The Cosmological Constant and Dark Energy: Old stuff probably of no value

But what does the cosmological constant mean physically?

In the Einstein field equations, Lambda just appears as a modification to how gravity affects spacetime. It is a "just-so" modification.

The cosmological constant is sort of an anti-gravity, but we do NOT call it that and it is NOT symmetric with gravity in any simple way.

In modern physics, there is a strong preference to interpret Lambda as representing a constant dark energy. The dark energy just grows with the expansion of space adding a balanced amount of relative kinetic energy and gravitational potential energy such as to keep the space growing at a constant relative rate (a time-constant Hubble constant) if there were no other mass-energy forms in the observable universe.

The dark energy is often said to have NEGATIVE PRESSURE, but this is so far just a formal NEGATIVE PRESSURE since the NEGATIVE PRESSURE does NOT pull on anything. The NEGATIVE PRESSURE is, in fact, a formal thermodynamics effect if you want to think of the dark energy in a certain hypothetical way.

1. Simplest Dark Energy:

   Now constant dark energy has a constant energy density in time and space. It is about the simplest kind of dark energy imaginable.

   That the cosmological-constant dark energy density is constant in time is UNUSUAL. For example, matter density must decrease because of the expansion of the universe. In fact, as cosmic scale factor a(t) increases, volumes increase by a(t)**3, and matter density falls as a(t)**(-3).

   The cosmological-constant dark energy density can be treated as a contribution to Omega: we denote this contribution by Omega_Lambda.

   Question: Density parameter Omega is:
   1. the cosmological constant by another name.
   2. the last letter of the Greek alphabet.
   3. the ratio of the mass-energy density of the universe (or our pocket universe) to the critical mass-energy density. It is the parameter that determines the geometry of space in the FE Λ=0 models and the FE Λ models.

   
   
   
   
   
   
   
   
   
   
   Answer 2 and 3 are right. But answer 3 is best in this context.

   From the analysis of the CMB data, galaxy cluster data, and Type Ia supernovae ASSUMING the dark energy is a cosmological-constant dark energy, one finds Omega_Lambda=0.6853(74) (see Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018).

2. Not Simplest Dark Energy:

   But the dark energy need NOT have constant density in either time or space and it may interact with other forms of mass-energy in ways we do NOT know.

   Until circa 2018, nothing in the observations told us to go beyond the simple theory of cosmological-constant dark energy.

   But currently, there is Hubble tension: see the discussion in the figure below (local link / general link: hubble_constant_problem.html).

   Is there any reason for believing there could be just a cosmological-constant dark energy from physical theory?

   Yes, quantum field theory (i.e., relativistic quantum mechanics) suggests there could be cosmological-constant dark energy, but alas predicts its density to be 10**120 times bigger than needed to fit the observed acceleration (e.g., Carroll, S. 2003, p. 3, Why is the Universe Accelerating?).

   This remarkable OVERESTIMATE suggests that the dark energy is more complex than the simple cosmological-constant dark energy with a density which is constant in time and space.

3. Dark Energy and the Multiverse:

   Another remarkable thing about dark energy is that the cosmological-constant dark energy density from the analysis of the CMB data is Omega_Lambda = 0.6853(74), which is COMPARABLE to the matter density Omega_matter = 0.3147(74). The reference for these values is Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018. There may be some deep reason why the dark energy and matter should be COMPARABLE in which case the dark energy CANNOT be simply a cosmological-constant dark energy.

   On the other hand, possibly the COMPARABILITY of Omega_Lambda = 0.6853(74) and Omega_matter = 0.3147(74) (Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018) is explained by the anthropic principle. (See IAL 0: A Philosophical and Historical Introduction to Astronomy: The Anthropic Principle.)

   Say there are an infinity or a quasi-infinity of pocket universes in a multiverse with different parameters set by some probability distribution of parameters.

   Those NOT somewhat like our own in mass-energy contents may NOT be able to support life.

   Too small a cosmological-constant dark energy density and the universe may NOT have formed the right kind of galaxies and stars.

   Too large a cosmological-constant dark energy density and the universe would have expanded too quickly ever to form galaxies and stars.

   So the ratio of dark energy and matter may just be a roll of the pocket universe parameter dice.

   Now it is very hard to prove an argument based on the anthropic principle.

   But such an argument could be falsified if the dark energy density and matter density (the sum of dark matter density and baryonic matter density) were fine-tuned beyond the needs (so far as we can tell) of making our pocket universes suitable for us to be here.

   For example, the ratio is now of dark energy density to matter density is approximately 2 to 1.

   If the ratio were exactly 2 to 1, that is more exactness than is needed for a pocket universe to that can support life like us, and strongly suggests dark energy and matter---NOT just that random throw of the pocket universe parameter dice.

   But there is NOT such exactness, and so the multiverse passes this significant falsification test.