In the journal "Nature" (12/14/73), Dr. Edward Tryon presented the theory that the sum of all energy in the universe is zero. Below is the mathematics behind that theory, quoted from the paper "Genesis of The Universe and Zero Point Energy" [*] (I would be very interested to hear any critiques of it):
"In 1973 the great contemporary scientific thinker Edward P. Tryon demonstrated how the universe could have formed [ from nothing ] without violating the principle of the conservation of energy. He said that the total energy of the universe is zero.  He said that the positive energy of the things we observe is balanced by a negative gravitational energy. Therefore the creation was formed without violating the principle of the conservation of energy. Let's explore his idea. When something falls it loses gravitational potential energy. The relationship between potential energy and position, in a force field, is given by equation #1. [ fixed-pitch font required ] /[*] Source: http://www.eskimo.com/~billb/freenrg/zpepaper.txt
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/\ PE = W = - | F . dr Eq #1 g | g / According to Tryon's theory if an object were to fall into the universe from an infinite distance away, the gravitational potential energy the object lost would equal the total mass energy of the object.  This is stated mathematically in equation #2: / rad of univ | -> -> mc^2 = - | F . dr Eq #2 | g /infinity Assuming that the universe is spherical with an isotopic mass distribution, the amount of gravita- tional potential an object will lose upon falling to the edge of such a universe is given by equation #3. / rad of univ | mc^2 = -(G)(M)(m) | (1/r^2) dr Eq #3 | /infinity Given a radius of the universe is 15 billion light years (1.42x10^26 meters) and the known gravitational constant G, the mass of the universe may be determined. M = 1.91 x 10^53 KG If this is the mass of the universe then the total energy of the universe is zero. To check this result the mass of the universe was calculated from its den- sity and volume. The universe was considered to be a sphere. This sphere has a radius of 15 billion light years and is filled with matter of the same density as the density of space in our galactic neighborhood. This "local" density is equivalent to one proton of ordinary matter and nine protons of "dark" matter per cubic meter.  Given that the volume of a sphere with a radius of 15 billion light years = 1.2 x 10^79 M^3 Please note that at one proton mass per cubic meter this is also the number of protons in the universe. The mass of the universe was derived from its volume and density in equation #4. Eq#4 M = ((1 proton/m^3) +(9 proton masses dark matter/m^3))(vol) The mass of the universe according to this second argument is: M = 2.00 x 10^53 KG Amazingly the resultant masses agree even though they were determined by two entirely different methods. This agreement indicates that the universe has a total energy of zero and that it formed without violating the principle of the conservation of energy. There is something very profound in what Edward Tryon said. CONCLUSION New scientific arguments have shown how something can be created out of nothing. These arguments have tre- mendous philosophical implications. ... NOTES  Edward P. Tryon, NATURE VOL 246, December 14, 1973.  Technically, nothing can exist outside of the universe. The universe is a closed structure in which, according to the cosmological principle, all positions are equivalent. The model presented in this paper, in which an object falls from an infinite distance away to the edge of the universe, does not represent reality. The model does, however, allow for the calculation of the negative gravitational potential shared by all objects within the universe.  Fritz Zwicky proposed that 90% of the matter in the universe is "dark" in 1933. He came to this conclusion from the study of clusters of galaxies. Vera Rubin confirmed that 90% of the universe's matter is composed of the so called "dark matter" from her study of the rotational speeds of galaxies in 1977." ======================== END EXCERPT =========================
2NOTE: I changed the awkward use of exponents as mc to the more standard ascii-style exponent notation: mc^2. I also took the liberty to insert footnote 2 where it seems to be properly indicated, since it never appears in the text. I also placed the footnote-numbers in brackets, for clarity.
"He who pursues learning will increase every day; he who pursues Tao will decrease every day." Lao Tzu (Tao Te Ching)