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Shape of the universe?

NASA and STScI

Adam writes into CMI with some questions about the Cosmic Microwave Background Radiation. Joshua Howells answers and explains a common misconception with the standard big bang model, namely that the standard big bang universe has a spatial centre point and can be thought of as a 3D ball.

Hi guys,

This question has arisen in my mind after purchasing and watching your recent movie Evolutions Achilles Heels …

Hi Adam,

Does the evidence of background microwave radiation support the view that the earths origin is much closer to the start point of the secular view of the big bang singularity than 4.54 billion years? … If i were to throw a grenade at you and it landed at your feet and exploded. Between us at various distances are other individuals. I’m sure we agree that the intensity of the burns each individual between us gets, is directly proportional to the distance they are standing from the centre of the explosion?

I’m sure we agree that the intensity of the burns each individual between us gets, is directly proportional to the distance they are standing from the centre of the explosion?

I think you must have meant inversely not directly proportional. In fact, intensity decreases with the square of the distance (inverse square law). The heat from an explosion or other point like source appears less intense to observers further back mainly because the heat is spread out more. The same power (energy every second) is spread over a larger surface area. Tripling the distance away from the point source would increase the area the same energy is spread over by a factor of 9 (because the area of a sphere is 4πr²). Therefore, photons per area received and heat received drops off by a factor of 9.

(Note that this relation is more accurate for a grenade that explodes in the air than on the ground)

If we extrapolate from this and apply it to the background microwave radiation, wouldn’t the measured colour intensity of the background microwave radiation from different directions be dependent on the distance from the centre of the explosion/singularity according to the secular model?

Yes, except that in the standard concordance model (most accepted Big Bang model), the Lambda-CDM model, the shape of the universe is given by the Friedmann–Lemâitre–Robertson–Walker (FLRW) metric. Under the FLRW metric, the point of last scattering,¹ where the CMB is said to be released, is more of a point in time than a point in space:

While we see the CMB coming from all directions at the same temperature/colour/redshift, from which we can infer its distance² (assuming a certain cosmological model). The FLRW metric with the Copernican principle says the distance to this ‘relic radiation,’ is the same from every current point in the universe.

The best way to visualise this is to first recognise that the FLRW metric describes the shape of space in 4D space time. Then imagine the closed universe option³ as 3D space mapped onto a 2D expanding sphere. As the sphere expands, every point recedes from every other point.

©CMI

The secular model does not have us at 4.5 billion years old, but 13.8 billion years, they say the earth and solar system came together after 9.3 billion years of Big Bang history.

Yes, the colour of the CMB is interpreted as being due to the stretching of space: The photons released from the CMB have stretched as they have travelled through expanding space. There is therefore a relationship between the colour of the photons and the distance and time they have travelled.

Note that this effect is distinct from the decrease in energy due to the inverse square law, which describes the decrease in intensity of light with distance from a point source.

The decrease in energy received because of the inverse square law is due to the number of photons received per area becoming smaller with greater distances. Whereas the decrease in energy received due to expanding space is because the energy received per photon is less because each received photon has a higher wavelength / decreased frequency at bigger distances under the standard big bang model.

By this, I believe you are referring to the fact that the microwave background radiation is 2.7 K in all directions, and that you’re asking, ‘doesn’t this prove we are in the centre?’

As mentioned above, under the FLRW metric (and the Copernican principle) all current points in space would see the CMB at 2.7 K in all directions.

But I believe your inference would be correct if in fact we were in a 3D sphere universe, like the LTB (Lemaitre–Tolman–Bondi) metric⁴ would describe if a homogenous 3D sphere of one density was embedded in space of another density.⁵

Secularists may argue that if we are in a LTB universe, that our LTB universe is embedded in a larger homogenous, isotropic universe, this accords with the speculative eternal inflation theory.

For further reading it would be worth looking at the small anisotropies found in the CMB and the given explanations for these anisotropies. E.g. The dipole component: The motion of the solar system through space. Start with this page.

I hope this helps Adam. The standard Big Bang model is quite hard to understand, as a full treatment requires a good knowledge of General relativity. But there are several videos online with graphical analogies to 4D spacetime that will further assist in understanding what is said to be going on.

It is interesting that a simpler explanation to the apparent expansion of the universe as discovered by Hubble is that we are at or near the centre of an expanding 3D sphere universe, just as I think you have, and indeed I believe most of us first assume.

Not long after Hubble first suggested an expanding universe, he said:

‘Such a condition [these red shifts] would imply that we occupy a unique position in the universe, … But the unwelcome supposition of a favored location must be avoided at all costs … is intolerable … moreover, it represents a discrepancy with the theory because the theory postulates homogeneity.’⁶

Kind regards
Joshua