It's bigger on the inside: Tardis regions in spacetime and the expanding universe


October 7, 2013

Is dark energy needed to accelerate the expansion of the universe? (Image: Shutterstock)

Is dark energy needed to accelerate the expansion of the universe? (Image: Shutterstock)

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Fans of Doctor Who will be very familiar with the stupefied phrase uttered by all new visitors to his Tardis: "It's...bigger...on the inside." As it turns out, this apparently irrational idea may have something to contribute to our understanding of the universe. A team of cosmologists in Finland and Poland propose that the observed acceleration of the expansion of the universe, usually explained by dark energy or modified laws of gravity, may actually be the result of regions of spacetime that are larger on the inside than they appear from the outside. The researchers have dubbed these "Tardis regions."

Perhaps the most surprising cosmological observation of the past few decades was the 1998 discovery by Perlmutter, Schmidt and Riess, that the expansion of the universe has been accelerating for the past five billion years. This result, which won the 2011 Nobel Prize, was quickly corroborated by observation of independent phenomena such as the cosmic background radiation.

Why the acceleration is occurring is not currently understood, although it can be described. In terms of conventional cosmological theory, it calls for the existence of a "dark energy," an energy field permeating the universe. However, because gravity attracts normal mass-energy, dark energy would have to have a negative energy density, something unknown as yet in nature. In addition, roughly 75 percent of the contents of the universe have to be made up of dark energy to get the observed acceleration of expansion. Even though dark energy provides a reasonable description of the universal acceleration, its value as an explanation is still controversial. Many have the gut reaction that dark energy is too strange to be true.

Professors Rasanen, and Szybkab, of the University of Helsinki and the Jagellonian University at Krakow, together with Rasanen's graduate student Mikko Lavinto, decided to investigate another possibility.

The "standard cosmological model," which is the framework within which accelerated expansion requires dark energy, was developed in the 1920s and 1930s. The FLRW metric (named for Friedmann, Lemaître, Robertson and Walker, the major contributors) is an exact solution to Einstein's equations. It describes a strictly homogeneous, isotropic universe that can be expanding or contracting.

Strict homogeneity and strict isotropy means that the universe described by an FLRW metric looks the same at a given time from every point in space, at whatever distance or orientation you look. This is a universe in which galaxies, clusters of galaxies, sheets, walls, filaments, and voids do not exist. Not, then, very much like our own Universe, which appears to be rather homogeneous and isotropic when you look at distances greater than about a gigaparsec, but closer in it is nothing of the sort.

Rasanen's research team decided to examine a model universe having a structure closer to ours, in an attempt to look for alternate explanations of the accelerating expansion we see. They took an FLRW metric filled with a uniform density of dust, and converted it into a Swiss cheese model but cutting random holes in it. This has the effect of making the model inhomogeneous and non-isotropic (except very far away), and hence the Swiss cheese model looks more like our own Universe, save for the fact that our Universe does not seem to be full of holes.

While Swiss cheese is delicious, a universe with holes is not. To rectify this, Rasanen's team filled in the holes with plugs made from dust-filled exact solutions of Einstein's equation. These plugs are a reasonable model of the region near a sizable body, such as a galaxy. By putting the plugs in the holes, and then smoothing the intersections between them, they obtained a rather uniform spacetime with a lot of smaller blobs of matter dispersed throughout it – a (very) simple analog to the structure of the universe in which we live.

Rasanen's team made the plugs from a model in which the spatial parts essentially fold in on themselves as the spacetime evolves. As suggested by the figure above, such folds increase the length of a path passing through the plug without changing the external dimensions of the plug. For some such plugs, the length of a path through the plug becomes longer throughout the life of the Universe.

The team calls such a plug a Tardis region, and a spacetime containing Tardis regions is called a Tardis spacetime. As seen in the figure below, the proper diameter and volume of a properly configured plug starts somewhat larger than the apparent quantities, but then grows to much larger sizes.

Let's get to the story about Tardis regions and expansion of the universe. Because gravity is universally attractive, in an inhomogeneous universe a denser region will tend to expand more slowly than will a less dense region – there is less gravitational interaction holding the less dense region together.

Although the Tardis regions expand faster than the surrounding dust space, this does not change their apparent size from outside, so at first glance it is difficult to see how this accelerates the expansion of the universe. The key is that when an observer looks at a distant object in a plugged Swiss cheese space, the light they see has passed through a number of plugs, the number increasing the further away the object. As the length of a path through a Tardis region rapidly becomes larger as time goes by, the total length of the path the light followed from an object increases faster than does the space outside the plugs. The result is that the expansion of the universe appears to be accelerating with time, without additional influences such as dark matter.

To sum up, a space with a large number of relatively small Tardis regions will appear initially to expand at roughly the same rate as does the dust space in which the Tardis regions are embedded. As time goes on, however, the Tardis regions expand faster than the Swiss cheese, and as they fill larger fractions of the photon paths between objects and observers, the expansion of the universe as measured by optical tests over large distances will appear to accelerate.

