2012年6月3日 · Because a is a scale and you need the equations to be scale invariant. a is an arbitrary number and you can pick any number of the current value of a (i.e. you can pick 1, 2, 3000, 0.333) since you don't care about a particular value of …

2015年4月21日 · How do you calculate the scale factor? The scale factor can be calculated by dividing the length or size of the object in the given scale by its actual length or size. For example, if an object is 10 cm in real life and 2 cm on a map, the scale factor would be 2 cm / 10 cm = 0.2. Can the scale factor be greater than 1? Yes, the scale factor can ...

2021年6月12日 · The cosmic scale factor is an important concept in cosmology as it helps us understand the evolution and expansion of the universe. It is a key component in various models of the universe, such as the Big Bang model, and is crucial in determining the age and future fate of the universe.

2018年11月1日 · Cosmology Derivation Relation Scale factor Temperature change In summary, Barbara Ryden argues that the first law of thermodynamics can be used to derive the relation T(t) ∝ a(t)-1. This relation is used to calculate the rate of expansion of the universe.

2019年11月2日 · In summary, the conversation discusses the scale factor in cosmology, which is a function of time. The equation $$\frac{d}{da}(\dot{a}(t)^{-2})$$ is brought up and it is unclear if the derivative is 0 or something else.

2016年8月3日 · From Introduction to Cosmology by Matt Roos, he wanted to derive the Hubble parameter in terms of the scale factor. From the Friedmann's equation, ##\frac{R'^2 + kc^2}{R^2} = \frac{8πG}{3}ρ## The density parameter is ##~Ω(a) = \frac{8πG}{3H_o^2}ρ(a)~## and let ##~Ω_k = \frac{-kc^2}{H_o^2}##

2019年10月13日 · If we take a flat universe dominated by radiation, the scale factor is ##a(t)=t^{1/2}## which can be derived from the first Friedmann Equation:$$(\dot... Insights Blog -- Browse All Articles -- Physics Articles Physics Tutorials Physics Guides Physics FAQ Math Articles Math Tutorials Math Guides Math FAQ Education Articles Education Guides Bio ...

2019年10月3日 · Imagine a Universe where the Hubble parameter is truly a constant, in both space and time. How much smaller would such a Universe be 14 billion years ago compared to today? Using the Hubble parameter in terms of scale factor: ##H(t) = \\frac{\\dot{a}}{a}## leads to the differential equation...

2015年1月11日 · d' will still increase if the comoving distance d0 increases. Also, as I said, a' constant leaves H as a varying quantity, you will end up with the same result for d' regardless of what formula you use.

2024年4月15日 · In summary, the fluid equation in cosmology relates the energy density \epsilon to the scale factor a through the equation of state P = w*\epsilon, which can be solved by integrating the differential equation \frac{d\epsilon}{\epsilon} = -3(w+1)\frac{da}{a}.