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 responses to “Some Definitions for Cosmology

  1. Kevin Fairweather

    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 ?

  2. Siddartha Gudipati

    professor , i have been told in the temple that it is written in the ancient indian texts(VEDAS) that GOD says ” I BREATHE IN AND BREATHE OUT ALL THE UNIVERSES “(in sanskrit universe is called as BRAHMAANDA) , hearing this i thought about the multiverse concept . So what i think might be possible is that gravitational waves might not only ripple inwards of the universe but may also travel outside of the universe ( SPEAKING OF HIGHER DIMENSIONS WOULD BE NEXT POINT BUT IS AN IMPORTANT POINT.). just like bubble expanding when air is blown into it , this expansion may create disturbances both outside & inside of the bubble . Now let us consider 2 or more bubbles expanding simultaneously in the same space near by , the expansion of each bubble may create disturbances in the space surrounding , the disturbance rippling outward of one bubble may produce disturbances inside some other bubble existing in the same space near by . so by using this example (not a perfect one) we can think that gravitational disturbances produced during the formation of other universes may also produce disturbances inside some other universe existing in the same ” SUPER SPACE”(i mean to say the space common to all universes.) .
    here i considered that existence of many universes were to be true even if there no direct scientific evidence.
    so what do you think about this professor?

    • I think that when discussing non-scientific opinions, you are free to believe or think what you would like. But the theory of gravitational waves comes with very specific equations that make very specific predictions as to how they behave. In those equations, it is impossible for gravitational waves in one universe to affect another universe. For the purposes of a scientific conversation, any changes such as the ones you are suggesting would have to be first put into new, modified equations, and from there into predictions, and then tested observationally. There would be many potential conceptual problems with such an idea, so it might be that there is no consistent mathematics that would allow this to occur without running into conflict with existing observations of the universe around us.

  3. Kevin Fairweather

    I see, so i take it, you are using the term dark energy because we do not know what type of energy it is..

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