The effect can be made large enough to reproduce the observed acceleration, so the idea isn't silly. But is this the explanation? It is too early to tell. The model is very artificial and simplistic, but does suggest that there is at least one possible alternate to dark energy within the bounds of classical general relativity.

Source: Average expansion rate and light propagation in a cosmological Tardis spacetime on[PDF]

About the Author
Brian Dodson From an early age Brian wanted to become a scientist. He did, earning a Ph.D. in physics and embarking on an R&D career which has recently broken the 40th anniversary. What he didn't expect was that along the way he would become a patent agent, a rocket scientist, a gourmet cook, a biotech entrepreneur, an opera tenor and a science writer. All articles by Brian Dodson

Dark energy is the new luminiferous aether.

Russ Pinney

This might be bad news for an Alcubierre drive.

Mike Trites

Why cannot these clever Scientists pick up on what I have been saying for donkeys years. I'll keep my explanation as simple as possible. The 'negative energy' is simply matter passing from our Universe and it does this through our well documented Black Holes. Nobody knows where the matter goes but if you imagine a volcano on our planet erupting the matter goes a certain distance until gravity brings it back. The same is probably true of the matter going back through the black holes. Our Universe is riddled with black holes so I would theorise that the matter layer is the boundary of our own Universe. It expands and contracts dependant on how much matter at any one time is being transferred from it. The other simple explanation is that we are a group of Universes and what passes from one becomes the Big Bang in the next, the outer layer of each of these grouped Universes is exactly the same as I have already described, i.e. the matter going through the black holes that are in each Universe. I don't consider these Universes to be 'Parallels' of ours just adjoining ones. The last time I posted my theories I found that I was stopped from writing too much text so you'll never know the rest of what is and always has been in my head.


I've got something of a counter theory.

Space itself is stretched by Mass or Energy occupying the volume. The gaps we see between galactic clusters are acutally areas that are more compressed space due to the lack of Mass and Energy occupying the void. Think of the Bubbles between the galactic Clusters and Galactic streams as being like an uninflated balloon. In order to Inflate said balloon, one has to fill it with SOMETHING, and in this case,.it's the Mass and Energy of the galaxies. (This also works, within limits, to explain the configuration of Galaxies without sufficent gravity to hold them together, space itself is acting like a limited balloon to hold the Galaxies together. When an object has too much kenitic energy to be held within both the galaxy and the Local Space encapsulation, it can and does escape). Ah what the heck. I am likely wrong, but this does seem to pass the Occams Razor test for me.



Perhaps RichDragon will post a fuller tale on his own blog or private site. I'd read it.

In the meantime, I have my own alternative to dark energy. We know that the unit of electric charge -- the charge on an electron or proton -- is constant, because... because, well we just know; that's all. It MUST be constant and not, say slowly reducing over time, because if it HAD been stronger in the distant past, then the emission lines from quantum transitions would have had higher energy. Thus emissions would seem to have had less red shift and be closer... as Perlmutter et al observed.


Acceleration does not occur in a "vacumn," that is without force applied either as a propellant, or as an attraction. My hunch is that a massive attraction force imay be working in that area of the universe. As in magnetism, the closer the two attracting forces get to each other, the stronger, and faster, they interact towards each other. Expect a "mini-bang" in a few billion years or so, if their theory holds up. It would be also intertesting to observe if the total area being accelerated is expanding, or static. For the mutually attracting forces theory to be valid, the area in question would also have to be expanding. I wonder as well if the leading edge of the acceleratiion is moving faster tha nthe trailing edge.

Barry Dennis

All this accelerating universe stuff explains why time seams to be speeding up so I can't get as much done in a day as I used to, or maybe it's just old age. At any rate the days seem to be going by faster and faster...


Another great article, thanks Brian.

I have never been a fan of dark matter/energy but it is a theory that does explain and predict. Maybe it will prevail or maybe it will be replaced with something else such as these Tardis regions.

We often make assumptions and simplify models so the equations can be solved. We then make the claim that the universe matches the model. Often this works and gives us insight into the real world. Sometimes the simplified model has holes in it. Surely Kepler has rolled over a few times.

The homogeneous, isotropic standard cosmological model of the universe being everywhere the same may need the closer look. Maybe the every when does too?

But I have a couple of questions or problems with the conventional cosmological theory. Perhaps this is a good time and place to pose them.

With the big bang being a point of origin for the universe, where was/is it? That is to say, what direction is it from here? Or more simply, in what constellation would you point your telescope to be looking at it? Is this even a sensible question to ask?

The other question is: considering the rate of the expansion of the universe, the age of the universe and our current location: how did we get to where we are now so we can see light that traveled 13 odd billion years to get to us from the near vicinity of the big bang; that is from the earliest stars that formed in the first half billion years (or even earlier) of the universe?


I love theories like this. It's always exciting to read peoples thoughts on how they think the universe works. This is how we actually get somewhere - brainstorming and whatnot.

Anyways, it's a shame that we have to use light and radiation to actually see and measure the universe when dealing with great distances like this. It's hard do differentiate illusions from reality

Per Andersson

It might be that the Big Bang theory of cosmetology is wrong an as long as you try to fit additional observations into the framework the explanations get stranger and stranger.

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