from the photocell.The source of light emits light of frequency lower than what is required for the photoelectric effect.So there is no photoelectric effect.Now the source of light starts moving towards the photocell with some constant velocity--the resultant doppler effect is sufficient to take the frequency beyond the threshold(in photocell's frame).The question is would the photoelectric effect now be observed?If yes,where does the photon get the extra energy from?

I thought of discussing this in a separate thread,but since our discussion is heading towards similar issues,I've included it here.May be I should do both--discuss it here as well as start a separate thread.

J.Singh

 

[Garth]

The classic doppler effect is not the same as relativistic (total) energy change.

In classical doppler the red shift is proportional to velocity, whereas the total energy change - kinetic energy - is proportional to velocity².

The relativistic doppler effect can be obtained from the classical doppler by factoring in the relativistic energy change. It is the difference between the classical and relativistic doppler effects that can be explained "in terms of energy levels".

Garth

 

[gptejms]

The classic doppler effect is not the same as relativistic (total) energy change.

In classical doppler the red shift is proportional to velocity, whereas the total energy change - kinetic energy - is proportional to velocity².

Yeah,but I never had the classical doppler effect in mind while talking of this problem.For relativistic doppler effect(which's what I had in mind) k.e. is not proportional to v^2(nor is the red-shift proportional to v).

The relativistic doppler effect can be obtained from the classical doppler by factoring in the relativistic energy change. It is the difference between the classical and relativistic doppler effects that can be explained "in terms of energy levels".

Garth

I thought of this:-however,you have to bring in two different effects(to explain the relativistic doppler effect)namely the change in energy levels due to increase in relativistic mass m/(1-v^2/c^2)^0.5 (provided we assume relativistic mass affects energy levels) and classical doppler effect(in which case you appeal to the wave-picture,but we are seeking an explanation in terms of particle picture only).Due to obvious reasons,one can't take this line of reasoning forward.

 

[gptejms]

Garth:

You didn't comment on the directional dependence of rest mass in SCC.Is there or is there not directional dependence of rest mass in SCC?

 

[Garth]

The increase in rest mass is not quite the same as a greater relativistic mass.In your case the rest mass may increase or decrease depending on whether the atom accelerates towards me(an observer at )or away from me

I'm not sure I understand you. Why should acceleration affect rest mass?

In SCC (Jordan Frame) rest mass is a function of gravitational potential energy and so has a positional dependence, (but so has G in such a way that Gm is constant,) but not a directional one.

As I said above, if you are trying to explain classical doppler as a variable rest mass effect it will not work. Any such variations in rest mass would be \propto v^2 whereas classical doppler z is \propto v.

Garth

 

[gptejms]

I'm not sure I understand you. Why should acceleration affect rest mass?

In SCC (Jordan Frame) rest mass is a function of gravitational potential energy and so has a positional dependence, (but so has G in such a way that Gm is constant,) but not a directional one.

'A particle undergoing acceleration' is the same as 'a particle moving in a gravit. field'--so according to your scc,every time a particle moves from rest to some constant velocity,its rest mass should change.

 

[Garth]

'A particle undergoing acceleration' is the same as 'a particle moving in a gravit. field'--so according to your scc,every time a particle moves from rest to some constant velocity,its rest mass should change.

First: the Equivalence Principle (EEP) does not hold for particles in SCC, the EEP only holds for photons or fully relativistic particles. It is a semi-metric theory.

Secondly even if the EEP did hold your statement would not be correct. 'A particle undergoing acceleration' would be equivalent to 'a particle in a gravitational field' not necessarily 'moving in a gravitational field'.

In GR a gravitational field and acceleration do not in themselves result in time dilation.

Time always passes at the tautological 'one-second-per-second'.

When the observation of one clock deep in the field is compared to the other clock in a laboratory well away from the field, it is the intervening space-time curvature between them that produces the time dilation effect. That is it is the change in g₀₀ between the two locations.

In a similar way in SR it is the build up of relative velocity following a period of acceleration that produces time dilation between moving observers not the acceleration itself. If a clock falls off a laboratory bench it remains synchronized to its identical twin that remains on the bench while they are both momentarily stationary, even though one is accelerating and the other not.

Garth

 

[gptejms]

Tell me what happens in the following situation according to scc:-an observer(photocell) accelerates towards a source of light.We know as a fact that it receives photons of higher and higher frequency as long as it accelerates(this could be quantified by the photo current).Now according to scc,since EEP does not hold for atoms,atoms of the source (or the photocell) do not undergo any change in rest mass.The photons do not undergo any change either.So,how do you explain the change in frequency of the received photons?

