One technique, called baryon acoustic oscillations (BAO) is able not only to detect the existence of the dark energy, it is able to place limits on what it might be.
The basic idea behind BAO is as follows: In the early Universe when baryons existed as an ionized plasma, radiation was tightly coupled to the baryons because photons were repeatedly scattered from electrons. Since negatively charged electrons tightly couple to positively charged protons, even when they are not bound together in atoms, the photons were also coupled to the protons.
Gravitational attraction between the baryons tended to make them collapse into clumps, but this collapse tended to compress the photon gas as well, heating it and raising its pressure. The outward pressure of the photons halted the collapse of the baryons and tended to cause them to expand. These two effects were in constant opposition, and the collapse followed by expansion set up sound waves (“acoustic” oscillations), which created denser and less dense regions in the plasma.
At the same time as the baryons and photons were creating oscillating patterns in the density of the plasma, the dark matter began to collapse due to its self-gravitation. Since cold dark matter does not interact at all with light, the photon gas pressure was not able to prevent its collapse as it did for the baryons (protons). Dark matter was therefore able to create small collapsed regions that became the seeds for later structure formation long before the baryons themselves could collapse into structures.
The waves created by the BAO had a characteristic sound speed that is easy to calculate. At this speed, the waves travel a given distance through the plasma in a given time, the relevant time being the Hubble time (age of the Universe) at the redshift in question. Thus, each local density enhancement in the plasma was surrounded by a region in which the sound waves had traveled, and since sound waves are regions of high and low pressure (or density), there were patterns of density enhancements surrounding each primordial density enhancement. The regions of high density were able to act as seeds for additional structures to form.
Eventually the Universe expanded and cooled to the point that the protons and electrons combined into neutral atoms. At that point the photons were no longer tightly coupled to the baryons because their interaction with neutral atoms is much weaker than it is with free electrons. These photons are the ones we see as the cosmic microwave background (CMB) in the Universe today.
Since the photons no longer prevented the baryons from collapsing into clumps, high density regions rapidly filled with baryons after this “decoupling” of matter and radiation. We then expect to see galaxies in these high density regions, and their separation should reflect the distance that sound could travel at the time of decoupling, at a redshift of around z ~1100.
Since we know the age of the Universe at that time, we know the physical size of the galaxy separation we expect to see: it is the sound speed times the age. We can also measure the angular size of this separation on the sky. These are the patterns we see in the CMB.
Those same patterns eventually formed the large scale structure of galaxies, so if we carefully measure the position of galaxies in space we will have the sound scale at two different redshifts: The expansion of the Universe carried the fluctuation pattern we observe in the CMB into the one we observe in the pattern of galaxies. Modeling the expansion allows us to measure several cosmological parameters by comparing the pattern at these two redshifts. In particular, it places strong limits on the evolution of the dark energy. The Friedmann equation, now shown with all gravitating terms, shows how the expansion is related to the various parameters:
\begin{equation} \left (\frac{\dot{S}}{S}\right )^2=H_0^2\left [ \frac{ \Omega_r}{S^3} + \frac{\Omega_m}{S^4} + \frac{ \Omega_k}{S^2} + \frac{\Omega_\Lambda}{S^{3(1+w)} }\right ] \end{equation}The parameter S is the scale factor, and the left hand side is the Hubble parameter written in terms of S. H0 is the Hubble constant, in other words, the Hubble parameter evaluated at the present time. All the other terms have their usual meanings, and we have included the curvature term Ωk for completeness rather than setting it to the measured value of zero.
The best measurements currently available indicate that the dark energy is constant over the history of the Universe, that it is a cosmological constant, not quintessence, and so baryon acoustic oscillations have made a vital contribution to our understanding of the cosmos.