## Rip, Crunch, Freeze: The Three Fates of our Universe

Written by: Laya Gopalakrishnan

Every action has an equal and opposite reaction, so states Newton’s Third Law of Motion. This idea pertains to every conceivable instance in spacetime, from two people playing catch to the collision of planets. However, how can we apply this same ideology to the existence of our universe? As scientists currently believe, an event called The Big Bang, an outward expansion of an infinitely dense singularity, was the genesis of our universe. Calculations made by examining Cosmic Microwave Background radiation left over from the Big Bang and the behavior of light according to the Doppler shift maintain this theory of indefinite expansion, but can this state of growth exist for eternity? In 1922, Russian physicist and mathematician Alexander Friedmann developed a dynamic set of equations that predicted the fate of the universe. Based on his findings, there are three possible explanations of the end of spacetime, or at least our perception of it. Either the universe will be torn apart due to its sheer gravitational power, implode into a singularity, or continue to expand indefinitely.

Density Destiny

Published in 1916 by Albert Einstein, the Theory of General Relativity states that rather than an object’s gravity being a linear attractive force it determines the warping of space around an object. However, despite its successes in explaining previously unexplainable gravitational occurrences, such as the orbital path of Mercury, the equation was primitive in defining the end state of the universe. To remedy this issue Einstein added a cosmological constant to the equation, making it a messy fix for an impactful matter. Enter Alexander Friedman. Friedman created an elegant mathematical solution, casting out the cosmological constant and creating a set of equations void of the assumption that the universe is static.

Figure 1

The first Friedman equation helps to remedy the rudimentary nature of Einstein’s theory of General Relativity. One remarkable fact about the creation of these equations was that they were created before the discovery of universal expansion.

Source: [HyperPhysics]

In short, the equations help explain the evolution path of any one universe depending on its expansion rate and content. The first Friedman equation [Figure 1]  makes use of the Hubble expansion rate, the concentration of matter and radiation in the universe in question, the radiation levels in said universe, and any remaining forms of energy present. It also utilizes the theory of General Relativity by taking into account the shape of the universe: flat, closed, or open [Figure 2].

Figure 2

An image depicting the three possible shapes of the universe: closed (top), open (middle), or flat (bottom.

Source: [OFluxo]

However, the equation’s end result boils down to one variable: k. In the equation, the k parameter, representing curvature, accomplishes two very important things. It determines the shape of the universe, a component of the equation stated previously, but it also determines the density of the universe in relation to its shape. This extremely important information to take into consideration as the universe’s density in relation to its critical mass density—“the average density of matter required for the Universe to just halt its expansion”—determines its fate.

Figure 3

The equation used to determine the critical mass density of the universe as a function of time.

Source: [HyperPhysics]

The Eternal Dark Age: The Big Freeze

If at a certain point in the future the k parameter of the first Friedman equation [Figure 1] equals 0 indefinitely, then the density of the universe will be exactly equal to its critical mass density, resulting in infinite expansion. The force of gravity would be unable to overcome dark energy’s outward pull and the universe’s breadth would extend into oblivion.

Applying this model to our universe, in a trillion years, only the closest galaxies near the Milky Way will be visible, all others being too far away to perceive or interact with our own. At this point, star formation will have ceased and black holes will no longer have material to consume in its reachable vicinity. A googol years from now, all matter will have evaporated via Hawking radiation—the thermal radiation emitted by black holes—and the universe will be an empty shell of what it once was.

It’s Crunch Time: The Big Crunch

If the k parameter exceeds 0, then the density of the universe will be greater than it’s critical mass density and gravity will take over as the main driving force. Eventually gravity will overpower the force of dark energy, a constant value in our universe. There are two possible outcomes that could result from this Big Crunch event.

In the event that all of creation compressed itself into a singularity, it is likely that this high density point in space time would create a supermassive black hole, enveloping our universe. However, it is equally likely that this singularity would pave the way for a new Big Bang, or the Big Bounce. The universe would begin a new genesis, and, if this theory stands true, who is to say that our version of the universe is it’s first iteration?

The Big Rip

In the final theorized scenario, if the k parameter is less than zero, the force of dark energy would far exceed the force of gravity, resulting in a sudden increase in the universal expansion rate. This would result in all matter being ripped apart, down to each atom’s subatomic particles. Rather than expanding consistently for infinity like the Big Freeze, this ending would result in a far more violent burst. Matter would be destroyed rather than slowly ceasing to exist due to the deprivation of matter-on-matter interactions.

This theory is extremely unlikely however due to the concentration of dark energy in our universe being a constant (as previously stated). This would mean that it as a variable force would not be able to adopt governance in our universe.

Figure 4

A graphical representation of The Big Rip, The Big Freeze, and The Big Crunch in relation to the rate of cosmic expansion.

Source: [Astronomy Magazine]

In Our Final Moments

The final fate of our cosmos remains a mystery. Each outcome has its flaws and likelihoods, each becoming more convincing as further research is conducted. It is also entirely likely that new theories will come to light as technological advances pave the way to more accurate cosmological concepts and theories. However, it is the ambiguity of these unanswered questions that drive those at the forefront of the theoretical sciences.

References and Sources