The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity. Some physicists, such as Lawrence Krauss or Alexander Vilenkin, call this state "a universe from nothingness" but, the zero-energy universe model requires both a matter field with positive energy and a gravitational field with negative energy to exist.
During WWII, Pascual Jordan first suggested that since the positive energy of a star's mass and the negative energy of its gravitational field together may have zero total energy, conservation of energy would not prevent a star being created by a quantum transition of the vacuum. George Gamow recounted putting this idea to Albert Einstein: "Einstein stopped in his tracks and, since we were crossing a street, several cars had to stop to avoid running us down". Elaboration of the concept was slow, with the first notable calculation being performed by Richard Feynman in 1962. The first known publication on the topic was in 1973, when Edward Tryon proposed in the journal Nature that the universe emerged from a large-scale quantum fluctuation of vacuum energy, resulting in its positive mass-energy being exactly balanced by its negative gravitational potential energy. In the subsequent decades, development of the concept was constantly plagued by the dependence of the calculated masses on the selection of the coordinate systems. In particular, a problem arises due to energy associated with coordinate systems co-rotating with the entire universe. A first constraint was derived in 1987 when Alan Guth published a proof of gravitational energy being negative to matter associated mass-energy. The question of the mechanism permitting generation of both positive and negative energy from null initial solution was not understood, and an ad hoc solution with cyclic time was proposed by Stephen Hawking in 1988. 
In 1994, development of the theory resumed following the publication of a work by Nathan Rosen, in which Rosen described a special case of closed universe. In 1995, J.V. Johri demonstrated that the total energy of Rosen`s universe is zero in any universe compliant with a Friedmann–Lemaître–Robertson–Walker metric, and proposed a mechanism of inflation-driven generation of matter in a young universe. The zero energy solution for Minkowski space representing an observable universe, was provided in 2009.
In 2010, it was proposed that zero-energy universes are born in pairs - with opposite rotation, thus ensuring the total energy and impulse of multiverse is still zero.
Experimental proof for observable universe being "zero-energy universe" is currently inconclusive. Gravitational energy from visible matter accounts to 26–37% of the observed total mass-energy density, therefore to fit the concept of "zero-energy universe" to observed universe, other negative energy reservoirs besides gravity from baryonic matter are necessary. These reservoirs are frequently assumed to be a dark matter.
Relation to quantum fluctuation
Although the hypothesis that a zero-energy universe was born out of a quantum fluctuation (vacuum genesis) is not consistent with modern physics as of 2015, this hypothesis is still widely cited in popular sources.
- "A Universe from Nothing". Astronomical Society of the Pacific. Retrieved 10 March 2010. by Alexei V. Filippenko and Jay M. Pasachoff
- "A Universe From Nothing lecture by Lawrence Krauss at AAI". 2009. Retrieved 17 October 2011.
- Christopher Isham, “Quantum Cosmology and the Origin of the Universe,” lecture presented at the conference “Cosmos and Creation,” Cambridge University, 14 July 1994. Christopher Isham, a British quantum cosmologist, points out that there still needs to be “ontic seeding” to create the positive and negative energy in the first place, even if on balance its sum is zero.
- Beyond Einstein: The Cosmic Quest for the Theory of the Universe - Michio Kaku, Jennifer Trainer Thompson - Oxford University Press, 1997 - p189
- A bot will complete this citation soon. Click here to jump the queue arXiv:gr-qc/0605063.
- Edward P. Tryon, "Is the Universe a Vacuum Fluctuation?", Nature, vol. 246, p.396–397, 1973.
- Alan Guth, in his book The Inflationary Universe, (ISBN 0-224-04448-6) Appendix A Since the negative energy of a gravitational field is crucial to the notion of a zero-energy universe, it is a subject worth examining carefully. In this appendix I will explain how the properties of gravity can be used to show that the energy of a gravitational field is unambiguously negative. The argument will be described [in the appendix] in the context of Newton's theory of gravity, although the same conclusion can be reached using Einstein's theory of general relativity.
- Stephen Hawking, A Brief History of Time, p. 129.
- "We might decide that there wasn't any singularity. The point is that the raw material doesn't really have to come from anywhere. When you have strong gravitational fields, they can create matter. It may be that there aren't really any quantities which are constant in time in the universe. The quantity of matter is not constant, because matter can be created or destroyed. But we might say that the energy of the universe would be constant, because when you create matter, you need to use energy. And in a sense the energy of the universe is constant; it is a constant whose value is zero. The positive energy of the matter is exactly balanced by the negative energy of the gravitational field. So the universe can start off with zero energy and still create matter. Obviously, the universe starts off at a certain time. Now you can ask: what sets the universe off. There doesn't really have to be any beginning to the universe. It might be that space and time together are like the surface of the Earth, but with two more dimensions, with degrees of latitude playing the role of time." -- Stephen Hawking, "If There's an Edge to the Universe, There Must Be a God" (interview), in Renée Weber, Dialogues With Scientists and Sages: The Search for Unity, 1986. (Also partially reprinted in "God as the Edge of the Universe", in The Scientist, Vol. 1, No. 7, February 23, 1987, p. 15.)
- A bot will complete this citation soon. Click here to jump the queue arXiv:gr-qc/9910015.
- Rosen, N. The energy of the universe. Gen Relat Gravit 26, 319–321 (1994). https://doi.org/10.1007/BF02108013
- Johri, V.B., Kalligas, D., Singh, G.P. et al. Gravitational energy in the expanding universe. Gen Relat Gravit 27, 313–318 (1995). https://doi.org/10.1007/BF02109127
- A bot will complete this citation soon. Click here to jump the queue arXiv:1012.4160.
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- Berkeley Lab, Smoot Group - http://aether.lbl.gov - Inflation for Beginners, JOHN GRIBBIN "Quantum uncertainty allows the temporary creation of bubbles of energy, or pairs of particles (such as electron-positron pairs) out of nothing, provided that they disappear in a short time. The less energy is involved, the longer the bubble can exist. Curiously, the energy in a gravitational field is negative, while the energy locked up in matter is positive. If the universe is exactly flat, then as Tryon pointed out the two numbers cancel out, and the overall energy of the universe is precisely zero. In that case, the quantum rules allow it to last forever." archived, 2014