 

[Garth]

Tell me what happens in the following situation according to scc:-an observer(photocell) accelerates towards a source of light.We know as a fact that it receives photons of higher and higher frequency as long as it accelerates(this could be quantified by the photo current).Now according to scc,since EEP does not hold for atoms,atoms of the source (or the photocell) do not undergo any change in rest mass.The photons do not undergo any change either.So,how do you explain the change in frequency of the received photons?

If the experiment is carried out all at the same gravitational potential level then there is no difference between SCC and SR/GR.

As I posted above Classical Doppler is not a 'relativistic mass' effect, it is a geometric effect caused by the relative movement; literally the photons are being 'squashed up' if the source is moving towards and are therefore observed at higher frequencies.

This is indicative of the frame dependence of energy levels. What is the zero point when measuring energies? To first order the relative motion shifts the frequency by an amount that is proportional to velocity. On top of his classical shift we factor in a relativistic correction, which does take time dilation into account.

(Here my LaTex has become all screwed up again )

Garth

 

[gptejms]

If the experiment is carried out all at the same gravitational potential level then there is no difference between SCC and SR/GR.

Of course,there is a difference--from GR perspective,the 'particle undergoing acceleration' is equivalent to a 'particle in a gravitational field'--so the change in photon's frequency can be explained.I don't see this happening in the case of scc--I don't see why the photon's frequency should change from the scc perspective.

As I posted above Classical Doppler is not a 'relativistic mass' effect, it is a geometric effect caused by the relative movement; literally the photons are being 'squashed up' if the source is moving towards and are therefore observed at higher frequencies.

This is indicative of the frame dependence of energy levels. What is the zero point when measuring energies? To first order the relative motion shifts the frequency by an amount that is proportional to velocity. On top of his classical shift we factor in a relativistic correction, which does take time dilation into account.

Yeah,this is one way of looking at it as I said in one of the posts above.There are two factors (1+v/c) (or (1-v/c)) coming from classical doppler and a factor of 1/(1-v^2/c^2)^1/2 coming from time dilation.

 

[Garth]

Of course,there is a difference--from GR perspective,the 'particle undergoing acceleration' is equivalent to a 'particle in a gravitational field'--so the change in photon's frequency can be explained.

But as I have said repeatedly acceleration by itself does not produce time dilation, or red shift, only the relative velocity that subsequently builds up.

I don't see this happening in the case of scc--I don't see why the photon's frequency should change from the scc perspective.

Are you talking about gravitational or relativistic doppler red shift?

If relativistic doppler red shift, with no gravitational potential difference between emitter and observer, then in SCC it is exactly as in SR/GR.

If you are talking about gravitational red shift, the predicted red shift in SCC is the same as in GR, however the explanation given is fundamentally different.

In the SCC (Jordan Frame) the local conservation of energy, and the consequential variation in rest mass, demand that gravitational mass is treated under the De Broglie hypothesis.

Mass is defined by the DeBroglie frequency of that particle.

The red shift caused by the curvature of space-time, a time dilation expressed by the metric component \sqrt{g_{00}} , is suffered not only by the photon but also by the atom with which it interacts and is thus undetectable.

The red shift that is detectable is caused by the increase in rest mass that fundamental particles undergo when raised to the higher level.

Gravitational red shift is interpreted not as a loss of gravitational potential energy by the photon, but as a gain of gravitational potential energy by the apparatus measuring it.

Thus the predicted red shift is equal to the difference in Newtonian potential and therefore identical with that of GR as confirmed in the Pound-Rebka experiment.

I hope this helps,

Garth

 

[gptejms]

Are you talking about gravitational or relativistic doppler red shift?

Relativistic doppler is what I was talking about--what else could it be when I talked of an observer/photocell moving towards a source of light.

If relativistic doppler red shift, with no gravitational potential difference between emitter and observer, then in SCC it is exactly as in SR/GR.

See the whole point is this:-you can derive the rel. doppler effect formula from an SR perspective(the way it's done in textbooks) as well as from a GR perspective if you consider the period of acceleration required to attain a constant velocity v,starting from rest(one of the threads in sr/gr forum also discusses this).I don't see this happening in the case of scc--i.e. you can't derive rel. doppler effect from an scc perspective.

 

[Garth]

Relativistic doppler is what I was talking about--what else could it be when I talked of an observer/photocell moving towards a source of light.

That's what I thought, but you kept referring to

the 'particle undergoing acceleration' is equivalent to a 'particle in a gravitational field'

But acceleration by itself does not produce time dilation/red shift.

