Is my understanding regarding the relationship between dark energy and the Hubble constant incorrect?

Question

The Hubble constant operates as follows: if it is 73 km/s/Mpc, it means a galaxy at 1 Mpc will be receding at 73 km/s, a galaxy at 10 Mpc will be receding at 730 km/s, and a galaxy at 1,000 Mpc will be receding at 73,000 km/s.

This relationship illustrates that the further you look, the faster an object at that distance will be receding. However, the Hubble constant has been decreasing since the Big Bang. While this decrease occurs, the general trend of objects receding faster with increasing distance (as described above) still holds true, albeit with a lower magnitude over time.

My question is: does dark energy increase the expansion rate (i.e., the Hubble constant itself)? For example, was the expansion rate of the universe 50 km/s/Mpc when the light from Type 1a supernovae was emitted, and then dark energy caused the expansion rate to increase during that light's travel time to its current value of 73 km/s/Mpc?

If this understanding is incorrect, could someone clarify how dark energy functions in relation to the expansion of the universe, particularly its impact on the Hubble constant?

Answer 1

Note that a Hubble constant produces exponentially-increasing distance and velocity (“expansion”): $$v=Hd\implies \frac{\text{d}x}{\text{d}t}=Hx$$ for which $x=e^{Ht}$ is a solution. The Hubble constant is the expansion rate, which is determined by dark energy density.

You get a Hubble constant determined by dark energy density when that dark energy’s energy density is constant over spatial expansion/doesn't “spread out” like regular matter (see the equation of state). Dark energy’s constant density yields a constant Hubble constant.

So, knowing DE’s energy density is proportional to the cosmological constant, which is constant…

was the expansion rate of the universe 50 km/s/Mpc when the light from Type 1a supernovae was emitted, and then dark energy caused the expansion rate to increase during that light's travel time to its current value of 73 km/s/Mpc?

…no.

Answer 2

As you may know there is a lot of discussion regarding the Hubble tension which was recently confirmed as being a real observed discrepency in our current models of the universe.

What is more interesting is the plethora of attempts to explain how to account for the discrepancy. It was noted in 2023 that there was an initial list of 123 subcategories of approaches to explain the Hubble tension. This was later reduced to some 19 subcategories.

Late time deformations of the Hubble expansion rate H(z): (1) Phantom dark energy; (2) Running vacuum model; (3) Phenomenologically emergent dark energy; (4) Vacuum phase transition; (5) Phase transition in dark energy.

Deformations of the Hubble expansion rate H(z) with additional interactions/degrees of freedom: (1) Interacting dark energy; (2) Decaying dark matter .

Deformations of the Hubble expansion rate H(z) with inhomogeneous or anisotropic modifications: (1) Chameleon dark energy; (2) Cosmic voids; (3) Inhomogeneous causal horizons.

Late time modifications: Transition or recalibration of the SNe Ia absolute luminosity: (1) Gravity and evolution of the SNe Ia intrinsic ; (2) Transition of the SNe Ia absolute magnitude M at a redshift z ≃ 0.01; (3) Late (low-redshift) w − M phantom transition.

Early time modifications of sound horizon: (1) Early dark energy; (2) Dark radiation; (3) Neutrino self-interactions; (4) Large primordial non-Gaussianities; (5) Heisenberg’s uncertainty principle; (6) Early modified gravity.

If you note multiple subcategories deal with modification of dark energy models in order to explain the Hubble tension.

If you read through the question comes down to either adding new parameters to existing models or better explanation of the Hubble constant with possibly new physics.

In short, if it comes to new physics then it is already well documented that we do not have a provable physical theory that explains the genesis or constituency of dark energy or a true basis for the cosmological constant. As such it is speculative to really make any statements about how dark energy works.

Answer 3

the Hubble constant has been decreasing since the Big Bang.

The Hubble parameter is defined as the rate of change of the proper distance between two points in the universe, divided by the proper distance between those two points. On the other hand, the Hubble constant refers to the present-day value of the Hubble parameter. Some sources will not be precise and confuse the two.

The effect of any component of the universe (e.g. baryonic matter, dark matter, radiation or dark energy) on the expansion rate depends on its equation of state.

Dark energy has an equation of state < -1/3 in order to produce the currently observed accelerated expansion rate. The equation of state for dark energy could, in general even be a function of redshift.

However the equation of state of dark energy is normally assumed in line with observations to be a constant -1 which corresponds to the cosmological constant or vacuum energy. In this case that dark energy is also called the cosmological constant, i.e. it has constant energy density and also a constant Hubble parameter. The equations which govern the dynamics are called the Friedmann equations.

Answer 4

I calculated the Hubble parameter for the composition of the universe measured by the Planck experiment in How does the Hubble parameter change with the age of the universe?

The answer is that the Hubble parameter decreases monotonically - it does not decrease then increase again. If you are curious to try this for yourself my answer to that question explains how to do the calculation.

Dark energy that behaves like a cosmological constant drives the Hubble parameter to a constant value i.e. if the universe contained only dark energy the Hubble parameter would remain constant with time. It would not increase. The Hubble parameter would increase only if the density of dark energy was increasing with time. This is theoretically possible, see for example the Big Rip, but there is no experimental evidence that this is happening.