D.3.4 - Density of the Universe

ACCELERATING (GREEN): Ωm is increasing or ρm<ρc: the universe will continue to expand, A universe filled with a (positive) cosmological constant will naturally lead to a Λ−dominated (Dark Matter) era in which the universe will eventually enter an accelerating phase as the matter content dilutes and ceases to affect the universe's large-scale dynamic behavior. Observations confirm this type of expansion.

In a universe without Dark Matter

CLOSED (YELLOW): Ω0>1 or ρm>ρc: the universe will stop expanding in finite time, after which it will reverse and (re-)collapse, in other words, there will be a maximum separation between coordinates; will eventually collapse in on itself, resulting in a “Big Crunch”

FLAT (RED): Ω0=1 or ρm=ρc: the universe will halt expansion in infinite time, the physical distances between coordinates will reach a maximum size in infinite time; gravity continually slows the expansion but takes infinite time to stop it

OPEN (BLUE): Ωm<1 or ρm<ρc: the universe will continue to expand, the physical distance between coordinates will continue to increase; Gravity may slow the expansion, but does not stop it.

A Flat Universe and Critical Density

Using a model of a Flat Universe (universe in equilibrium), we can determine the Critical Density (ρC ). The Critical Density will determine the fate of the universe.

It can be modeled using the following assumptions:

The total Energy in the universe is equal to zero (ET = 0).
Newtonian Laws of Gravitation apply. All potential energies are negative if separated by less than infinity.
If we imagine a homogenous sphere of gas with radius r and density p, and a galaxy of mass m on the surface of the sphere, the galaxy will be moving away with a recessional speed of v away from the centre.
Hubble's law determines the velocity of the galaxy, v = H0 r
The mass density (ρM) is compared to the critical density (ρC ) to determine if the universe is Open, Flat, or Closed.

Show that the critical density of the universe is:

The Density Parameter ( Ω0 )and its Implications

The density of the universe is greater than the critical density. Therefor the universe is 'Open'
1. Not only is the universe open, it is VERY open.
For the Universe to be open, as scientists believe it is, there must be 5000x more dark matter in the Universe than there is luminous matter

Recently, scientists used data from supernovas to determine that the expansion rate of the Universe is in fact increasing!

This data helps to support the open model of the Universe
Determining the fate of the Universe should be quite simple, assuming we can accurately calculate the mass of the entire Universe (simple!)

Unfortunately, we can only “see” less than 5% of the Universe

The rest is comprised of “dark matter”
- Dark matter is so named because we do not know what it consists of not because it isn’t luminous!
- Similarly, there is a concept of “dark energy” that is unrelated to the luminosity of the energy but rather to its mysterious nature

Dark Matter

Dark matter is a form of matter that does not emit, absorb, or reflect light, making it completely invisible to electromagnetic radiation, including visible light. Its presence is inferred from its gravitational effects on visible matter, radiation, and the large-scale structure of the universe.

Evidence in support of Dark Matter

Stars near the center of a Galaxy (BULGE):

lf we imagine a star, of mass m near (<8000 ly) the centre of a spiral galaxy at a radius of r, with total mass M, we can use Newtonian mechanics to determine the rotational velocity, v, of the star. We can equate the centripetal force (FC ) with Newton's Law of gravitation (Fg ).

Since the star is near the centre of the galaxy, we can't use the total mass, but must use the mass within the radius of it's orbit. We can do this by multiplying the volume by the density (assuming it is a sphere):

Show that:

So the velocity is directly related to the radius. Close to the center of a galaxy, the data matches the theoretical.

Galaxy rotation curve - Wikipedia

The star near the outer edge of the galaxy travels much faster than expected…But, why?

Stars near the EDGE of a galaxy:

For stars near the edge of a galaxy the model changes slightly. We can assume that the entire mass of the galaxy acts as a point mass (eliminating the need for the density calculation).

Using the same relationship of centripetal force and force gravity, SHOW that the tangential velocity of a star is:

If there were a halo of dark matter surrounding the outer rim of the galaxy.

This extra matter would increase the total mass, allowing for high rotational speeds, far away from the centre of the galaxy.

Additional Sources of Evidence:

Orbiting Galaxies:

Galaxies orbit each other too fast, similar to stars at the edge of galaxies

Cosmic Microwave Background (CMB):

Observations of the CMB radiation provide a snapshot of the early universe, showing fluctuations that suggest dark matter helped to form the large-scale structure of the universe.

Gravitational Lensing:

The bending of light from distant galaxies by nearer massive objects (like galaxy clusters) suggests there is more mass present than what we can see, indicating the presence of dark matter.

True or false: Does gravitational lensing reveal dark matter's nature?The best evidence for dark matter is astrophysical and indirect. Do new lensing observations point to ultra-light, wave-like dark matter?

Gas bound to galaxies that shouldn’t have enough gravity to hold on

Dark Energy - Cutting Edge

While Dark Energy is not a very well understood concept at this point in time, it is thought to be

[1] the force/energy that is causing the expansion of the universe to accelerate.

[2] Dark Energy is an energy filling all space. Unlike dark matter, which pulls objects together through gravity,

[3] dark energy appears to be pushing objects apart.

[4] This dark energy makes up about 70% of the energy of universe.

[5] The amount of dark energy is directly dependent upon the volume taken up by vacuum in the universe. This means that as the universe expands, dark energy will become more and more abundant. Since it is a repulsive force, an increase in dark energy will lead to an acceleration in the universe’s expansion.

[6] Currently, the evidence suggests that dark energy will continue to drive the accelerated expansion of the universe.

There is a lot of research going on at this time to try to understand how dark energy may play a role in our universe, but it’s currently thought that this dark energy is a major player. The ESA’s Plank mission provided data to understand how much of the universe may be made up of dark energy.

Next time you're late to work, blame dark energyEver since Lemaitre and Hubble's first proposed it in the 1920s, scientists and astronomers have been aware that the universe is expanding. And from these observations, cosmological theories like the Big Bang Theory and the "arrow of time" emerged. Whereas the former addresses the origins and evolution of our universe, the latter argues that the flow of time in one-direction and is linked to the expansion of space.

Evidence for Dark Energy:

Accelerating Universe:

Observations of distant supernovae have shown that the universe is expanding at an accelerating rate. Dark energy is the most widely accepted explanation for this acceleration.

Cosmic Microwave Background:

The CMB also provides evidence for dark energy through its impact on the geometry and expansion rate of the universe.

Possible Candidates as Sources of Dark Energy:

Black Holes

Neutrinos

Brown Dwarfs

Episode 112 - Brown Dwarfs, Dark Matter and Dark Energy - AstrotalkUKEuclid, a @esa science mission, will shed light on both dark matter and dark energy. It was launched in July 2023 and arrived in its L2 orbit a month later. It has just two instruments which will produce a high-resolution 3-D map of a third of the sky, stretching back 10 billion years during its initial 6-year operational lifetime.

Massive Compact Halo Object / MACHO

Weakly Interacting Massive Particle /WIMP

They neither absorb nor emit light and don't interact strongly with other particles. But when they encounter each other, they annihilate and make gamma rays.

Two Possible Futures of Universe:

Heat Death: The universe could continue expanding forever, becoming colder and emptier over time, eventually reaching a state where no thermodynamic free energy exists, and hence, no life or motion is possible.

Big Rip: If dark energy increases in strength over time, it could tear apart galaxies, stars, and eventually atoms themselves.

Summary of Forms of Matter and Energy in the Universe

Where do we go from here?

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