M22 - The Ultimate Fate of the Universe

Hubble’s Law

Tells us the universe is expanding

• Redshift indicates distant galaxies are moving away from us

• Spacetime is expanding

Big Bang Model Interpretation of Hubble’s Law

This model tells us the universe began in a hot, dense state about 14 billion years ago

• Cosmic Microwave Background

Cosmic Microwave Background

Provides extremely strong evidence for the Big Bang

• Leftover radiation from the universe’s extremely hot and dense state

Hubble’s Law Deviation

There’s a deviation in actual observations from Hubble’s Law

• Distant galaxies are farther than expected

• Expansion of the universe is accelerating

Dark Energy

Responsible for the acceleration of the universe

• Makes up 68.3% of the universe

Contents of the Universe

Ordinary Matter - 4.9%

Dark Matter - 26.8%

Dark Energy - 68.3%

Observational Limit

The further away we look in the universe, the further back in time we are looking

Observational Limit and the Sun

We see the Sun as it was 8 minutes ago because it takes light from the Sun 8 minutes to reach us

Observational Limit and CMB

Farthest visible thing we will ever see is the CMB

• 13.8 billion years ago

Observable Universe

The portion of the universe we can see from Earth

• Earth at the center

• Limited by how far light has had time to travel since the Big Bang (13.8 billion years ago)

Other Observable Universes

Each observer has their own observable universe

• Only contains objects whose light has had time to reach them

Expansion of the Universe

The expansion of the universe means the radius of the observable universe has been stretched to about 46.5 billion ly

Whole Universe

The whole universe is likely much bigger than the observable universe

• Other regions physically exist but light has not reached us yet

Geometry of the Universe

We can measure the size of the universe (including the parts impossible to see) using the curvature of the universe

Curvature of the Earth

To measure the curvature of the Earth, we can use triangles

• On a flat surface, angles inside a triangle always add to 180°

Positively Curved Surface

On a positively curved surface (e.g. a sphere) the angles add up to more than 180°

• The corners “open up” a bit

Measuring the Curvature of the Earth

1. Triangles made in a relatively small area (e.g. a city) will have interior angles adding up to roughly 180°

   1. The surface would seem flat

2. Triangles made in a relatively large area would add up to more than 180°

Measuring the Curvature of the Universe

We can use the CMB to measure the curvature of the universe

• Types of curves:

  • Closed (positive curvature)

  • Open (negative curvature)

  • Flat (no curvature)

CMB temperature variations

We can use the CMB’s temperature variations to measure the universe’s curvature

• This is the equivalent of measuring the angles inside a very large cosmic triangle

Closed Universe

Positive curvature. Has a finite size but is unbounded (there’s no edge)

• i.e. you can start at one point and moving in the same direction causes you to loop back to your starting point

Open Universe

Negative curvature. Can be infinite in extent with no edges

• i.e. you can start at one point and move in the same direction but never return to your starting point

Flat Universe

No curvature. Can be infinite in extent with no edges

• i.e. you can start at one point and move in the same direction but never return to your starting point

3D volume

The 3D volume of the universe can be curved around a fourth, mathematical dimension

Measured Geometry

As precisely as we can measure, the geometry of the universe is flat

• “Flat” means no intrinsic curvature; lines are straight, drawing triangles at any orientation results in angles that sum up to 180°

Flat Misconception

When we say the universe is flat we don’t mean that’s like a piece of paper

• It means the parallel lines never converge, and the sum of the angles inside large triangles is 180°

Infinite Size

The most obvious way to interpret a geometrically flat universe is that it has infinite size

• You could head off in any direction and never encounter an edge or return to your starting point

Geometry and Ultimate Fate of the Universe

Geometry of the universe is determined by how much “stuff” (matter and energy) there is in the universe

• This determines how the universe evolves over time

Geometry and Density

The geometry of the universe is related to its overall density

• Quantified by the density parameter (omega ‘Ω’)

Total Density of the Universe

Ω = Ω_m + Ω_Λ​ + Ω_rad

total density = density of matter and dark matter + density of dark energy + density of radiation (all the light in the universe)

Negligible Radiation

In our universe, the total amount of radiation contributes a negligible amount to the overall density

Instead we could use:

Ω = Ω_m + Ω_Λ​

Density Parameter Definitions

The density parameter is defined so that

Ω = 1 (universe is flat)

Ω < 1 (universe is open)

Ω > 1 (universe is closed)

Closed, matter-dominated universe

When matter dominates (ordinary + dark matter)

• We get a CLOSED universe that ends by collapsing in a reverse Big Bang known as the Big Crunch

Ωₘ = 5, ΩΛ = 0

Flat, matter-dominated universe

When matter is just the right amount (ordinary + dark matter)

• We get a FLAT universe that expands forever at a decelerating rate

Ωₘ = 1, ΩΛ = 0

Open, matter-dominated universe

With less matter AND no dark energy

• We get an OPEN universe that expands forever

Ωₘ = 0.3, ΩΛ = 0

Flat, dark energy dominated universe

When dark energy dominates

• We get a FLAT universe that expands and accelerates indefinitely

Ωₘ = 0.3, ΩΛ = 0.7

Heat Death of the Universe

In the far future, an accelerating universe (i.e. our universe) will experience heat death

• All matter and energy will be spread so thinly that interactions become impossible

• Everything becomes cold, dark, and isolated

Heat Death of the Universe Characteristics

Star formation slows

Galaxy isolation

CMB undetectable

Black hole dominance

Star Formation SLows

Galaxies will be populated by old stars, night skies will grow dark

• Already happening

Galaxy Isolation

Relentless expansion will isolate individual galaxies

• i.e. each galaxy will be in its own personal observable universe, no other galaxies will be visible from it

CMB Undetectable

CMB will be redshifted to undetectable wavelengths

• At this point, astronomers will have difficulty proving there even was a Big Bang

Black Hole Dominance

More and more matter will end up inside black holes

Problems with the Big Band Model

The conventional Big Bang model predicts the heat death

• But it has some known problems to it