The Bianchi type I cosmologies represent a spatially homogeneous, anisotropic and non-rotating Universe. In a suitable c

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The Bianchi Type I Cosmologies Represent A Spatially Homogeneous Anisotropic And Non Rotating Universe In A Suitable C 1 (531.28 KiB) Viewed 27 times

The Bianchi type I cosmologies represent a spatially homogeneous, anisotropic and non-rotating Universe. In a suitable coordinate system, the metric of this space-time takes the diagonal form ds² = c²dt² A(t)²dx² - B(t)²dy² - C(t)²dy². a) b) c) Determine all non-zero affine connections in the Bianchi metric. Determine all non-zero components of the Ricci tensor in the Bianchi metric. Show that the analog of Friedmann's equations for a Bianchi type I cosmology in the presence of an ideal fluid are ĊA АВ BĊ + AB BC + CA ÄB + AB + AB AB BC + BC + BC - 8πGp 8TG c² 8TG c² -р BC CA+CA+CÄ CA where P and p represent the density of matter and pressure of the ideal fluid, respectively. 8TG c² -P,