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Massive gravity
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Title: Is there vacuum when there is mass? Vacuum and non-vacuum solutions for massive gravity
Authors: Prado Martin-Moruno (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)

Massive gravity is a theory which has a tremendous amount of freedom to describe different cosmologies; but at the same time the various solutions one encounters must fulfil some rather nontrivial constraints. Most of the freedom comes not from the Lagrangian, which contains only a small number of free parameters (typically 3 depending on counting conventions), but on the fact that one is in principle free to choose the background reference metric almost arbitrarily --- which effectively introduces a non-denumerable infinity of free parameters. In the current paper we stress that although changing the reference metric would lead to a different cosmological model, this does not mean that the dynamics of our own universe can be entirely divorced from its matter content. That is, while the choice of reference metric certainly influences the evolution of the physically observable foreground metric, the effect of matter cannot be neglected. Nevertheless, the relation between matter and geometry can be significantly changed in some specific models; effectively since the graviton would be able to curve the spacetime by itself, without the need of matter. Thus, even the set of vacuum solutions for massive gravity can have significant structure. On the other hand, in some cases the effect of the reference metric could be so strong that no conceivable material content would be able to drastically affect the cosmological evolution.

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RE: General relativity
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General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein on the 20th March, 1916.
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Light from galaxy clusters confirm theory of relativity

All observations in astronomy are based on light emitted from stars and galaxies and, according to the general theory of relativity, the light will be affected by gravity. At the same time all interpretations in astronomy are based on the correctness of the theory of relatively, but it has never before been possible to test Einstein's theory of gravity on scales larger than the solar system. Now astrophysicists at the Dark Cosmology Centre at the Niels Bohr Institute have managed to measure how the light is affected by gravity on its way out of galaxy clusters. The observations confirm the theoretical predictions. The results have been published in the prestigious scientific journal, Nature.
Observations of large distances in the universe are based on measurements of the redshift, which is a phenomenon where the wavelength of the light from distant galaxies is shifted more and more towards the red with greater distance. The redshift indicates how much the universe has expanded from when the light left until it was measured on Earth. Furthermore, according to Einstein's general theory of relativity, the light and thus the redshift is also affected by the gravity from large masses like galaxy clusters and causes a gravitational redshift of the light. But the gravitational influence of light has never before been measured on a cosmological scale.

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Theory of relativity
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Albert Einstein published his special theory of relativity on April 11, 1905 in the physics journal Annalen der Physik.

The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance.
The term "theory of relativity" was based on the expression "relative theory" used by Max Planck in 1906, who emphasised how the theory uses the principle of relativity. In the discussion section of the same paper Alfred Bucherer used for the first time the expression "theory of relativity".

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RE: General relativity
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General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein on the 20th March, 1916.
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As we near the centenary of Einstein's general theory of relativity, a quiet revolution is under way. A number of groups around the world are attempting to test the validity of general relativity on the scale of the universe. So far the tests are inconclusive, yet they herald a striking shift in the way that Einstein's theory is perceived. And testing general relativity is rapidly becoming one of the core endeavours for some of the most powerful satellite and ground-based experiments being developed.
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On this day in 1905, Albert Einstein revealed his paper "On the Electrodynamics of Moving Bodies".

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Princeton scientists say Einstein's theory applies beyond the solar system

A team led by Princeton University scientists has tested Albert Einstein's theory of general relativity to see if it holds true at cosmic scales. And, after two years of analysing astronomical data, the scientists have concluded that Einstein's theory, which describes the interplay between gravity, space and time, works as well in vast distances as in more local regions of space.
The scientists' analysis of more than 70,000 galaxies demonstrates that the universe -- at least up to a distance of 3.5 billion light years from Earth -- plays by the rules set out by Einstein in his famous theory.

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Einstein's Gravity Confirmed on a Cosmic Scale

The theory of gravity proposed by Albert Einstein nearly a century ago can explain the dance of galaxies around one another just as well as it can model the motion of planets around the sun, according to a new study.
The finding suggests that the invisible substance called dark matter and the even more mysterious force known as dark energy are not just figments of physicists' imaginations.

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Study validates general relativity on cosmic scale, existence of dark matter

An analysis of more than 70,000 galaxies by University of California, Berkeley, University of Zurich and Princeton University physicists demonstrates that the universe - at least up to a distance of 3.5 billion light years from Earth - plays by the rules set out 95 years ago by Albert Einstein in his General Theory of Relativity.
By calculating the clustering of these galaxies, which stretch nearly one-third of the way to the edge of the universe, and analysing their velocities and distortion from intervening material, the researchers have shown that Einstein's theory explains the nearby universe better than alternative theories of gravity.
One major implication of the new study is that the existence of dark matter is the most likely explanation for the observation that galaxies and galaxy clusters move as if under the influence of some unseen mass, in addition to the stars astronomers observe.

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