The Toroidal Universe


This article outlines a theory that explains why the universe isn’t expanding evenly in all directions, and it relates to the geometry of space-time. Most scientists believe that space is ‘flat’, unless it is being ‘curved’ by the presence of matter (which results in gravity). The Toroidal Universe Theory proposes that the universe may not actually be expanding but only appears to be because space-time dynamically flows with the geometry of a torus. So the universe may be simultaneously expanding and contracting in a closed loop – stretching at the top where space-time emerges from the centre of the torus, and contracting at the bottom where space-time flows back into the centre. The Toroidal Universe Theory also explains why time only flows in the one direction – forwards!

Toroidal Universe


The big bang wasn’t a one-off explosion that occurred 14 billion years ago. It was a rapid expansion of space, and since space is still expanding the big bang is still happening. It is commonly assumed that the big bang originated from a single point called a “singularity” but there is actually no direct evidence of this. If the current expansion of the universe is tracked back through time, it obviously started out much smaller than it is today, but the assumption that the universe emerged from a singularity is just an extrapolation of that trend. In fact, the equations that seem to suggest the expansion of the universe can be tracked back to a singularity are incompatible with quantum mechanics, so they probably aren’t correct. The truth is, scientists simply don’t know how the universe began, or if it even had a beginning.

Cyclic Universe

A promising new theory of a “cyclic universe” has been proposed by Anna Ijjas of the Max Planck Institute and Paul Steinhardt of Princeton University. In a cyclic universe, periods of expansion alternate with periods of contraction. Such a universe would have no beginning and no end. Anna and Paul propose that the current expansion of the universe is driven by an omnipresent energy field (whose behaviour is currently attributed to dark energy). Then when the energy field weakens, the universe begins to gently deflate, but not all the way down to a singularity, because the contraction recharges the energy field and expansion begins again.

Cyclic Universe

When I saw the above image in an article on, I felt excited because it bears some similarities to my own theory, which I will outline below. And who knows, it may even provide the scientists with some “new ideas”.

It would be pure arrogance to claim we have already figured out nearly everything. Quite the opposite – we need new ideas.

Anna Ijjas

Theoretical Physicist, Max Planck Institute

A Flash of Inspiration

I am not a physicist or a cosmologist, so this theory wasn’t conceived by studying data or devising complex formulas. I am an explorer of consciousness, and the idea came as a flash of inspiration while I was meditating and inquiring with a friend, Valerie. A few days beforehand, I saw the following image on the Wikipedia

Curved Universe

And we had been experiencing torus-shaped energy fields (like the one pictured below) during our meditations and self inquiries for several weeks…

Animated Torus

Then, in a flash of inspiration, the two images came together (as pictured below) and we realised that the universe had toroidal geometry. This is not a new idea, but it was new to us, and we knew it was significant.

Torsion (twisting energy) within the central vortex of the torus prevents the inflowing energy-matter from forming a singularity, so it can emerge anew from the top of the torus in an eternal cycle of creation, existence and dissolution (or Brahma, Vishnu and Shiva).

Torus Universe

Most scientists believe that the universe is flat and open, not curved and closed (like a torus is), but that could just be a matter of scale. After all, the earth seems to be flat from our everyday perspective, even though it is actually a giant curved sphere. So the observable universe could just be a very small area emerging from the top of the torus. But for that to be true, there would need to be some evidence for the universe being curved and closed, and there is…

Curved Closed Universe

An article on describes how data from the European Space Agency’s Planck satellite suggests that the universe is “curved and closed, like an inflating sphere”. The research team, led by Eleonora Di Valentino of Manchester University, discovered that the Cosmic Microwave Background radiation is being curved more than would be expected if the universe was flat. “A closed universe can provide a physical explanation for this effect” and the data has a 99.8% confidence level.

The above research suggests that the universe is “curved and closed, like an inflating sphere”, but it doesn’t state that the universe is a sphere. So the universe could be a sphere or a torus, because both are curved and closed. The curved/closed model is generally assumed to be a hypersphere, which has a surface volume of 2π2r3. Interestingly enough, the surface volume of a torus is also 2π2r3, so the spatial geometry of a curved/closed universe could just as easily be toroidal. If the universe was spherical it would be expanding evenly in all directions, but if it was toroidal it would be expanding differently in different directions, due to the more complex geometry. So now we just need some evidence that the universe is expanding unevenly…

Uneven Expansion

The rate of expansion of the universe is known as the “Hubble Constant”. It has been measured many times but no two measurements agree, which could imply that the universe is expanding differently in different directions.

For years, most scientists have believed that space is expanding at a constant rate, everywhere and in all directions, but a recent article on (the European Space Agency’s website) seems to suggest otherwise. The research was a joint project between the University of Bonn and Harvard University, and it suggests that the expansion of the universe isn’t isotropic, i.e. it is not the same in all directions. X-ray analysis of distant galactic clusters suggests that the universe may be expanding at different rates in different directions.

Based on our cluster observations we may have found differences in how fast the universe is expanding depending on which way we looked… This would contradict one of the most basic underlying assumptions we use in cosmology today.
Gerrit Schellenberger

Harvard-Smithsonian Center for Astrophysics

Uneven Cosmic Expansion

This is not the first time that researchers have found evidence of the uneven expansion of the universe, but it is the most convincing evidence so far.

The generally accepted explanation is that dark energy (the assumed driving force behind the expansion of the universe) is not uniform. Or put simply, dark energy is stronger in some parts of the universe than others, which results in different expansion rates. But dark energy is only hypothetical – it has never been found. It is something that scientists use to fill a gap in their current understanding of the universe. The uneven expansion of the universe could also be explained by toroidal geometry.

Toroidal Universe Theory

The toroidal geometry of the Toroidal Universe Theory can account for the curved nature of space-time, the forward directionality of time, the closed nature of the universe and its uneven expansion. And it can do all this without the need for hypothetical, elusive and mysterious dark energy. Or another way of looking at it is that these toroidal energy fields are dark energy.

Toroidal Universe
Animated Torus

When I’m working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong.

Buckminster Fuller

Smaller-Scale Toruses

Torus-shaped energy fields don’t just exist at the universal scale; they exist at every scale of reality… 

This video shows that our Local Group of galaxies is located near the centre of a 1.7 billion light-year-wide toroidal energy flow between the Dipole Repeller and the Shapley Attractor.

The Next Article continues the theme of toroidal geometry down to the galactic scale.