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The Expanding Universe and the Cosmic Microwave Background

January 07, 2025Science1862
The Expanding Universe and the Cosmic Mi

The Expanding Universe and the Cosmic Microwave Background

The universe has expanded dramatically since its inception during the Big Bang. This expansion is not uniform, but rather, it has followed a series of distinct stages characterized by varying forms of energy domination. One of the key markers of this expansion is the cosmic microwave background (CMB), released approximately 380,000 years after the Big Bang when the universe had reached a temperature of about 3,000 Kelvin. This background radiation provides critical insights into the size and scale of the universe at different points in time.

Understanding the Big Bang and the CMB

During the early stages of the universe, it was an ionized plasma, where electrons were free and scattered. As the universe cooled, these electrons began to combine with nuclei to form neutral atoms, a process known as recombination. This event, occurring at approximately 380,000 years post the Big Bang, marked the release of the CMB. The temperature of this radiation at that time was significantly higher, around 3,000 Kelvin, as opposed to the 2.73 Kelvin observed today.

Current Radius of the Universe

Today, the observable universe has an approximate radius of 46.508 billion light-years. However, determining the exact size of the universe beyond our observable limit is currently beyond our reach due to the ongoing expansion and the possible infinite nature of the universe.

Size of the Universe at the Start of CMB

At the time of CMB release, the scale factor was approximately 1/1,090 of its current size. This means that the universe was about 1090 times smaller than it is today. Therefore, the radius of the observable universe at that time would have been around 42.7 million light-years. For the entire universe, it is much more speculative. If we assume the universe is infinite, it was infinite back then and will always be infinite.

Calculating the Scale

To understand these scale factors, we can use the scale factor ( a(t) ) to express the size of the universe. The scale factor ( a ) is a dimensionless measure of the expansion of the universe, with ( a 1 ) representing the current state of the universe.

For instance, at the time of the CMB (t 380,000 years), the scale factor ( a ) was approximately 1/1,090. This can be expressed in the equation:[ r(t) r_0 cdot a(t)^{2/3} ]where ( r ) is the radius, ( r_0 ) is the current radius of the observable universe (46.508 billion light-years), and ( a(t) ) is the scale factor at the given time.

Therefore, the radius at the time of the CMB would be:[ r_{CMB} 46.508 times 10^{9} times left(frac{1}{1,090}right)^{2/3} approx 42.7 text{ million light-years} ]

Recent and Past Measurements

More recently, the universe was measured to be approximately 1100 times smaller than it is today, with the CMB as the marker of this transition. This gives us an approximate size of the observable universe at that time as 100 million light-years diameter.

For a more precise calculation, using the scale factor for the last 5.4 billion years (Λ-dominated universe), the radius can be estimated as:[ r_{Lambda} approx 31.6 text{ billion light-years} ]And for 2 billion years ago (assuming a matter-dominated universe):[ r_{matter} approx 40 text{ million light-years} ]

During Inflation and Early Stages

The early stages of the universe, including the inflation period and early recombination, present even more extreme scales. At the end of the inflation period (about ( t leq 10^{-32} ) seconds), the universality would have been incredibly small, estimated to be around 7.7 meters in diameter based on the Planck length. This measurement, however, is highly speculative due to the limitations of current physical models and theories.

Conclusion

The expansion of the universe and the release of the CMB provide significant insights into the early stages of the universe. The size and scale of the universe at different points in its history help us to understand the fundamental nature of space, time, and the laws of physics.