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References used in this blog

[1] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, vol. -1. John WIley & Sons, Inc., Jul, 1972. http://adsabs.harvard.edu/abs/1972gcpa.book.....W.  [2] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation. W H Freeman and Company, first ed., 1973.  [3] S. Weinberg, The first three minutes : a modern view of the origin of the universe. Basic Books, New York, 1993.  [4] S. Dandelson, Modern Cosmology. Academic Press, 2003.  [5] S. Weinberg, Cosmology. Oxford Univeristy Press, 2008.  [6] M. Camenzind, “Modern Cosmology Part III: The Friedmann Cosmos,” Mod. Cosmol. no. C, (2010) . www.lsw.uni-heidelberg.de.  [7] M. Blau, “Lecture Notes on General Relativity,” 2018. http://www.blau.itp.unibe.ch/Lecturenotes.html.  [8] M. A. Pahre, S. G. Djorgovski, and R. R. de Carvalho, “A Tolman Surface Brightness Test for Universal Expansion and the Evolution of Elliptical Galaxies in Distant Clusters,” Astrophys. J. 456 no. 2, (Jan, 199
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Why we need a new metric in GR

Two metrics are mainly used in general relativity to describe most of the observable universe.  At cosmological scales where universe appears to be isotropic and homogeneous everywhere, FLRW metric is used to calculate equations of motion. ΛCDM model based on this metric explains successfully many observations in cosmology like cosmic redshift, luminosity versus redshift relation of Type 1a supernovae, stretching of supernovae light curves due to time dilation, Cosmic Microwave Background (CMB) and many more (1–7). One basic observation in cosmology where ΛCDM model has not been really successful is the galactic mass and angular size relation evolution with redshift. It has been observed by multiple studies that angular sizes for a given mass or luminosity do not match the predicted values unless a high degree of size or luminosity evolution is assumed (8–16) (some of these studies measure surface brightness which is a function of luminosity and size). Strong arguments have been put ag
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