The Cosmos


Do We Live in an Anamorphic Universe?

A century ago, we knew virtually nothing about the large scale structure of the universe, not even the fact that there exist galaxies beyond our Milky Way. Today, cosmologists have the tools to image the universe as it is today and as it was in the past, stretching all the way back to its infancy when the first atoms were forming. These images reveal that the complex universe we see today, full of galaxies, black holes, planets and dust, emerged from a remarkably featureless universe: a uniform hot soup of elemental constituents immersed in a space that exhibits no curvature.1

Anamorphic is a term often used in art or film for images that can be interpreted two ways, depending on your vantage point. Önarckép Albert Einsteinnel/Self portrait with Albert Einstein, Copyright Istvan Orosz

How did the universe evolve from this featureless soup to the finely-detailed hierarchy of stars, galaxies, and galaxy clusters we see today? A closer look reveals the primordial soup was not precisely uniform. Exquisitely sensitive detectors, such as those aboard the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck satellites, produced a map that shows the soup had a distribution of hot and cold spots arranged in a pattern with particular statistical properties. For example, if one only considers spots of a certain size and measures the distribution of temperatures for those spots only, it turns out the distribution has two notable properties: it is nearly a bell curve (“Gaussian”) and it is nearly the same for any size (“scale-invariant”). Thanks to high-resolution computer simulations, we can reproduce the story of how the hot and cold spots evolved into the structure we see today. But we are still struggling to understand how the universe came to be flat and uniform and where the tiny but critical hot and cold spots came from in the first place.

Looking Beyond Inflation

One leading idea is that, right after the big bang, a period of rapid expansion known as inflation set in, smoothing and flattening the observable universe. However, there are serious flaws with inflation: inflation requires adding special forms of energy to the simple big bang picture that must be arranged in a very particular way in order for inflation to start, so the big bang is very unlikely to trigger a period of inflation; and, even if inflation were to start, it would amplify quantum fluctuations into large volumes of space that result in a wildly-varying “multiverse” consisting of regions that are generally neither smooth nor flat. Although inflation was originally thought to give firm predictions about the structure of our universe, the discovery of the multiverse effect renders the theory unpredictive: literally any outcome, any kind of universe is possible.

Another leading approach, known as the ekpyrotic picture, proposes that the smoothing and flattening of the universe occurs during a period of slow contraction. This may seem counterintuitive at first. To understand how this could work, imagine a film showing the original big bang picture. The universe would be slowly expanding and become increasingly non-uniform and curved over time. Now imagine running this film backwards. It would show a slowly contracting universe becoming more uniform and less curved over time. Of course, if the smoothing and flattening occur during a period of slow contraction, there must be a bounce followed by slow expansion leading up to the present epoch. In one version of this picture, the evolution of the universe is cyclic, with periods of expansion, contraction, and bounce repeating at regular intervals. In contrast to inflation, smoothing by ekpyrotic contraction does not require special arrangements of energy and is easy to trigger. Furthermore, contraction prevents quantum fluctuations from evolving into large patches that would generate a multiverse. However, making the scale-invariant spectrum of variations in density requires more ingredients than in inflation.

The best of both worlds?

While experimentalists have been feverishly working to determine which scenario is responsible for the large-scale properties of the universe—rapid expansion or slow contraction—a novel third possibility has been proposed: Why not expand and contract at the same time? This, in essence, is the idea behind anamorphic cosmology. Anamorphic is a term often used in art or film for images that can be interpreted two ways, depending on your vantage point. In anamorphic cosmology, whether you view the universe as contracting or expanding during the smoothing and flattening phase depends on what measuring stick you use.