See the whole point is this:-you can derive the rel. doppler effect formula from an SR perspective(the way it's done in textbooks) as well as from a GR perspective if you consider the period of acceleration required to attain a constant velocity v,starting from rest(one of the threads in sr/gr forum also discusses this).I don't see this happening in the case of scc--i.e. you can't derive rel. doppler effect from an scc perspective.

If the significant thing is the relative velocity produced by the acceleration then the two theories are equivalent. However, I am not familiar with your derivation of rel. doppler from GR.

Garth

 

[Garth]

A Problem fitting SN Ia in SCC?

Type Ia Supernova are important as the whole of cosmological acceleration is based on the observation of distant SN Ia.

These supernovae are hydrogen deficient and show a strong Si II line.

The best agreement between the theoretical and observed spectra is obtained by modeling the explosion of an accreting carbon-oxygen white dwarf in a close binary system. The white dwarf accretes material from its companion until core carbon burning begins and it deflagrates, with the shock front moving slower than local sound speed.

The light curves of local Type Ia are sufficiently similar to each other that it is thought they can be used as standard candles.

This supernova model is by no means unquestioned.

At z ~ 1 these candles appear dimmer than was previously expected, an effect that is explained by their distance being greater than expected. This would have meant the universe had expanded faster than expected, hence the inference of cosmological acceleration caused by DE on which the present \LambdaCDM model is based.

At even higher red shift z > 1 their apparent magnitudes become brighter again, which would give a handle on how DE behaves, if that \LambdaCDM model is the correct interpretation of the data.

However. as I have previously posted, the linear expanding freely coasting model also fits the z ~ 1 SN Ia remarkably well.

In the Accelerating universe? thread I responded to Juan Casado in my post #5:

Another explanation for SNe Ia faintness

This explosions would seem farther away than they really are (were) because of a small negative curvature of space. In a slightly hyperbolic Universe, the wave front of light is spreading out faster than in a flat one (the light cone resembling a horn) so that luminosity distances would appear longer than they are.
In such scenario no dark energy would be needed.

You are correct, hyperbolic space will cause initially parallel light rays to diverge and objects will appear smaller, further away and fainter than in flat space, similar to a concave lens effect.

This effect is convoluted with the expansion rate of the universe, because an accelerating universe will also result in objects that will actually be further away than at the same red shift z in a non-accelerating or decelerating universe.

There is always a degeneracy in the interpretation of cosmological effects, however in this case both the curvature and expansion effects have already been taken into account in the models that then are compared to the observations of these distant Type Ia supernovae.

The standard model fits several parameters to the data, not only that of these standard candles but also the WMAP data, quasar lensing data and other cosmological constraints.

That mainstream fit does require DE.

However as an example of your suggestion see Figure 2 in the primary paper on the subject of high red-shift Type Ia supernovae: Perlmuter et al's paper:Measurements of Omega and Lambda from 42 High-Redshift Supernovae (page 23)

The (\Omega_M,\Omega_{\Lambda}) = (0,0) plot being the empty, [URL=[PLAIN]http://arxiv.org/abs/astro-ph/0306448[/URL] model universe which has hyperbolic space and no DE. (It also doesn't require undiscovered non-baryonic DM either, but that is another story!)

As a caveat I must also add that this (\Omega_M,\Omega_{\Lambda}) = (0,0) plot is not such a good fit at higher red-shifts where the supernovae begin to become brighter than expected.

Notice also that this cosmic acceleration interpretation depends on the assumption that Type Ia supernovae are standard candles. They are standard candles in our own galaxy, which is why this type of supernova is used as such, but that is no guarantee that they remain of the same intrinsic luminosity over cosmological time, especially if physical constants actually vary over such time scales.

There may be several alternative explanations for these observations.

Garth

Previously, as SCC mimics the Freely Coasting Model (FCM) I had assumed that SSC also fitted the SN Ia data.

However the above response to Juan Casado set me thinking.

The difference between SCC and FCM is the linear, freely coasting model has hyperbolic space, k = -1, whereas SCC is linearly expanding but with spherical space, with k = +1. This should make the SN Ia apparent magnitudes brighter in SCC than they appear in the k = -1 model, and hence to fit the data they must actually be less luminous than expected if they were standard candles.

But why should the SN Ia be less luminous in the past than the model suggests?

Here I am 'hand waving', but reasons could be - a selection effect as most distant SN are detected after peak luminosity, and the further away they are the more might be missed.

Or, at high z the progenitor stars might well be expected to have less metallicity than more recent ones.

Now these are speculations only, but perhaps no more so than the standard model's bland acceptance that their luminosities do not change over such cosmological time scales.

Garth