# Criteria for causal independence (new paper, Planck data)

1. May 19, 2013

### marcus

I don't know whether this has much general interest. I am interested by communication horizons in cosmology, or causal horizons if you prefer. This paper claims to study several cases including how far apart two quasars would have to be to have been out of contact ever since the end of the putative inflation epoch. That is very far back---the very start of post-inflationary expansion. It struck me as impressive to attempt to calculate these things, especially if they can do a creditable job. So here's the paper:

http://arxiv.org/abs/1305.3943
The Shared Causal Pasts and Futures of Cosmological Events
Andrew S. Friedman, David I. Kaiser, Jason Gallicchio
(Submitted on 16 May 2013)
We derive criteria for whether two cosmological events can have a shared causal past or a shared causal future, assuming a Friedmann-Lemaitre-Robertson-Walker universe with best-fit ΛCDM cosmological parameters from the Planck satellite. We further derive criteria for whether either cosmic event could have been in past causal contact with our own worldline since the time of the hot "big bang", which we take to be the end of early-universe inflation. We find that pairs of objects such as quasars on opposite sides of the sky with redshifts z ≥ 3.65 have no shared causal past with each other or with our past worldline. More complicated constraints apply if the objects are at different redshifts from each other or appear at some relative angle less than 180 degrees, as seen from Earth. We present examples of observed quasar pairs that satisfy all, some, or none of the criteria for past causal independence. Given dark energy and the recent accelerated expansion, our observable universe has a finite conformal lifetime, and hence a cosmic event horizon at current redshift z = 1.87. We thus constrain whether pairs of cosmic events can signal each other's worldlines before the end of time. Lastly, we generalize the criteria for shared past and future causal domains for FLRW universes with nonzero spatial curvature.
38 pages, 16 figures, submitted to Physical Review D

2. May 20, 2013

### Chronos

This suggests a causal disconnect between objects within the observable universe. I'm not insisting the observable universe must be logical, but, this puts the Copernican principle in the dumpster.

Last edited: May 20, 2013
3. May 20, 2013

### Haelfix

Under the standard FRW scenario, there can and is a causal seperation between regions in our visible universe. This is perfectly well understood. There is simply not enough time for all cosmic event horizons to have overlapped significantly.

This is straightforward calculation and illustration of the horizon problem of cosmology, which is done in most textbooks (and the appendix in the paper) where you can enumerate the number density of causally distinct horizons (something like 10^80) as well as the avg angular seperation between them. The paper above simply rewrites this in more convenient variables and generalizes the calculation to different redshift/angular seperations (basically a selection criteria which allows us to distinguish whether or not two objects share a past event) which is a much more ardous calculation.

4. May 20, 2013

### Mordred

Good paper thanks for posting it. The paper does an impressive job with the descriptives and worldlines.

5. May 20, 2013

### Chronos

So, does this justify abandoning the Copernican principle as a fundamental premise of cosmology? I think not.

6. May 20, 2013

### Haelfix

Why do you think that distant regions not having time to be in causal contact has anything to do with the Copernican principle?

Every observer in any particular region will see the same thing on average, and will be able to make the same deductive leap.

7. May 20, 2013

### WannabeNewton

I too am having trouble seeing how isotropy and homogeneity are threatened by the existence of causal disconnects. There do exist causal disconnects in the FRW universe with homogeneity and isotropy intact so I'm not seeing what the issue is.

8. May 20, 2013

### Chalnoth

Because the only reasonable way for different parts of the universe to know they should be the same density is for them to have a shared past.

The fact that different parts of our observable universe are similar today may not seem particularly special, but remember that at the time the CMB was emitted, the density differences were only one part in 100,000.

9. May 20, 2013

### Jorrie

I thought they shared the past before/during inflation, solving the horizon problem. After that it should not matter if they can ever share again.

10. May 20, 2013

### George Jones

Staff Emeritus
This paper is interesting, but it doesn't seem to make any surprising conclusions. I am reading this at a coffee shop while on a trip with my family, so I have only had a quick scan, and I might have missed some important stuff. It seems to quantify, using recent data, results that were already known at least qualitatively. I will try and have a more leisurely read in a few days when I return home.

Last edited: May 20, 2013
11. May 20, 2013

### Mordred

This paper does cover the shared past in the appendix sections. Where it determines the minimal number of e-folds to solve the horizon problem to be 62.5 (think I have that value right will have to double check).
the time they set as T=0 is after inflation.

However it does state a shared past prior to T<0 in the appendix sections.
So I don't see this as a violation as the paper does cover a shared past in regards to CMB distributions and the horizon problem.
If I'm reading this correctly then all its doing is stating t=0 in this paper is the point where causal seperations would occur.

The required number of e-folds to solve the horizon problem in this paper is n>=65.95 (sorry for long hand on phone).

Last edited: May 20, 2013
12. May 20, 2013

### Chalnoth

Right. That's generally expected to be part of the solution of the horizon problem. The main issue is that for inflation to start at all, you need a causally-disconnected region to have nearly the same excited value of the inflaton field. I think most physicists feel that the fact that this causally-disconnected region need only be of the order of $10^{-30}$ meters across or so makes it at least seem more likely.

So inflation doesn't so much solve the horizon problem as it pushes it to much smaller scales.

We might imagine that this is a fluke: tiny, random excitations of the inflaton field might happen all the time, and it is only when an exceptionally rare one that spans a large enough distance with nearly the same inflaton field value generates a new inflating region.

Alternatively, perhaps it's instead down to some dynamics that we don't know: the physical process which generates this initial inflating region brings those apparently-disconnected regions into causal contact before inflation begins.