The fate of the universe: “Friedmann equations”. The evolution of the universe has always been
a mysterious problem, hundreds of theories have tried to describe such an existential topic both
from a philosophic and a scientific point of view. How and when was the universe formed? Is it
infinitely big? Will our universe “die”? These are just some of the questions that we would like
to deal with when talking about Universe. Most of us will say that it’s almost impossible to answer
even to just one of them, but they might be wrong… Did you know that there are three equations,
called the Friedmann equations, that can help us find a solution for all these incomprehensible
interrogatories? Do you want to know more about them? Stick with me and I’ll tell you
everything in a moment. Several different
views about the universe started to arise during the nineteenth century with the development of
astronomy and the use of telescopes. The major belief was that our universe must be
stationary and infinite, like a little balloon that never changes his size. Unfortunately,
nobody managed to create a theory that explained how the universe was formed. As a result of that,
the scientific community was considering our world as something that has always existed, something
totally immutable, boundless and infinite. Therefore, this structure was proved to be wrong
by a simple paradox known as the Olbers paradox. Have you ever heard anything about that? It
just tries to explain why the night sky is dark. Even if it seems to be irrelevant and useless to
describe something we see every night, this little paradox has taken us to astonishing conclusions.
As a matter of fact, the night sky can be dark only if the universe is limited in space or time.
Let’s try to understand why. If the universe is infinitely big, we can find a star in every
direction of the sky, and if it’s infinitely “old” enough time has passed for the light of that star
to reach us. Consequently, the night sky should be really shiny and bright in every direction. Since
we see a dark sky, we have just two options left. The first is that the universe is not infinitely
big, there are no stars in some directions and those areas will never shine. The second is that
the universe is infinitely big, but not infinitely old, so that the light from some parts of the sky
is so far away from us that it would need more time than the age of the universe to reach us.
This little paradox has a great power and is considered to be the foundation
of modern cosmology, the science that studies the development of the universe as a system.
Since the universe is not infinite, this suggests that it has to change during time
and that it has to be formed in a detailed way. As a matter of fact, with the beginning
of the twentieth century scientists were very puzzled about a possible description of the
universe as a single system and they created a theory that would definitely change the way we
perceive our world: the theory of Big Bang. Firstly, three physicists called Robertson,
Friedmann and Walker developed a strange way to locate things in space. Usually on Earth
everything is described by two coordinates called longitude and latitude. The same can
be done with space, but the possibility of an instable universe that might expand or contract
required a different type of coordinates. The three scientists came up with a great idea that
was really useful to describe such a phenomenon. They introduced the so-called scale factor R,
that describes if the universe has expanded or not. A good comparison can be made with an air
balloon similar to our earth. Let’s imagine that it has a scale factor R=1 and a little point with
its coordinates is drawn on it. If we inflate the balloon and its size doubles, the point will
always have the same coordinates, but the balloon will be bigger than before and its scale factor
will be R=2. In physics we say that the point is located by a system of “comoving coordinates” that
don’t change in time and the size of the balloon is described by the scale factor that changes in
time if the size increases or decreases. This system is also known as FRW metric.
Furthermore, this useful type of coordinates depends even on a “curvature parameter”, called K,
that describes the shape of space. There are three types of curvature: flat (k=0) like an
even ground, positive or “closed” (k=1) like that of a spheric object as the Earth and negative or
“open” (k=-1) like that of a Pringles potato chip. What is the curvature of our universe?
Our universe is supposed to be flat, but we’ll discuss that later on in this video.
In 1915 Albert Einstein published the General Theory of Relativity, one of the most successful
theories in the history of physics that resulted to be a crucial element in the development of
cosmology. As a matter of fact, seven years later Aleksandr Aleksandrovich Friedmann developed the
three most famous equations about the evolution of our universe by using Einstein’s discoveries and
the FRW metric he helped to create years before. The Friedmann Equations are partially derivable
from Newton gravitational theory of the seventeenth century,
but the math might be a little tricky and puzzling, so let’s just try to make it simple.
What are those equations about? They are three laws that link the scale factor of our universe
to the space curvature and some other parameters that can be measured observing stars and galaxies.
The first one shows that the velocity, which is the change of the scale factor, is linked to the
density and the curvature of our universe. The second Friedmann equation deals with
the acceleration of the universe, that results to be always negative.
Consequently, the rate of expansion or contraction is slowing down with time.
