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No Boundary Condition

General relativity predicts that the universe originated from a single point- singularity. At this point, both the curvature of space and the density of matter are infinite. Since infinity is not defined in current physical theories such a condition is considered unacceptable. Theoretical physicist has had an uphill struggle to avoid singularity as the origin of the universe. However, not much success has been reached, and the problem remains open.
One of the proposals for the initial state of our universe is the "no-boundary" suggestion of James Hartle and Stephen Hawking, dating back from 1983. The no-boundary universe theory posits that the universe did not start with singularity. It claims that the universe has always been finite and had no initial singularity to produce a boundary. The geometry of the no-boundary universe would be similar to the geometry of the surface of a sphere. Therefore, it predicts that the universe is closed.

The problem with Hartle and Hawking's theory is that it predicted the a closed universe. However, observations favor the idea of an "open" universe, a universe that will continue to expand. [6] [7]

Zeros and infinities pop up in any physical theories and their related mathematics and are the basis of mathematics in general. In my view, avoiding zeros and infinities is ignoring a big portion of existence.


The problem with a singularity that possesses infinite density is that there is no force in the universe to overcome the infinite gravity and start the inflation. This means that it is classically impossible for the universe to start from zero size with infinite density. Classically, an object that does not have enough energy to climb over a hill will not get to its other side. However, a quantum mechanical object that does not have enough energy to climb over a hill can nevertheless suddenly disappear from one side and appear on the other. One example of tunnelling is the spontaneous radioactive decay of certain atomic nuclei. In nuclear decay, subatomic particles tunnel out through high energy barrier. Applying this picture to the beginning of the universe, one can thus envisage the universe as starting from zero size with infinite matter density via a quantum tunnelling event. Implementations of this idea, known as the tunnelling proposal, have been advocated by Andrei Linde and Alexander Vilenkin.[8]

Continuity Equation Principle

We are faced with a universe expanding at an accelerating pace. The Continuity Equation Principle In electromagnetic theory, the continuity equation is derived from two of Maxwell's equations. It states that the divergence of the current density is equal to the negative rate of change of the charge density. requires that the density of matter in a region of space stay the same. In addition, the density of the universe is currently close to the critical density,which means the gravitational force from the matter/energy density inside the universe can counteract the expansion force and keep the universe almost flat (please see the section on the "Flatness Problem"). Chances are that the density of the universe has always been close to critical density.

It is believed that dark energy and dark matter contribute to the density of the region as space expands. In fact, 70 percent of the density in the universe is attributed to dark energy. Another 25 percent is made of dark matter. Since the universe is constantly expanding, we would need constant matter creation for the continuity equation to hold. Where does the matter come from? What is the origin of the additional matter or dark energy being continuously created? One is led to look at other possible scenarios for the creation of matter besides the initial Big Bang. We need another source readily accessible within every minuscule of space to supply the matter needed


Fluctuating fields

Where does the energy for field fluctuation come from? Steven Hawking takes the lead: “The uncertainty principle of quantum theory means that fields are always fluctuating up and down even in apparently empty space, and have an energy density that is infinite.” [9]

Please note that infinite energy cannot belong to a finite world. He further continues, “The universe may contain what is called Vacuum energy that is present even in apparently empty space…Vacuum energy causes the expansion (of the universe) to accelerate” [10]

Besides, infinite energy defies the law governing the conservation of matter and energy (the first law of thermodynamics). Many quantum mechanical and astrophysical observations require a new definition for the conservation law. A positive cosmological constant may indicate that matter and/or energy constantly penetrate inside space-time. If we assume that dark energy can leak in from Planck's pores throughout our universe, the result would be an exponentially expanding universe.

On the other hand, the expansion of the universe requires space either to stretch or to be built from inside. If we believe that space is a continuum, then it has to stretch to provide expansion. However, if we take space as a discrete entity, then the building blocks must come from within. In this model, space is discrete. Therefore, we have to look for mechanisms that can create space blocks. In fact, we need to consider space-time grains as building blocks that need to increase.

Hawking, Stephen. The Universe in a Nutshell. Bantam Books, 2001. 
Hawking, Stephen. The Universe in a Nutshell. Bantam Books, 2001. 
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