# Will the Universe actually end in a big rip?

What the Guardian got wrong…

The Helix Nebula is 700 light-years away from Earth, but screened before audience's eyes in reconstructed 3D in Hidden Universe, released in IMAX® theatres and giant-screen cinemas around the globe and produced by the Australian production company December Media in association with Film Victoria, Swinburne University of Technology, MacGillivray Freeman Films and ESO. The original image was taken by ESO's VISTA Telescope.

Yesterday, the Guardian published an article with the headline “Not with a bang, but with a Big Rip: how the world will end”. In it they discuss a recently published paper by some physicists in Tennessee, claiming “scientists have concluded that we could be heading for an equally dramatic cosmic finale: the Big Rip”. Now part of my PhD is on this exact topic of cosmology, and I find it really interesting to see how the mainstream media report my own field. So I thought I’d write a blog post putting the article in context, and explaining what the Guardian got wrong.

Firstly, some maths. You might think that modelling the universe as a whole would be quite a complicated problem, but actually if we make a few reasonable assumptions then it is not too difficult. We start with the assumption that on large scales the universe is roughly the same everywhere. Mathematically we say that space is homogeneous and isotropic. Then we define a function called the scale factor of the universe, $a(t)$, which tells us the rate at which the universe is expanding. The actual value of $a$ is not important, all we care about is how it changes over time. So if $a(t)$ is constant, this tells us the universe is static; if $a(t)$ is increasing then the universe is expanding and if $a(t)$ is decreasing then the universe is contracting. In order to find an equation for this scale factor, we use Einstein’s equation from general relativity, which relates the scale factor to the energy content of the universe.

We then need to make some further simplifying assumptions. We choose to model all the galaxies in the universe as a simple fluid with an energy density $\rho$ and pressure $p$. Then it is posited there is a simple equation of state relating the pressure to the energy density, of the linear form
$$p= w \rho,$$
where $w$ is a constant which we call the equation of state parameter. Einstein’s equation now allows us to find a solution for the scale factor in terms of this parameter $w$, with the solution given simply by
$$a(t)= \begin{cases} a_0 (t-t_0)^{\frac{2}{3(w+1)}}, &\quad w>-1 \\ e^{H_0 t}, &\quad w=-1 \\ a_0 (t_0-t)^{\frac{2}{3(w+1)}}, &\quad w<-1 \end{cases}$$
where $a_0$, $H_0$ and $t_0$ are just constants.

What is remarkable about this simple equation is that it tells us that the entire fate of the universe depends on just the value of this one parameter $w$! If $w>-1$, then $a(t)$ will increase forever and the universe will end in what cosmologists call a big freeze. However if $w<-1$, then the scale factor will actually become infinite in a finite amount of time, occurring at $t=t_0$. This is because the exponent $2/3(w+1)$ is negative, so $a(t)=a_0/0=\infty$ when $t=t_0$. At this time all points in the universe will be an infinite amount of distance apart: this is what is meant by a big rip.

The accelerated expansion of the universe was first discovered by observing distant supernova. Source: wikimedia commons.

Astronomers can measure the equation of state by observing the acceleration rate of the universe. It was observed in the late 1990s that the universe was not only expanding, as had been discovered Hubble in the 1930s, but that this rate of expansion was accelerating. This was a remarkable and unexpected discovery, and left cosmologists baffled, as some unknown energy source in the universe was required to explain it. So they invented the term dark energy to describe this mysterious energy. For the universe to be accelerating, we require an equation of state $w<-1/3$. In fact, very high precision measurements indicate an equation of state parameter roughly equal to $-1$, which is exactly on the borderline between the scenario of a big freeze and a big rip. In order to explain dark energy, scientists have suggested thousands of potential theories, all of which predict a different effective equation of state parameter $w$.

In the particular paper the Guardian reported on, they take into account a property of fluids called bulk viscosity, and claim that this leads to a big rip, in particular an equation of state with $w<-1$. It’s an interesting idea, but I find it kind of bizarre the Guardian picked up on this aforementioned paper. This is just another model amongst a multitude of theories, some of which also predict a universe with a big rip; many others do not. In fact, I recently published a paper on a different model in the same journal which also predicts a big rip. For the moment, the proposed model is certainly not a hot topic of research (the paper has yet to receive any citations), so it is odd the Guardian chose to pick up on it, and scientists have certainly not “concluded” anything of the sort.

Having said this, I think it’s great that the Guardian has found a hook to engage the public and explain these exciting ideas about dark energy. But, as is often the case in how journalists report science, the way the article is phrased misleads the public into how science research actually works. The Guardian is certainly far from the worst culprit in this regard. Journalism and science are not always an easy mix, science does not necessarily fit into a daily news agenda, which must portray everything as a ground-breaking new discovery. These are extremely rare in science: progress requires many years of gradual improvement by a large collaborative community, all working together to uncover the truth behind Nature’s grand mysteries.

And finally, to answer the question I posed in the title of this blog: the answer, as is often the case, is maybe.

Matt is a PhD student at UCL, working in the fields of general relativity and cosmology.
ucl.ac.uk/~ucahawr    + More articles by Matthew

• ### Tennis maths: how long should a deuce point last?

Using Markov chains to calculate some interesting tennis stats!
• ### A brief history of gravitational waves

The discovery of gravitational waves offers a new way of looking at the universe. Who knows what we will discover?
• ### In conversation with Ian Stewart

We speak to one of Britain's most successful popularisers of maths
• ### New largest prime number discovered!

Amaze your friends with our top facts about the new largest known prime number
• ### What’s your favourite function? Part II

We have received loads of feedback from people telling us their favourite function
• ### Weekend at MathsJam

Chalkdust visits popular maths' biggest conference