If you are measuring the distance between two points, you can use the Compton wavelength of a particle, such as an electron or proton, as your fundamental unit of length. Another possibility is to use the Planck length, the distance formed by combining three fundamental physical “constants”: Planck’s constant, the gravitational constant and the speed of light. In Einstein’s theory of general relativity, both lengths are fixed for all times, so measuring contraction or expansion with respect to either the particle Compton wavelength or the Planck length gives the same result. However, in many theories of quantum gravity—that is, extensions of Einstein’s theory aimed at combining quantum mechanics and general relativity—one length varies in time with respect to the other. In the anamorphic smoothing phase, the Compton wavelength is fixed in time and, as measured by rulers made of matter, space is contracting. Simultaneously, the Planck length is shrinking so rapidly that space is expanding relative to it. And so, surprisingly, it is really possible to have contraction (with respect to the Compton wavelength) and expansion (with respect to the Planck length) at the same time!

The anamorphic smoothing phase is temporary. It ends with a bounce from contraction to expansion (with respect to the Compton wavelength). As the universe expands and cools afterwards, both the particle Compton wavelengths and the Planck mass become fixed, as observed in the present phase of the universe.

By combining contraction and expansion, anamorphic cosmology potentially incorporates the advantages of the inflationary and ekpyrotic scenarios and avoids their disadvantages. Because the universe is contracting with respect to ordinary rulers, like in ekpyrotic models, there is no multiverse problem. And because the universe is expanding with respect to the Planck length, as in inflationary models, generating a scale-invariant spectrum of density variations is relatively straightforward. Furthermore, the conditions needed to produce the bounce are simple to obtain, and, notably, the anamorphic scenario can generate a detectable spectrum of primordial gravitational waves, which cannot occur in models with slow ekpyrotic contraction. International efforts currently underway to detect primordial gravitational waves from land-based, balloon-borne and space-based observatories may prove decisive in distinguishing these possibilities.

1According to Einstein’s theory of general relativity, space can be bent so that parallel light rays converge or diverge, yet observations indicate that their separation remains fixed, as occurs in ordinary Euclidean geometry. Cosmologists refer to this special kind of unbent space as “flat.”

Go Deeper
Editor’s picks for further reading

arXiv: The anamorphic universe
Authors Anna Ijjas and Paul Steinhardt introduce anamorphic cosmology in this 2015 paper.

arXiv: The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
In this 2001 technical paper, Paul Steinhardt and his colleagues Justin Khoury, Burt Ovrut, and Neil Turok explain how an “Ekpyrotic” universe could solve some of the open questions around the standard big bang model.

arXiv: Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
Authors Anna Ijjas and Paul Steinhardt review the implications of Planck satellite data on anamorphic and other cosmological models.

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Anna Ijjas

    Anna Ijjas is a theoretical cosmologist whose research explores the origin, evolution, composition and future of the universe.  She obtained her bachelor’s degree at the University of Munich in 2009, a PhD in the Philosophy of Physics at Munich in 2010, and a PhD in Physics (cosmology) in 2014 from the Max Planck Institute for Gravitational Physics.  She won a Thyssen Research Fellowship, which she spent at the Center for Astrophysics at Harvard in 2012-3.  She is currently a postdoctoral fellow at the Princeton Center for Theoretical Science at Princeton University.  Ijjas has pointed out problems with the standard inflationary picture arising from recent cosmological observations and, together with Paul Steinhardt, she has proposed the anamorphic picture described in this blog post.


    Paul Steinhardt

      Paul J. Steinhardt is the Albert Einstein Professor in Science and on the faculty of both the Departments of Physics and Astrophysical Sciences at Princeton University. He is one of the leading theorists responsible for inflationary theory. He constructed the first workable model of inflation and the theory of how inflation could produce seeds for galaxy formation. He was also among the first to show evidence for dark energy and cosmic acceleration, introducing the term "quintessence" to refer to dynamical forms of dark energy. He has pioneered mathematical and computational techniques which decisively disproved rival theories of structure formation such as cosmic strings. With Neil Turok, he introduced the ekpyrotic theory of the universe which is currently the leading competing idea to inflation.