Envision energy trajectories that curve and cross each other. Now envision energy trajectories that are straight lines and do not cross. Now see an explosion of energy at the points where the curved energy trajectories cross. There you just created an infinitely dense point in space-time. You have created a singularity at the meeting point of multiple curved energy trajectories. In creating a singularity, you have created a black hole. Black holes absorb whatever crosses their event boundary. In theory, that is.

**What if Singularities Are Created by Math Alone? **
But what if black hole singularities are the result of the math applied to curves? What if different math applied to

straight lines eradicates black hole singularities? In that event, we would lose theoretical black holes; we would lose the Big Bang, which originated from a singularity that cannot be defined or explained; and we would lose dark matter and its dark energy, which account for the universe's inexplicably missing density.

We would also gain a few things. We would gain a universe with no missing density because it would have a stable state. The universe would be stable because there would be no black hole singularity marking its origination point (What would be its origination point, then? Well, there wouldn't be an originating point in space or in time). We would gain a universe that is infinite with no need for dark matter and dark energy to explain missing density, which is only a problem in an unstable, expanding state (expanding from the force of the Big Bang, which is now eradicated).

**Present Model and New Model of the Universe**
*Present model*
The

present model of the universe theorizes a beginning point and an age for the universe. It theorizes that the universe came after the explosion of an infinitely dense point in space-time (a singularity) that produced a very big bang projecting the universe outward in all directions. Theorists can attempt to explain and predict conditions up to the Big Bang, that is what CERN's

Large Hadron Collider (LHC) is attempting to do (and it is due to start hurling protons again soon), but theorists cannot explain the singularity (the infinitely dense point) from which the big bang originated.

The present model is weakened by this inability to explain the beginning point (some suggest a fourth dimensional singularity that erupted into our three dimensional reality) or the cause for the big bang that resulted in a finite universe, which is still expanding from that propulsion but which will ultimately lose force so the universe collapses back in on itself to form another

black hole singularity (an infinitely dense point).

The theoretical model is disrupted by the observation that the universe is continuing to expand. Enter dark energy and dark matter as the sources of this expansionary push and as the explanation for why the universe is not as dense as the model predicts.

*New model*
The new model opposes this theoretical view in its entirety. There is no beginning. There will be no end. The universe has no age. There was no singularity. There was no big bang. There was no initial explosive expansion. There are no black holes. There is no missing density. There is no dark matter. There is no dark energy. There is an infinite universe with stable density.

**All This Happened Because of a Switch from Curved Lines to Straight Lines?**
Curved lines and their trajectories are called geodesic lines and geodesic trajectories. Geodesic lines are an element of the geometry of curved surfaces, which posits that lines extending from curved surfaces are themselves curved. Random curved geodesic trajectories (of geodesic lines) will eventually cross each other because they are not parallel since they curve in response to a curved surface.

Straight lines and their trajectories are called Bohmian lines and Bohmian trajectories for David Bohm and describe quantum particle wave functions. Bohmian lines reflect straight line geometry of flat surfaces. Random straight Bohmian trajectories (of Bohmian lines) cannot cross each other because they are parallel across a flat surface.

Cosmological equations forming the foundation of the present model of the universe — singularities, Big Bang, black holes, dark matter/energy — use geodesic trajectories (curved) that assume space-time as a curved surface; these equations assume the curvature of space-time.

Cosmological equations forming the foundation of the new model of the universe — no age, no beginning, no end, no black holes or dark matter/energy — use quantum trajectories (straight) that assume a non-curved quantum space-time; these equations disregard the accepted nature of a curved space-time.

Singularities appear at the points where the trajectories cross in equations applying geodesic (curving) trajectories. If trajectories cross, singularities appear in the equations. If trajectories do not cross, no singularities appear in the equations.

Singularities do not appear in equations applying Bohmian (quantum wave) trajectories because there are no points where trajectories cross. If there are no crossing trajectories and no singularities appearing in the equations, then there is a new model of the universe that does not encompass a beginning and an ending, which originate and culminate in singularities (big bang beginning and big crunch ending are gone).

**The Detailed Stuff**
Ahmed Farag Ali and coauthor Saurya Das applied these Bohmian quantum trajectories to the Raychaudhuri equation (significant in Penrose–Hawking singularity theorems). This gave quantum-correction to the Raychaudhuri equation (the foundation of singularity physics) making it responsive to quantum, rather than geodesic, trajectories. This resulted in quantum-correction to Friedmann equations (significant in representing the expansion of space at the time of and following — but not before — the Big Bang) as a consequence of correcting geodesic to Bohmian trajectories.

**Why Undertake This?**
The model proposed by Ali, of Egypt's Benha University and Zewail City of Science and Technology, and coauthor Das, of the University of Lethbridge, Alberta, Canada, confirms the work by physics professor

Laura Mersini-Houghton, of the University of North Carolina at Chapel Hill, North Carolina, that was published in September 2014.

Mersini-Houghton sought to resolve the Einstein information loss paradox. In the process she mathematically proved that collapsing stars cannot collapse to an infinitely dense point to form black hole singularities. She proved that in a star's last gasp, it swells then explodes eliminating any chance of being compressed by its own gravity into a black hole. Her work's results left her "shocked": Black hole singularities cannot exist. She concludes that since singularities cannot form, the fabric of space-time needs to be reexamined and the model of the origin of the universe needs to be rethought.

These are the two things Ali and Das achieve. They approach space-time as flat, not curved, and they propose a model of the universe without a beginning, without a singularity that explodes. As UNC-Chapel Hill News reported:

The work not only forces scientists to reimagine the fabric of space-time, but also rethink the origins of the universe.
“I’m still not over the shock,” said Mersini-Houghton. “We’ve been studying this problem for a *[sic]* more than 50 years and this solution gives us a lot to think about."