Introduction to Cosmology

Expansion in a Newtonian World 21 Thus it is clear that the presence of matter influences the dynamics of the Universe. Without ...

22 From Newton to Hubble (iii)훺 0 >1, the mass density is overcritical and the Universe is closed. As the scale factor푎(푡)inc ...

Expansion in a Newtonian World 23 [5] Wesson, P. S. 1991Astrophys. J. 367 , 399. [6] Efstathiou, G., 2013. Preprint arXiv:1311.3 ...

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2 Special Relativity The foundations of modern cosmology were laid during the second and third decade of the twentieth century: ...

26 Special Relativity Lorentz Transformations. Consider two linear axes푥and푥′in one-dimensional space,푥′being at rest and푥moving ...

Lorentz Transformations 27 produced in cosmic ray collisions in the upper atmosphere, they appear to have a longer lifetime by t ...

28 Special Relativity transformations between frames which are rotated or translated at a constant velocity with respect to each ...

Lorentz Transformations 29 Timelike World line locations Particle horizon x Past light cone Event horizon Spacelike locations Fu ...

30 Special Relativity to aDoppler redshiftfor a receding source, and to a correspondingblueshiftfor an approaching source. Actua ...

Metrics of Curved Space-time 31 C θ φ P z R x y S r Figure 2.2A two-sphere on which points are specified by coordinates(휃,휙). ha ...

32 Special Relativity includes the coordinate d푥^0 ≡푐d푡so that the invariant line element in Equation (2.7) can be written d푠^2 ...

Metrics of Curved Space-time 33 wherethemetricmatrixis g= ( 푅^20 0 푅^2 sin^2 휃 ) . (2.22) The ‘two-volume’ or area퐴of the two-sp ...

34 Special Relativity positive curvature like a two-sphere the angles would add up to more than 180∘.Cor- respondingly, the angl ...

Metrics of Curved Space-time 35 An observer located at any one point would see all the other points recede radially. This is exa ...

36 Special Relativity The Robertson–Walker Metric. Let us now include the time coordinate푡,thecos- mic expansion scale푎(푡)and th ...

Relativistic Distance Measures 37 velocities) with clocks running at different local time, but from our vantage point we would l ...

38 Special Relativity Similarly, the area of a three-sphere centered at the origin and going through the galaxy at휎is 퐴= 4 휋푎^2 ...

Relativistic Distance Measures 39 Particle and Event Horizons. In Equation (1.14) we defined the Hubble radius푟H as the distance ...

40 Special Relativity Thus when the particle horizon grows with time, bodies which were at spacelike dis- tances at earlier time ...