Utah State University DigitalCommons@USU General Relativity Notes 1-8-2018 General relativity, 9 David Peak Utah State University,
[email protected] Follow this and additional works at: https://digitalcommons.usu.edu/ intermediate_modernphysics_general Part of the Physics Commons Recommended Citation Peak, David, "General relativity, 9" (2018). General Relativity. Paper 9. https://digitalcommons.usu.edu/intermediate_modernphysics_general/9 This Course is brought to you for free and open access by the Notes at DigitalCommons@USU. It has been accepted for inclusion in General Relativity by an authorized administrator of DigitalCommons@USU. For more information, please contact
[email protected]. General relativity, 9 Cosmic development As discussed in GR 8, the cosmic scale factor a in the FLWR s-t obeys the Friedmann 2 ⎛ da ⎞ 8πG 2 k 4 3 equation a , with ρ = ρ ⎡ Ω a + Ω a + Ω ⎤ . Recent data from ⎜ ⎟ − 2 ρ = − 2 C ⎣( r ) ( m ) V ⎦ ⎝ dT ⎠ 3c r0 −5 the WMAP satellite indicates that (±2%) ΩV ≈ 0.72, Ωm ≈ 0.28, Ωr ≈ 5x10 . (See table at the end.) This implies that, if we set a = 1 (today), and k 0 . One interpretation of this is that the ρ ρC FLWR s-t is infinite in (spatial) extent. The full time-course for how a changes can be obtained by integrating the k = 0 Friedmann equation: 1/ 2 a da′ ⎛ 8πGρ ⎞ T C tH . = ⎜ 2 ⎟ = 0 ∫0 Ω Ω ⎝ 3c ⎠ a r m ′ 4 + 3 + ΩV a′ a′ It is instructive to evaluate the time between a = 0 and a = 1, i.e., the “age of the universe,” if, in turn, only radiation, only matter, and only vacuum-energy were ever present.