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http://www.sciencedirect.com/science/article/pii/S0370269314009381#
Basically the gist is this. In General Relativity, gravity is treated not as a force, but as curved space-time. Instead of thinking of the earth as tugging apples down to it, think of the earth as sitting on a giant trampoline, and the dimple it makes in the trampoline is the distortion of space. That means that equations of motion in general relativity aren't written for flat spaces, like you made have done when figuring out classical trajectories using Newtonian mechanics in high school, but rather on curved spaces. Now in the absence of external forces (and remember, gravity isn't a force in General Relativity), particles will follow the shortest line between themselves and their destination. The shortest line on curved spaces isn't a straight line, it is called a geodesics (like how airplanes don't fly straight their destination). When the equations in General Relativity are solved, they are solved by treating particles with no external forces applied to them as moving on geodiscs, and these results predict that the universe was once collapsed into a point-like state.
Now shelve that for a second. Bohmian mechanics is an area I'm intimately familiar with, as do development on Bohm's theories. Bohmian mechanics differs from the popular Copenhagen interpration of Quantum Mechanics you are used to. Under Bohmian mechanics, particles do not existed in "all possible states" and "collapse". Instead, in Bohmian mechanics, quantum particles are actually a field of "fluid-like" particles, and their positions and momentum are set and defined. The fluid then evolves in time according a "Guidance equation", which is determined by the systems wavefunction. An equation for the motion of the individual fluid particles was derived independently by Bohm and deBroglie, and looks almost likes Newtons second law (F=ma), except there is a second force between fluid particles, that also depends on the amplitude of the wavefunction, called plainly, the quantum potential.
What the above authors did was merge Bohmian mechanics into General Relativity. Bohmian particle trajectories don't necessarily follow the relativistic geodisics because of the the quantum potential. So they derived Friedmann's equations (the central equations in expansion of space time and the prediction of the big bang) using the Bohmian trajectories instead of geodesics, and what they see is that there is a second term, a radiation term, arising. Basically as the universe crunches, the quantum potential explodes and causes particles to radiate until the radiation pressure kicks off new expansion. Likewise, when the universe expands to much, the quantum potential will serve to pull it back down. The result isn't a Big Bang or a Big Crunch to a singlularity, but rather an infinite oscillation of small universe to large universe to small universe again, forever onward.
Anyway, thought it was interesting. Feel free to discuss the origins of the universe.
Further reading if you are interested:
Background:
https://en.wikipedia.org/wiki/Raychaudhuri_equation
https://en.wikipedia.org/wiki/Geodesics_in_general_relativity
https://en.wikipedia.org/wiki/Friedmann_equations
https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory
Scientific reading:
Very digestable and easy description of Bohmian mechanics: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.82.5190
A longer but still readable description from Bohm himself: http://www.sciencedirect.com/science/article/pii/037015738790024X#
Quantum potential in dense Bose-Einstein condensate predicts no singularity, gives correct cosmological constant: http://arxiv.org/abs/1411.0753
Basically the gist is this. In General Relativity, gravity is treated not as a force, but as curved space-time. Instead of thinking of the earth as tugging apples down to it, think of the earth as sitting on a giant trampoline, and the dimple it makes in the trampoline is the distortion of space. That means that equations of motion in general relativity aren't written for flat spaces, like you made have done when figuring out classical trajectories using Newtonian mechanics in high school, but rather on curved spaces. Now in the absence of external forces (and remember, gravity isn't a force in General Relativity), particles will follow the shortest line between themselves and their destination. The shortest line on curved spaces isn't a straight line, it is called a geodesics (like how airplanes don't fly straight their destination). When the equations in General Relativity are solved, they are solved by treating particles with no external forces applied to them as moving on geodiscs, and these results predict that the universe was once collapsed into a point-like state.
Now shelve that for a second. Bohmian mechanics is an area I'm intimately familiar with, as do development on Bohm's theories. Bohmian mechanics differs from the popular Copenhagen interpration of Quantum Mechanics you are used to. Under Bohmian mechanics, particles do not existed in "all possible states" and "collapse". Instead, in Bohmian mechanics, quantum particles are actually a field of "fluid-like" particles, and their positions and momentum are set and defined. The fluid then evolves in time according a "Guidance equation", which is determined by the systems wavefunction. An equation for the motion of the individual fluid particles was derived independently by Bohm and deBroglie, and looks almost likes Newtons second law (F=ma), except there is a second force between fluid particles, that also depends on the amplitude of the wavefunction, called plainly, the quantum potential.
What the above authors did was merge Bohmian mechanics into General Relativity. Bohmian particle trajectories don't necessarily follow the relativistic geodisics because of the the quantum potential. So they derived Friedmann's equations (the central equations in expansion of space time and the prediction of the big bang) using the Bohmian trajectories instead of geodesics, and what they see is that there is a second term, a radiation term, arising. Basically as the universe crunches, the quantum potential explodes and causes particles to radiate until the radiation pressure kicks off new expansion. Likewise, when the universe expands to much, the quantum potential will serve to pull it back down. The result isn't a Big Bang or a Big Crunch to a singlularity, but rather an infinite oscillation of small universe to large universe to small universe again, forever onward.
Anyway, thought it was interesting. Feel free to discuss the origins of the universe.
Further reading if you are interested:
Background:
https://en.wikipedia.org/wiki/Raychaudhuri_equation
https://en.wikipedia.org/wiki/Geodesics_in_general_relativity
https://en.wikipedia.org/wiki/Friedmann_equations
https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory
Scientific reading:
Very digestable and easy description of Bohmian mechanics: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.82.5190
A longer but still readable description from Bohm himself: http://www.sciencedirect.com/science/article/pii/037015738790024X#
Quantum potential in dense Bose-Einstein condensate predicts no singularity, gives correct cosmological constant: http://arxiv.org/abs/1411.0753
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