Dark Matter and Dark Energy

Cosmological model with dark matter, dark energy, and accelerated expansion.

Conceptual context

Modern cosmology asks not only whether the universe expands, but which ingredients control the rate of that expansion. Ordinary matter explains stars, gas, and visible galaxies, yet it cannot reproduce the observed dynamics by itself. Dark matter adds gravity without emitting light, while dark energy behaves as an almost uniform component that becomes dominant late and drives accelerated expansion. $z$ orders this cosmic history: higher $z$ means looking into denser earlier epochs, where matter had a stronger dynamical role.

🟢 Essential level

The key question is how $H(z)$ changes when $z$ increases. In a universe with dark matter and dark energy, the components do not evolve in the same way.

Matter, including dark matter, is diluted as space expands, so it was packed into a smaller volume in the past and had a stronger gravitational effect. Therefore, at high $z$, $\omega_{m0}$ dominates the expansion and tends to oppose acceleration. Dark energy, represented by $\omega_{lambda0}$, behaves in the basic model as an almost constant density. Its relative influence grows in recent epochs after matter has been diluted. Thus a graph of $H(z)$ against $z$ is not a simple straight line; it shows a change of regime between an early matter-dominated universe and a recent dark-energy-dominated universe.

In 1998, two independent teams studying distant type Ia supernovae discovered that expansion is accelerating rather than slowing down, a result so unexpected that it led to the 2011 Nobel Prize in Physics. Today's estimates put $\omega_{m0}$ near 0.3 and $\omega_{lambda0}$ near 0.7, with dark matter making up most of that material component.

🔵 Formal level

Basic formulas

The reference model is flat Lambda-CDM. First, the normalization scale is set by the present critical density, which depends on $H0$, $G$, and $\pi$.

Present critical density

From $\rho_{c0}$, the present fractions are defined: $\omega_{m0}$ compares $\rho_{m0}$ with the critical density, and $\omega_{lambda0}$ compares $\rho_{lambda0}$ with the same reference.

Matter density parameter

Dark energy density parameter

Real student questions

Are dark matter and dark energy the same thing? No. Dark matter attracts gravitationally and clusters in halos; dark energy is modeled as a very uniform component that dominates recent expansion.

Why use $z$ instead of time? Because $z$ is measured directly from observed light and orders cosmic epochs before one reconstructs the full age of the universe.

Does dark energy push stars inside a galaxy? Not in a useful way in this model. On galactic scales, local gravity dominates and orbital dynamics is used.

Why does $\omega_{m0}$ include dark matter? Because gravity responds to total mass, not only to what shines.

Final synthesis

Dark matter dominates structure gravity and the dense past; dark energy dominates recent acceleration. $z$ turns that history into a graph: the way $H(z)$ changes reveals which component governs each epoch.