From General Relativity to Dark Energy

Adwit · Jun 10, 2022

If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.

Typeset equations (2.5) and (2.6): R_μν = Γ^α_μν,α − Γ^α_μα,ν + Γ^α_μν Γ^β_αβ − Γ^α_μβ Γ^β_αν, with the sentence 'The contraction of the Ricci tensor gives the Ricci scalar (scalar curvature)' and R = g^μν R_μν.

Typeset equations (2.9) to (2.11) listing non-vanishing Christoffel symbols for the FLRW metric, including Gamma^0_ij = a^2 H gamma_ij, Gamma^i_0j = H delta^i_j, Gamma^1_11 = Kr/(1 - Kr^2), and terms in sin and cot of theta.

Printed text from a physics text stating that from Eqs. (2.5) and (2.6) the Ricci tensor and scalar curvature are R00 = -3(H^2 + Hdot), R0i = Ri0 = 0, Rij = a^2(3H^2 + Hdot + 2K/a^2) gamma_ij (2.13), and R = 6(2H^2 + Hdot + K/a^2) (2.14).

Orodruin · Jun 10, 2022

Please show your own efforts in accordance with the homework guidelines.

Adwit · Jul 27, 2022

Orodruin said:

Please show your own efforts in accordance with the homework guidelines.

Here is my own effort. Now, will you please tell me where I went wrong? What do I have to do?

Orodruin · Jul 27, 2022

Please read points 5 and 6: https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.635513/

If you cannot be bothered to type things out in a legible format and explain what you are attempting to do in each step, then I certainly don’t feel any will to strain my eyes unnecessarily and spend triple the effort to try to help you comparef to what would be necessary if you followed the guidelines.

Let me also remind you of your own words:

Adwit said:

Ok, this is the last time I posted image of calculation. For now, I will write the calculation.

From General Relativity to Dark Energy

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