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Quantum fluctuations led to early universe's expansion from "summary" of The Grand Design by Stephen Hawking,Leonard Mlodinow

According to the theory of quantum mechanics, particles can appear and disappear in a vacuum due to quantum fluctuations. In the case of the early universe, these fluctuations were amplified by the extreme conditions present at that time. As a result, tiny quantum fluctuations in the density of matter and energy in the early universe led to the formation of structures we see today, such as galaxies and clusters of galaxies. The key to understanding the expansion of the early universe lies in the concept of inflation. Inflation is a period of extremely rapid expansion that occurred in the first fraction of a second after the Big Bang. During this period, the universe grew exponentially in size, smoothing out any irregularities and setting the stage for the formation of large-scale structures. Quantum fluctuations played a crucial role in the process of inflation. These fluctuations were responsible for the tiny non-uniformities in the density of matter and energy that eventually grew into the large-scale structures we observe in the universe today. Without these fluctuations, the universe would have been much more homogeneous and lacking in structure. One of the key predictions of the theory of inflation is the existence of a background of gravitational waves. These gravitational waves are ripples in the fabric of spacetime itself, generated by the violent processes that occurred during inflation. Detecting these gravitational waves would provide strong evidence in support of the theory of inflation and the role of quantum fluctuations in the early universe. In summary, quantum fluctuations in the density of matter and energy in the early universe led to the formation of structures we see today through a process of inflation. This period of rapid expansion smoothed out any irregularities and set the stage for the formation of galaxies and clusters of galaxies. The existence of gravitational waves would provide strong evidence in support of this theory and our understanding of the early universe.
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    The Grand Design

    Stephen Hawking

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