Suppose the Universe is dominated by a strange substance with an equation of state w = -0.7. This substance fills the Universe in a uniform way, and is the only dynamically important constituent. Suppose further that in some time interval the Universe doubles in (linear) size, i.e. the scale factor doubles. By what factor has the energy density of this substance changed during this time interval, i.e., what is εfinal/εinitial? The energy density substance dilutes in proportion to a to some power p, i.e. ε(a) ∝ ap

Suppose the Universe is dominated by a strange substance with an equation of state w = -0.7. This substance fills the Universe in a uniform way, and is the only dynamically important constituent. Suppose further that in some time interval the Universe doubles in (linear) size, i.e. the scale factor doubles. By what factor has the energy density of this substance changed during this time interval, i.e., what is εfinal/εinitial? The energy density substance dilutes in proportion to a to some power p, i.e. ε(a) ∝ ap

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 39P

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Concept explainers

Stellar evolution

We may see thousands of stars in the dark sky. Our universe consists of billions of stars. Stars may appear tiny to us but they are huge balls of gasses. Sun is a star of average size. Some stars are even a thousand times larger than the sun. The stars do not exist forever they have a certain lifetime. The life span of the sun is about 10 billion years. The star undergoes various changes during its lifetime, this process is called stellar evolution. The structure of the sun-like star is shown below.

Red Shift

It is an astronomical phenomenon. In this phenomenon, increase in wavelength with corresponding decrease in photon energy and frequency of radiation of light. It is the displacement of spectrum of any kind of astronomical object to the longer wavelengths (red) side.

Question

Suppose the Universe is dominated by a strange substance with an equation of state w = -0.7. This substance fills the Universe in a uniform way, and is the only dynamically important constituent.

Suppose further that in some time interval the Universe doubles in (linear) size, i.e. the scale factor doubles. By what factor has the energy density of this substance changed during this time interval, i.e., what isε_final/ε_initial?

The energy density substance dilutes in proportion to a to some power p, i.e. ε(a) ∝ a^p

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The correct answer is 2^-0.9which is 0.536

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