Finally, the third law, also known as the “fluid equations”, describes the correlation
among the change of the density, the pressure of radiation and the scale factor R. The first
one favours a contraction, because matter has a strong gravitational force that tends to gather
everything together, as the sun does with our planets. On the other hand, the pressure of
radiation enables a possible expansion. What is pressure of radiation? The universe is filled with
electromagnetic radiation (like light, x rays, gamma rays, infrared and other types) that has
the ability to warm objects (we experiment this when we take sunrays at the beach for example),
but even to have a small pressure on things, similar to that of a wind. As a result of that,
the presence of radiation goes against gravity and might slow down the contraction or cause an
expansion of the universe. As a matter of fact, we distinguish between a radiation-dominated era and
a matter-dominated. This law predicts that the density is bigger if the scale factor becomes
smaller. This equation is the main source from which the idea of Big Bang came up:
at the beginning the universe was extremely dense and small and after a period of
expansion it has reached the actual size. Moreover these equations are a powerful
tool to derive the age of universe, which happens to be around 13/14 billions of years.
However, the most important parameter that can define the real evolution of the universe
is the curvature that appears in the first equation. If we live in a flat space (K=0)
the scale velocity is positive, the universe will tend to expand at a decelerated rate
stopping in an infinite time. In this case the density is called “critical density”.
Instead, if we live in an open space (K=-1) the density will be smaller, the velocity bigger,
and the universe will expand at a constant rate forever. The galaxies will be so far
away from us that their light won’t be able to reach us, the night sky will start to become
darker and darker. Moreover, the space will become colder and colder. We call
these possible end of the universe “Big Rip”. On the other hand, if space is closed (K=1) the
density will be bigger than the critical one. The velocity will decrease becoming negative,
the universe will start to contract returning to the size it had in the
first instants of its life: the “Big Crunch”. Could you imagine that the fate of our universe
depends on small changes of a parameter? But what is the actual curvature of
the space? How has it been measured? We previously said that space is almost
flat. This result has been calculated by measuring some elements of the cosmic microwave background,
a radiation that fills space and is like a last emission of the big bang explosion. This “light”
is almost uniform in every direction, and the size of the small differences in intensity indicates
that the curvature parameter is nearly 0. Consequently, at the end of the last century
physicists thought to be in a flat universe expanding at a decelerating rate. However,
they were proved to be wrong by an astonishing discovery. In 1998 a group of astronomers leaded
by Samuel Perlmutter was measuring the light of several supernovae (explosions of big stars
at the end of their lives) and they noticed that their light was fainter and more red
than expected. In physics this effect, called redshift, means that the universe is expanding
and the lower intensity measured means that the supernovae were further than expected. As
a result of this discovery scientists suggested that the universe was expanding with a positive
acceleration. Instead of slowing down, it was speeding up! After that, Perlmutter and his
group received the Nobel Prize in 2011. Are Friedmann equations wrong? What
is the cause of acceleration? These are the two main questions
physicists tried to answer in the last twenty years after Perlmutter’s observations. It was
crystal clear that Friedmann equations needed to be modified and a small but
significative alteration was made indeed. In the first two laws a “cosmological constant”
was added. This quantity is positive and is a sort of addictive pressure opposed to the gravitational
contraction. It was first introduced by Einstein, that lately admitted to have probably committed
an error and described it as his “biggest blunder”. However, the cosmological constant
resulted to be perfect for the description of the accelerated expansion through the Friedmann
equations. The addiction of this quantity made the acceleration positive in the second law and
it can be considered as an extra-density. Unfortunately, it’s totally unknown what
the constant represents, what is the cause of the acceleration. Scientists think that
the universe is filled with an obscure energy called “dark energy” which opposes to gravity.
The major problem is that through various measurements physicists found out that dark
energy is nearly 70% of the universe abundances. Its impact on the evolution of the Universe is
way more important that the density matter. Finally, the universe is almost flat and
is expanding an accelerated rate. If this trend will continue the universe will end in a Big Rip,
a cold epilogue with all the galaxies very distant from each other. However,
we know very little about the dark energy, which is the most predominant constituent of space,
and more observation are surely needed to find out more about the fate of the Universe.
"This video ends here! Thanks for watching everyone! Did you find this topic exciting?
Are you amazed by the possible endings of the universe? Are you afraid by discovering that it
could all end in a Big Crunch or Big Rip? Is there anything more you want to hear about time? Let me
know in the comments below, be sure to subscribe, and I'll see you next time on the channel!"