Some Definitions for Cosmology

© Matt Strassler [March 19, 2014]

Energy Scales

Particle physicists describe the amoung of energy in an object or process in terms of eV (electron-volts) or GeV (1,000,000,000 electron-volts).

The mass M of a proton (which is about the same as the mass of a hydrogen atom) is about 1 GeV/c², where c is the universal speed-limit [the “speed of light”]; thus it’s mass-energy Mc² is about 1 GeV.  [Actually the number is about 0.938 GeV/c².]

The Large Hadron Collider [LHC] makes protons collide with energy of a few TeV (and 1 TeV = 1000 GeV).

Roughly speaking, the energy required to make the lightest possible black hole is called the [“reduced”] Planck energy, a million million million GeV (i.e., 1,000,000,000,000,000,000 GeV.)  For particle collisions at this energy, in contrast to collisions at lower energy, gravity is as important a force in determining how the collision plays out as are any of the other forces.

The Planck mass is the Planck energy divided by c², the Planck time is Planck’s constant h divided by the Planck energy, and the Planck length is the Planck time times c.  Quantum gravity — where space and time themselves become subject to quantum jitter (“quantum fluctuations“) — becomes important when an amount of energy comparable to the Planck energy is compressed into a ball with a radius of the Planck length.

The Energy Scale of “Dark Energy’ “

The amount of “dark energy’ ” or “cosmological constant’ ” Λ (which is neither energy nor necessarily constant in time — it is really an amount of energy density [energy per unit volume] along with negative pressure of exactly the right amount) is measured as an energy per unit volume, i.e., energy/length3.

By multiplying by (hc)3, where h is Planck’s constant and c is the universal speed limit (“the speed of light”), physicists form a quantity which is an energy to the fourth power.  Taking the square root of the square root of that quantity [i.e., the “fourth root”] gives them an energy.  So the “energy scale” of the “dark energy’ ” is

• [(hc)3 Λ]1/4

Important: remember this is the overall scale associated with the dark energy, NOT the amount of dark energy per unit volume.  If I increase the energy scale by a factor of 10, I increase the amount of dark energy per unit volume by a factor or 104 = 10,000 !

The maximum energy scale that dark energy could possibly have during inflation is the Planck scale.  The dark energy in the universe today has a scale about a million million million million million times smaller than that!  [i.e. 1030 = 1,000,000,000,000,000,000,000,000,000,000 times smaller!]

5 thoughts on “Some Definitions for Cosmology”

1. Professor, are you implying that the dark energy in the universe today, which is driving the increasing expansion, is connected to the energy that drove the inflation period of the very early universe ?

• No. Energy is energy — there can be many sources of it.