Common misconceptions of cosmological horizons and superluminal expansion

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I recently came across this paper on

Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
Authors: Tamara M. Davis, Charles H. Lineweaver

Comments: To appear in Publications of the Astronomical Society of Australia

We use standard general relativity to illustrate and clarify several common misconceptions about the expansion of the Universe. To show the abundance of these misconceptions we cite numerous misleading, or easily misinterpreted, statements in the literature. In the context of the new standard Lambda-CDM cosmology we point out confusions regarding the particle horizon, the event horizon, the ``observable universe'' and the Hubble sphere (distance at which recession velocity = c).

We show that we can observe galaxies that have, and always have had, recession velocities greater than the speed of light. We explain why this does not violate special relativity and we link these concepts to observational tests. Attempts to restrict recession velocities to less than the speed of light require a special relativistic interpretation of cosmological redshifts. We analyze apparent magnitudes of supernovae and observationally rule out the special relativistic Doppler interpretation of cosmological redshifts at a confidence level of 23 sigma.

- end abstract -

I was wondering if someone familiar with SR and GR could briefly take a look at the main points in this paper. Is this paper spot on? It really makes me think that I have been misled be over-simplifications in previous texts I have read, and the authors state that many scientists themselves are confused about some basic ideas. Their paper seems Ok to me, but I'm not an authority on this (or anything, I suppose.) I'd appreciate it if you could give me your thoughts.



George Jones

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This paper is fairly famous and often cited. I think that it does use some terms in non-standard ways, but it makes clear when this happens.

A paper well worth studying.


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The Lineweaver & Davis paper is a good paper. There are several sources of common confusion which the paper addresses. One of the ones we see in the forums a lot relates to superluminal velocities. Cosmologists routinely use coordinates (co-moving coordinates) in which the speed of light (coordinate speed, the rate of change of the distance coordinate with the time coordinate) is not constant.

Cosmologists also base their concept of simultaneity on cosmological time (the time of an osberver moving with the Hubble flow) which is a different notion of simultaneity than any single inertial observer will have.

As a consequence of this, the 'distance' between objects is measured along paths of constant cosmological time - this path is not a geodesic, so it's not the shortest distance between the two ponts.

Between the fact that the speed of light is not constant, and that the distance between objects is not measured along "straight lines" (i.e. geodesics), one gets several bizarre behaviors. One of them is the fact that a visible object can be moving away from us at a speed greater than 'c', and can always have been moving away from us at a speed greater than 'c' - but still remain visible. This specific "gotcha" is mentioned in the paper specifically, I belive.
I think that a lot of the confusion is because cosmologists changed the coordinate system they used sometime about 1980 without telling anyone. Before this the speed of light was the ultimate limit, but with the general adoption of comoving coordinates ideas such as 'expanding space' had to be introduced. I am very doubtful about this. See:

Stretchy Space? and Cosmology, Special Relativity and the Milne Universe.

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A look at tethered and untethered galaxies and Cosmology under Milne's shadow

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