Cosmological Space -Times Lecture notes compiled by Geoff Bicknell based primarily on: Sean Carroll: An Introduction to General Relativity plus additional material Thursday , 10 September 2009 1 Metric of special relativity ds 2 = -c dt + dx + dy + dz 2 2 2 2 2 = -dx 02 + dx + dy + dz 2 2 2 = µ dx dx µ where µ µ, = = Minkowski tensor = diag [-1, 1, 1, 1] 0, 1, 2, 3 This is the metric of four-dimensional flat ... The 3-sphere is expanding 3. ...

... The primary channel receives the desired astronomical signal corrupted by RFI (radio frequency interference ) coming in the sidelobes of the main beam. ... If the interference-to-noise in the reference and primary channels are equal ([pic]), the noise in the system output (at the frequencies where the interference signal was located) will be almost twice as high as in the primary input before filtering. ... The signal path through the adaptive filter illustrates the iterative nature of this system. ...