The Cosmic Inflation Never Happened

The Big Bang theory holds the premise that the universe originated from a singularity which came into being out of nothing through a single massive explosion. The concept of the minuscule size of such primeval singularity born from the thought projection of the current universe's expansion backward far in time.

The theory has at least two dubious primary grounds. The first one is the speculative concept of nothingness. The Big Bang theory presumes, violating the first law of thermodynamics, that energy (and matter) was created out of nothing. This idea came from the mindset that the creation of the universe (4-spacetime) was the beginning of everything. Notwithstanding, the theory takes for granted that the quantum fluctuation which stimulated the primeval explosion held in the nothingness before such creation.

The second speculative ground is about the size of the universe which can be shrunk indefinitely backward in time from the current size into a singularity. Close to the moment of creation, the size exponentially shrunk about 10⁶⁰ smaller just within 10⁴ seconds, from 10^-33 to 10^-37 second posterior to the explosion, the rate of which was exceedingly faster than the speed of light¹.

As we have elucidated so far, there can be no such thing as nothingness. The energy, as the only reality in nature, can neither be created out of nothing nor destroyed into nothing. The universe was born as the result of the interplay between the opposite (positive and negative) energies that created the universe and everything within, not out of nothing.

We can mathematically describe energy in its pure condition as waves' spectrum of different frequencies and amplitudes expressed in terms of Fourier series or its complex form, the Laurent series:

                         f(z) = F⁺(z) + c₀ + F^–(z)

It is a wave function expressed as the sum of its positive frequency (F⁺(z)) and negative frequency (F^–(z)).

Globally, we can depict this wave function in terms of Riemann sphere, the positive frequency F⁺(z) extends holomorphically into the southern hemisphere, and the negative frequency F^–(z) extends holomorphically into the northern hemisphere, where the equator represents the real coordinate and the longitudinal circles its imaginary time coordinate.

The domain of the positive and negative frequencies, however, does not fully extend to the poles, as the Riemann sphere has an annulus of convergence which excludes the domain around the zero points (singularity) as well as the infinity (Figure-1). 

 This pure mathematical analysis indicates that the split of the energy cannot create a stable interface (hypersurface) from the beginning when the energy started to split up to a certain period where it reaches the minimum size (represented by the Riemann sphere's inner ring of convergence).  The interface created in this period would instantly dissolve into energy.

It is only after reaching this limit that the hypersurface comes into being where it stabilized until it reaches its maximum size (represented by the Riemann sphere's outer ring of convergence).

The doomsday comes when the hypersurface reaches its maximum size.  At this particular time, the hypersurface becomes extremely unstable that makes it break down into pieces dissolving back into pure energy.  We illustrate these phenomena in Figures-2 and 3A.

This cosmology scenario avoids the need of either the concept of singularity to represent the beginning of the creation or the big crunch at the end of the universe's life as well as the everlasting expansion where the universe has no dead end.

This cosmology theory also excludes the need of the concept of cosmic hyper-inflation in the early period of the creation (Figure-3B), as the baby universe was born in an exceedingly larger size than that of the singularity which the Big Bang theory presumed.

The interplay between the positive and negative energies generates quantum fields across through the interface (hypersurface) ^a), located in between the two, perpetually creates quantum sparks (fundamental particles), the building block of the universe. As the split (hypersurface) area is enlarging with time, new matters are created in the expanding horizon keeping the average matter density per area almost constant.

This cosmology concept resembles the one of the continuous creation, steady-state expanding universe put forward by Fred Hoyle².

Notes:

a) We use the split area, interface, hypersurface, and space interchangeably.

References:

1.  Guth, A.: "The Inflationary Universe," Basic Books, New York, 1997

2.  Gregory, Jane: "Fred Hoyle's universe," Oxford University Press, New York, 2005

Energy, Spacetime and Riemann Sphere

The ultimate goal of the special relativity theory, if we are aware of, is the unification of the spacetime and energy. The union of these two would reveal the reality of energy which differs entirely from what we used to think about. Energy is a substance whose geometrical structure is reflected by the dimensionality of its spacetime.

Our ordinary [four-dimensional] spacetime is the physical manifestation of the energy whose vibrations are four-dimensional. As a [three-dimensional] human being we can only perceive this pure energy through its superficial three-dimensional aspect. Many underlying higher-dimensional ambient spaces which physicists have discovered, as they are adventuring deeper and deeper into the micro-world realms, are nothing but the reflections of various hyper-vibrations energies.

The relativity theory demonstrates that energy as a whole is inherently composed of positive and negative energies, as implicitly expressed in the relativistic energy equation E² = m²c⁴ + p²c². The segregation of its opposite parts that resulted in the split of energy created a 3-hypersurface (space) between the two halves of its separated respective spacetime. The world was not created through the "big" tiny bang bursting out of nothing.

In the quantum realm, energy as a wave can be described proportionally to its frequency as expressed by the Planck equation, E=hv.  We can express the energy, not only microscopically but also macroscopically, in term of the wavefunction whose character is completely holistic and non-local. However, the more natural way for us to grasp, is to express it in a periodic function such as a Fourier series ^a) or its complex form: the Laurent series ^b). 

In the relativistic framework, we map events in a complex plane where we express time in term of an imaginary variable. In such a plane, we have a Laurent series written as:

              f(z) = F⁺(z) + c₀ + F^–(z),

which is a wave function expressed as the sum of its positive frequency (F⁺(z)) and negative frequency (F^–(z)). Physically, the constant term c₀ represents the real space at t=0 (the present now). This c₀, wholly or partially, becomes either the part of F⁺(z) or F^–(z) or maybe both. However, as there is only positive energy, at least in this corner of the world where we live in, the space (c₀) should be part of the positive ocean of energy, F⁺(z), and on the other side of the world it should be part of negative ocean of energy, F^-(z).

Geometrically, we can figure out this more clearly in terms of the Riemann sphere, the stereographic projection of the complex plane. On this sphere, we can transform the real axis (X) of the complex plane into a circle located on the equator, while the imaginary time coordinate (it) by the longitudinal circles. The positive frequency F⁺(z) extends holomorphically into the southern hemisphere, and the negative frequency F^–(z) extends holomorphically into the northern hemisphere (Figure 1). 

From this description, we have a complete similarity between that of purely mathematical geometry with the relativistic (Minkowski) spacetime geometry (Figure 2 A and B). The real circle on the Riemann sphere represents the 3-hypersurface (space) in the Minkowski 4-spacetime which separates it into two 4-halves. The positive energy segregates to one half, and the negative energy segregates to the other half of the spacetime. We can These two halves are respectively represented by the southern and northern hemispheres on the Riemann sphere. The real circle on the Riemann sphere and the hypersurface in the Minkowski spacetime, each represents the loci of all matters which may exist in the whole universe.

With this simple mathematical representation, we can have a deeper insight into how nature may work. As we have figured out previously, the real circle in the Riemann sphere represents the space, and the imaginary circle represents the time path. As time passes by along the imaginary circle, space (real circle) is rotating accordingly along the time direction (imaginary circle). As time flows resemble electric current, space is also rotating on its plane following the right-hand rule. The rotation of this space as a whole rotates, in turn, all celestial bodies from the super-galaxies down to galaxies, solar systems, and the earth.

Notes:

References:

1. Penrose, R.: “The Road to Reality”, Vintage Books, London, 2005, pp. 157-162.