What would you think if we told you that not just the room you are currently in, but the direct "vacuum" of the universe itself has a specific temperature? When you look up at the night sky, the dark space between the stars appears completely cold and desolate. However, thanks to modern cosmology and quantum physics, we know that every point in the universe is bathed in an invisible radiation that is the echo of the Big Bang. We call this the Cosmic Microwave Background (CMB) radiation.
To understand the properties of this immense cosmic light and the current general temperature of the universe, we once again turn to our fundamental thermodynamic law, Wien's Displacement Law.
What is CMB Radiation?
About 380,000 years after the Big Bang, the universe had cooled enough (to about $3000 \text{ K}$) for free electrons to combine with protons and form the first atoms (hydrogen and helium). At this moment of "recombination", light (photons) freed from the electrons was liberated and began to travel unhindered in all directions of the universe for the first time.
As time progressed and the universe expanded, space itself stretched. While space was expanding, the wavelength of this first light that set out billions of years ago also stretched and lengthened. Today, the wavelength of that first glow emitted from a dense gas cloud at a temperature of $3000 \text{ K}$ (from reddish visible light) has lengthened so much that it has shifted all the way down to the invisible microwave region.
Discovered entirely by accident in 1965 by radio astronomers Arno Penzias and Robert Wilson, this radiation is the strongest evidence for the Big Bang theory.
What is the "Temperature" of the Universe?
The CMB has the most perfect blackbody radiation spectrum in the universe. Extremely precise measurements made by space telescopes like COBE (1989), WMAP (2001), and Planck (2009) showed that this microwave radiation comes from every direction in space almost completely equally (isotropically).
According to current measurements, the characteristic temperature of this radiation is just slightly above absolute zero: $T \approx 2.725 \text{ K}$ (about $-270.4^\circ\text{C}$). This value is considered the current "average background temperature" of the universe.
CMB Analysis with Wien's Law
So, at what wavelength does such a cold blackbody emit its energy into the spectrum? We can calculate this using the law formulated by Wilhelm Wien in 1893.
Wien's Displacement Law is as follows:
$$\lambda_{\text{max}} = \frac{b}{T}$$
In this formula, $b$ is Wien's displacement constant ($\approx 2.89777 \times 10^{-3} \text{ m}\cdot\text{K}$).
When we plug the CMB temperature ($2.725 \text{ K}$) into the formula:
$$\lambda_{\text{max}} = \frac{2.89777 \times 10^{-3} \text{ m}\cdot\text{K}}{2.725 \text{ K}} \approx 1.063 \times 10^{-3} \text{ m}$$
If we do the unit conversion, we see that this value is approximately $1.063 \text{ mm}$ (millimeters).
What Does This Result Mean?
The peak wavelength of approximately $1 \text{ mm}$ we obtained corresponds to the microwave region of the electromagnetic spectrum (between radio waves and infrared). This is exactly why this ancient radiation filling the universe is called the "Cosmic Microwave Background Radiation." If the temperature of the universe had been higher (as it was in the past), according to Wien's law, this peak wavelength would have been shorter, and the radiation would have been in the form of infrared or visible light.
When you turn to an empty channel on old tube televisions, about 1% of the source of the "snow" (static noise) you see on the screen is these $1 \text{ mm}$ cosmic microwave photons hitting your antenna. Isn't it fascinating to be able to see the light left over from the birth of the universe on your television?
The Secret of Tiny Fluctuations in CMB Temperature
Although we say that the average temperature of the universe is around $2.725 \text{ K}$, this radiation is not completely smooth. Sensitive instruments like the Planck satellite have detected very small (on the scale of microkelvin, or one-millionth of a kelvin) temperature fluctuations in the microwave background coming from different directions in the sky.
The meaning of these tiny differences in the context of Wien's law is that there are infinitesimal (very, very small) differences in the peak wavelengths of the radiation coming from different directions. So why are these small deviations important? Because quantum fluctuations that occurred immediately after the Big Bang caused matter to be slightly denser in some regions of the universe and slightly sparser in others. The temperatures of the gases in these denser regions showed extremely small changes compared to their surroundings.
Over billions of years, these slight density differences combined under the influence of gravity to form stars, galaxies, and galaxy clusters, i.e., the massive cosmic web of the universe as we know it today. If it were not for those microkelvin-scale heat differences in the CMB spectrum (and the wavelength variations calculated by Wien's formula), neither galaxies, nor stars, nor you reading this article would exist today. The universe would have remained just a uniform and boring soup of gas.
What Will Happen as the Universe Continues to Cool?
We mentioned that the CMB temperature today is approximately $2.725 \text{ K}$ and its radiation peak is around $1 \text{ mm}$ (microwave). However, the universe is not static; under the influence of dark energy, it is expanding at an accelerating rate.
This continuous expansion of the universe causes the photons to experience "cosmological redshift". As time progresses, these ancient photons in the spectrum will stretch even further, and their wavelengths will increase from millimeters to centimeters and even to meters.
If we think of Wien's law in reverse, we can easily predict that as the wavelength ($\lambda_{\text{max}}$) increases, the temperature of the universe ($T$) will continue to drop. Billions of years from now, future astronomers (if there are any) will perhaps measure the background temperature of the universe at $1 \text{ K}$ or below. The CMB radiation will move out of the microwave region and completely transform into ultra-long radio waves (similar to AM/FM radio frequencies). Wien's law is one of the clearest mathematical telescopes we have to observe this "heat death" scenario and the cooling evolution of the universe.
Our Tool for Cosmic Calculations
You can apply Wien's law not only to the universal CMB but also to newly discovered distant planets, asteroids, or cold gas clouds. To speed up and verify such astronomical calculations, you can use our Wien's Displacement Law Calculator tool.
By using the tool in the "Temperature to Wavelength" mode and entering values like $2.725 \text{ K}$ (CMB), $100 \text{ K}$ (cold gas clouds), or $5778 \text{ K}$ (the Sun), you can quickly find out at what wavelength (and in which region of the spectrum) blackbodies in different corners of the universe emit their energies. The tool's automatic unit conversions from nanometers to meters will provide great convenience in astronomical studies.
