Density parameter Definition and 13 Threads

For Ω=1, κ=0. Does the value of κ simply follow from the value of Ω, or can its value have an independent existence? So if Ω>1, does κ have to be 1?

Hi,I'm reading about critical density and I'm a bit confused about it's derivation.Solving the Einstein equations using the cosmological principle we get the (second) Friedmann equation: $$ \bigg( \frac{\dot{a}}{a} \bigg)^2...

Does ##w## = -1 by itself imply that spacetime is flat, or is it only due to ##\Omega##Matter + ##\Omega##Λ = 1 ?

I am busy with an effort to show how the energy density parameters evolve over time in an update of the LightCone7 calculator. See the posts on the thread Steps on the way to Lightcone cosmological calculator. As part of this effort, I ran into some difficulties with deciding how to find and...

I'm trying to plot the density parameters against redshift in Python, so I suppose this is kind of a cross over of programming and physics. I've been given the following two equations in order to do so $$r(z) = \lambda_H \int_{0}^{z} \frac{dz'}{E(z')}$$ $$E(z) = \frac{H(z)}{H_0} = \sqrt...

Homework Statement This is a basic cosmology problem. The Friedmann equations are ##\Big( \frac{\dot{a}}{a}\Big)^{2}+\frac{k}{a^{2}}=\frac{8\pi}{3m_{Pl}^{2}}\rho## and ##\Big( \frac{\ddot{a}}{a} \Big) = - \frac{4\pi}{3m_{Pl}^{2}}(\rho + 3p)##. Using the density parameter ##\Omega \equiv...

I've understood that the main evidence for a non-zero ##\Omega_\Lambda## comes from supernova 1a measurements where one measures the redshifts along with the luminosity distances (equivalently magnitude) of the supernovae and, plots them against each other, then compares the result with...

Homework Statement One of our homework problems asks us to state the density of Baryons, Cold Dark Matter, Radiation, Dark Energy, and the total density of the universe in terms of the critical density today. It also states to give the density of each quantity in dimensionless Omega units (the...

Homework Statement Decide the density parameter from the following data: z=0.04, m= 17.38 and σ=0.19 Homework Equations Definition of the density parameter: Where p0 is the current density and pc is the critical density. The Attempt at a Solution I feel like I don't...

This is from Matts Roos' text on cosmology. I don't follow the final step and when he integrates I understand the first part of the left side, and the right side. But I don't see where -a'^2(t0) comes from

Greetings everyone , Can anyone point me into the right direction on how to come out with a value/ expression for the density parameter of a radiation dominated universe. Things that I know of/ can recall are: Friedmann equation : 8/3 \pi G ρ R^2 -kc^2 Also when radiation dominates...

Homework Statement Starting with the equation below, I need to: - Show that there is a range of values for a for which Ωm≈1 - Derive expressions for the values of a at the endpoints of this range. Homework Equations Ωm(a) = Ωm0/[Ωm0+Ωr0/a+Ωv0a3]. (0 signifies present day values, m=matter...

Hi everyone-- I'm trying to get a technical explanation of the expansion of the Universe. I posted something similar in the Cosmology forum, but got a lot of unlettered and wishy-washy responses. I'm hoping here in the SR/GR forum I can find a more mathematically rigorous treatment...