Ovidio Universe: Friedmann Universe Model

January 08, 2021

Friedmann Universe Model

The "Friedmann model" is a model of the Universe governed by the Friedmann equations, which describes how the Universe expands or contracts. These equations are a solution to Einstein's field equations, and with two very important assumptions they form the basis for our understanding of the evolution and structure of our Universe. These assumptions, together called "the cosmological principle", are that the Universe is homogeneous, and that it's isotropic.

The cosmological principle

Homogeneity

That the Universe is homogeneous means that its "the same" everywhere. Obviously, it's not, really. For instance, under your feet is a dense, rocky planet, whereas above your head there's thin air. We live in a galaxy full of stars and molecular clouds and what not, while 100,000 lightyears from the Milky Way, there is virtually nothing. But on very large scales, say above half a billion lightyears, the Universe actually looks the same all over.

Isotropy

That it's isotropic, means that it looks the same in all directions. Again, obviously it doesn't on small scales, but on large scales, it does. If it didn't, it would mean that we occupied a special place in the Universe, and we don't think we do.

So, neither of these assumptions have to be true, but observations tell us that apparently, they are.

You might think that a homogeneous Universe would also be isotropic and/or vice versa, but that's not the case.

Three possible solutions

It turns out that, for these assumptions, there are three possible solutions to the Friedmann equation. We call the three possible universes flat, positively curved (or "closed"), and negatively curved (or "open"). Which of these possible universes we live in, turns out to depend upon the average density in the Universe, so by measuring this, we can determine the "geometry" of our own Universe. And it seems that it's "flat".

A flat universe

The reason it's called flat is that the geometry is like that of a flat 2D table, only in 3D. That is, a triangle has 180º, parallel lines never meet, etc. And it's infinitely large. Intuitively, we'd think that this is the way the Universe is, and definitely on small scales (say within our own Galaxy), it's an adequate approximation. In the 2D analogy, the 2D surface of Earth seems flat locally, and for all practical purposes the parking lot outside is flat. But if you draw a triangle from Congo→Indonesia→the North Pole→Congo, you'd measure it's sum of angles to be roughly 270º. That's because the geometry of the surface of Earth is not flat, but is "closed".

A closed universe

If the Universe were "closed", it's geometry would, in the 2D analogy, correspond to that of the surface of a ball, i.e. a triangle has more than 180º, lines that start out being parallel will at some point meet, etc. But like the surface area of a ball is finite (but doesn't have a border), so is the Universe. So if you take you spaceship and fly straight away from Earth, you would end up back here (assuming the Universe doesn't collapse before you get back, or expand too fast for you).

An open universe

If it were "open", it's geometry would, in the 2D analogy, correspond to that of the surface of a saddle, i.e. a triangle has less than 180º, lines that start out being parallel will diverge, etc. And it's infinitely large.

This picture from here visualizes the 2D analogies.

In 3D, only a flat geometry can be pictured, and this doesn't look "flat" by any means; it is simply your good old 3D ("Euclidian") space that you know from your everyday senses.

Expansion of the Universe

The Friedmann equation, together with the densities of the constituents of the Universe (radiation, normal matter, dark matter, and dark energy) tell us how the Universe expands. So, again by measuring these densities, we can prediect the evolution of the Universe. And it seems that the Universe not only expands, but actually expands faster and faster.

Density parameters
Whether the geometry of the Universe as described above is flat, closed, or open, depends on whether the total density $ρ_{t o t}$ is exactly equal to, above, or below a certain critical threshold $ρ_{c r} \sim 10^{- 29} g {c m}^{- 3}$ . It is customary to parametrize the density of the $i$ 'th component as $Ω \equiv ρ_{i} / ρ_{c r}$ .

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Black Holes and Wormholes FAQ

1 - What is a wormhole?

Wormholes are tunnels in space-time that can theoretically allow travel anywhere in space and time, or even into another universe. In many ways, wormholes resemble black hole.

2- How is wormhole created?

In principle, building a wormhole is pretty straightforward. According to Einstein's Theory of General Relativity, mass and energy warp the fabric of space-time. And a certain special configuration of matter and energy allows the formation of a tunnel, a shortcut between two otherwise distant portions of the universe

3- Is a wormhole possible?

A physicist has shown that wormholes can exist: tunnels in curved space-time, connecting two distant places, through which travel is possible.

4- Can black holes be wormholes?

From the outside, wormholes can appear similar to black holes. But while an object that falls into a black hole is trapped there, something that falls into a wormhole could traverse through it to the other side. No evidence has been found that wormholes exist

Baryon Matter

Baryon matter is the foundation that 
constitutes every body and object in 
our Universe. 
To better understand how it is structured, 
it is necessary to refer to the classification 
scheme  of the Standard Model as it has 
been structured over the last century.  
The Standard Model predicts that matter 
is basically the product of two types of
particles,light ones,leptons, and heavy ones, 
baryons. 
Both terms derive from the Greek. 
While leptons are truly fundamental particles, 
i.e. not further divisible into other particles, 
baryons are aggregates of other elementary 
particles such as leptons, quarks that are 
endowed with fractional charge,
 i.e. a fraction of the charge of an electron.

Light Year

The light-year is a unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometres (9.46×10¹² km) or 5.88 trillion miles (5.88×10¹² mi).As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year (365.25 days).Because it includes the word "year", the term light-year may be misinterpreted as a unit of time.

The light-year is most often used when expressing distances to stars and other distances on a galactic scale, especially in non-specialist contexts and popular science publications.

1 light-year	= 9460730472580800 metres (exactly)
	≈ 9.461 petametres
	≈ 9.461 trillion kilometres (5.879 trillion miles)
	≈ 63241.077 astronomical units
	≈ 0.306601 parsecs

What is the antimatter

The antimatter is missing – not from CERN, but from the Universe! At least that is what we can deduce so far from careful examination of the evidence. For each basic particle of matter, there exists an antiparticle with the same mass, but the opposite electric charge. The negatively charged electron, for example, has a positively charged antiparticle called the positron. When a particle and its antiparticle come together, they both disappear, quite literally in a flash, as the annihilation process transforms their mass into energy.

The evidence spoke for itself

The ‘case file’ of antimatter was opened in 1928 by physicist Paul Dirac. He developed a theory that combined quantum mechanics and Einstein’s special relativity to provide a more complete description of electron interactions. The basic equation he derived turned out to have two solutions, one for the electron and one that seemed to describe something with positive charge (in fact, it was the positron). Then in 1932 the evidence was found to prove these ideas correct, when the positron was discovered occurring naturally in cosmic rays.

For the past 50 years and more, laboratories like CERN have routinely produced antiparticles, and in 1995 CERN became the first laboratory to create anti-atoms artificially. But no one has ever produced antimatter without also obtaining the corresponding matter particles. The scenario should have been the same during the birth of the Universe, when equal amounts of matter and antimatter would have been produced in the Big Bang.

“Just one more thing…”

So if matter and antimatter annihilate, and we and everything else are made of matter, why do we still exist? This mystery arises because we find ourselves living in a Universe made exclusively of matter. Didn't matter and antimatter completely annihilate at the time of the Big Bang? Perhaps this antimatter still exists somewhere else? Otherwise where did it go and what happened to it in the first place?

Such questions have led to speculative theories, from a break in the rules to the existence of an entire anti-Universe somewhere else! The way to solve the baffling disappearance of antimatter, and to learn more about this substance in general, is by studying both particles and antiparticles to find and decipher the subtle clues.