Astronomy
How the Integrated Sachs–Wolfe Effect Reveals Dark Energy
Quick fact
The integrated Sachs–Wolfe effect is so subtle that it was only confirmed in the early 2000s by cross-correlating CMB temperature maps with galaxy surveys, providing independent evidence for dark energy.
Why this is interesting
Photons from the early universe carry a hidden message about dark energy—one that only appears when they travel through gravitational wells that are changing. Why would the expansion of the universe alter the energy of light that passed by billions of years ago?
Read the full explanation
Understanding How the Integrated Sachs–Wolfe Effect Reveals Dark Energy
Imagine a photon, a particle of light, that has been traveling for nearly 14 billion years from the cosmic microwave background (CMB) to our telescopes. As it travels, it passes through vast regions where matter clumps together, creating gravitational wells, and also through underdense regions where the pull is weaker. According to general relativity, a photon climbing out of a deep gravitational well loses energy, becoming 'redshifted' (its wavelength stretches). Conversely, falling into a well gives it energy. In a static universe, the net energy change for a photon entering and then leaving a well is zero—it loses energy climbing out after gaining energy falling in. However, if the gravitational well itself changes while the photon is inside, the net energy is no longer zero. The integrated Sachs–Wolfe effect is the name for this net energy change, which is 'integrated' along the photon's entire path. When does this happen? In a universe dominated by matter, gravitational wells stay roughly constant because the expansion is slowing down. But if the universe's expansion is accelerating—as it is now—then gravitational wells get stretched out and become shallower. While a photon is inside such a well, it doesn't have to climb out as far as it would have if the well had stayed the same. As a result, the photon leaves with more energy than it entered with, leading to a slight temperature increase in the CMB. Conversely, photons passing through overdensities, which also decay, leave with a net blueshift. The key is that this effect only appears if the gravitational potentials are changing over time, which is a direct signature of cosmic acceleration—the hallmark of dark energy.
A deeper explanation
The integrated Sachs–Wolfe effect arises from the time derivative of the gravitational potential Φ along the line of sight. The temperature fluctuation in the CMB is given by ΔT/T = -2 ∫ ∇Φ·dℓ, where the integral is along the path from the last scattering surface to the observer. In a matter-dominated universe, Φ is constant in time, so the integral vanishes for a single potential well. However, if dark energy starts to dominate, the growth of structure is suppressed by the accelerated expansion, causing Φ to decay. Specifically, the potential well is 'drained' as the universe accelerates, so when a photon traverses a decaying well, it gains less energy climbing out than it lost falling in, or vice versa, resulting in a net positive temperature fluctuation (for a decaying negative potential). This effect is strongest on the largest scales, where the potential gradients are smoother and the transit time is longer. To measure this, astronomers cross-correlate maps of the CMB temperature with maps of large-scale structure, such as galaxy density. Galaxies trace the gravitational wells; wherever there is a galaxy cluster, there is a potential well. If the ISW effect is present, the CMB temperature should be slightly higher in directions toward galaxy clusters (or lower, depending on the sign of the potential). The cross-correlation signal is small, at the microkelvin level, but it has been detected at high significance in combined data from Planck and galaxy surveys like SDSS. This detection is crucial because it provides a direct measurement of the evolving gravitational potentials, which requires the presence of dark energy or a modified theory of gravity that mimics cosmic acceleration. The ISW effect thus serves as a powerful probe of the dynamics of the universe's expansion and the nature of dark energy.