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According to quantum mechanics we have the uncertainty principle:

$$\Delta E \ \Delta t \geq \frac{\hbar}{2}$$

Near the beginning of the Universe $\Delta t$ is very small and therefore $\Delta E$ is large enough to produce matter-antimatter particle pairs just by the uncertainty principle alone.

If the Universe is expanding fast enough then these pairs would be unable to recombine and annihilate.

Maybe this process is the source of particles in the Universe rather than a singularity of infinite energy density at the big bang?

Edit: I don't assume that the uncertainty principle itself creates the particles. Instead the particle-antiparticle pairs borrow energy from the vacuum when the Universe is young (and possibly naive!) and then 'go on the run' in such a way that their creditor can never catch up with them.

John Eastmond
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    Well, that equation has nothing to do with the uncertainty principle, and it's not even correct (not in the interpretation you gave in the post at least). Also, matter-antimatter production has nothing to do with no uncertainty principle (that is just a misinterpretation of algebraic expressions that populates pop-science writings)... – AccidentalFourierTransform Mar 16 '16 at 14:58
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    That $\Delta t$ does not mean what you think it means, cf. this question, so this question does not make sense. – ACuriousMind Mar 16 '16 at 14:59
  • You said its expanding. What expands? something that is compressed. Or something singular. – Anubhav Goel Mar 16 '16 at 15:37
  • General Relativity says space expands. – John Eastmond Mar 16 '16 at 15:49
  • The Particle-antiparticle pairs you are talking about are taken as an energy 'debt' from the universe...they have to annihilate to return it. The uncertainty principle doesn't CREATE these particles.....It just provides an explanation for this creation (and subsequent annihilation) .... – GRrocks Mar 17 '16 at 09:39
  • I'm assuming that the particle-antiparticle pairs borrow energy from the vacuum when the Universe is young and then 'go on the run' so that their creditor can never catch up with them. – John Eastmond Mar 18 '16 at 13:57
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    The picture where particles "borrow energy" stems from an interpretation of perturbation theory. In an exact calculation, there is no "borrowing energy" and energy is always completely conserved. See also this question: http://physics.stackexchange.com/questions/103724/energy-conservation-limited-by-uncertainty-principle – Martin Mar 18 '16 at 14:22
  • @Martin but I believe the OP means that the period between the 'creation'(if you will) and 'annihilation'; if disturbed, will cause an apparent violation of energy conservation(which, ofcourse is taken care of by hawking radiation normally).....so even in such scenarios will the perturbations cancel out exactly? Could you please provide a reference for such a calculation? Seems interesting. – GRrocks Mar 18 '16 at 15:31
  • @GRrocks: The simplest reasoning is that QM is still time-translation invariant. That dictates conservation of energy at any instance. See also http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html . A calculation within perturbation theory where everything cancels out is, I believe, impossible. You have to solveeverything without perturbation theory (which is never done in physics classes and hardly ever possible with our current knowledge) and then compare results. – Martin Mar 18 '16 at 15:57
  • @Martin thanks...but how about if we scale things down?(like Gaussian coordinates or something).....say we work with the Raychaudhuri equation in such a system....wouldn't it be possible to ignore the rotation terms, but retain the components of the shear...this will cause an apparent 'reduction' in the avg. rate of congruence curving and the only way to explain this in normal sense seems to cause an excess 'perturbation' in the parameter we are working with throughout the congruence. I know; it is pretty unworkable, but atleast in principle maybe? – GRrocks Mar 18 '16 at 16:05
  • @GRrocks: I doubt I can answer that... What I'm saying refers purely to quantum mechanics in non-curved spacetime. This is enough for the OP, because he wants to get the energy from the "energy-time-uncertainty". I claim that this doesn't really do what he believes it does in QM without GR. Once you enter GR, I have no idea what happens - I know hardly anything about the topic (sadly). However, any GR+QFT is perturbative at the moment, so it might be that we simply don't know. In any case, that seems like a good high-level question... – Martin Mar 18 '16 at 16:17

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Could the uncertainty principle create matter in the Universe?

The uncertainty principle does not stand alone in quantum mechanics. It is a consequence of the operator structure of the theory, and an uncertainty relation can be derived for all the conjugate variables describing the system. A good analysis of how the energy/time uncertainty is derived from the theory is in this answer here.

Near the beginning of the Universe Δt is very small and therefore ΔE is large enough to produce matter-antimatter particle pairs just by the uncertainty principle alone.

The beginning of the universe is defined in the standard cosmological model as a locus in space time where the energy momentum tensor of general relativity has very high curvatures, and is represented in the Big Bang model which developed from having a singularity for t=0, to an undefined region,

bigbang

for times less than 10^-32 seconds.

In that region the model uses an effective quantum mechanical theory, because at the moment there is no definitive quantization of gravity. This effective theory involves inflatons, hypothetical particles that carry all of the energy processes at that time, and create an inflation as seen in the graph.

Between 10^-32 seconds and 1microsecond the universe is a soup of elementary particles and finaly protons are formed.

In this region virtual loops of particle antiparticle can be imagined, whose "reality" starts at the proton formation time.

If the Universe is expanding fast enough then these pairs would be unable to recombine and annihilate.

It is these pairs in the soup that start becoming real protons and antiprotons and other particles , but this is not because of the heisenberg uncertainty, but because of the the universe cooling enough due to the expansion that the available energy can coalesce into masses and remain stable because of lack of interactions that would destroy/annihilate them.

Maybe this process is the source of particles in the Universe rather than a singularity at the big bang?

From the moment one assumes an expansion of the universe, as you do, the model implies a beginning region much compressed if not a singularity. Which brings us to the current cosmological model.

So it is not the heisenberg uncertainty that generates particles , but the available energy and the thermodynamic interactions that allow the persistence of matter. In the Big Bang model using the standard model of particle physics, it is not yet known how the asymmetry between particles and antiparticles ( our universe is composed out of particles) is generated, this is an ongoing research question.

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