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DrRocket
Post  Post subject: Foundations of modern cosmology  |  Posted: Fri Aug 05, 2011 8:28 pm
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The pillar of modern cosmology is one of the pillars of modern physics, general relativity.

General relativity (GR) was formulated by Albert Einstein and announced in 1915. It has since received a great deal of attention, the mathematical foundations have been examined, the presentation refined, and a host of confirming experiments performed. General relativity, with its mathematical roots in Riemannian geometry is a formidable subject, and some of its predictions are contrary to everyday experience – i.e. “common sense” can be badly mistaken. That is no surprise as even special relativity, the precursor and “little brother’ of GR is surprising at first encounter.

http://math.ucr.edu/...baez/gr/gr.html
http://en.wikipedia....eral_relativity
http://en.wikipedia....eral_relativity
http://rspa.royalsoc...1732/5.full.pdf

GR treats the universe over all time as a single entity – spacetime. This can also be done in Newtonian mechanics, so there is nothing really new about spacetime. What distinguishes GR is that spacetime is not just affine 4-space, but in fact is a Lorentzian 4-manifold of undetermined topology, with a curvature tensor that is also unknown but is determined by the distribution of mass/energy via a stress-energy tensor defined by a very complex set of partial differential equations. These equations, the Einstein field equations can only be explicitly solved in a few simple circumstances. Gravity is the result of curvature of spacetime.

In general because of curvature neither space nor time have any global meaning. However, if one makes the assumption that spacetime is homogeneous and isotropic, then spacetime decomposes as a 1-parameter foliation by space-like 3-dimensional hyperplanes of constant curvature. The parameter serves as a surrogate for time and the hyperplanes as a surrogate for space. The hyperplanes inherit a true Riemannian metric from spacetime and expansion of space means that the distance between points increases as the value of the time-like parameter increases.

Astronomical observations support the assumption that the universe is homogeneous and isotropic on the largest scales. Observations also support the expansion of space.

http://scienceworld....leConstant.html
https://www.cfa.harv...~huchra/hubble/
http://map.gsfc.nasa..._expansion.html
http://map.gsfc.nasa.gov/
http://en.wikipedia....nisotropy_Probe
http://aether.lbl.go...cience/cmb.html
http://aether.lbl.go...cience/cmb.html

Based on these assumptions and observations Hawking and Penrose in a series of papers used general relativity to conclude that, as a logical consequence, the universe began in an extremely compact form, and in fact predicted singular behavior (which is generally thought to indicate a limitation of general relativity to predict the first fraction of a second)

http://web.archive.o...ing_text.shtml/
http://rspa.royalsoc...b7-91869da35ea6
http://rspa.royalsoc...b7-91869da35ea6
http://rspa.royalsoc...b7-91869da35ea6
http://rspa.royalsoc...9.full.pdf+html

So, while nobody knows what happened in the first fraction of a second, the big bang hypothesis in terms of subsequent expansion from an extremely compact state is on firm empirical and theoretical grounds.

Inflation is not necessary to the big bang, but does use ideas from quantum field theory to explain why the universe is homogeneous on the large scale, yet exhibits anisotropy on smaller scales. It is not a fully verified, or even rigorously formulated, theory, yet. It is promising. It is supported by what has been seen in surveys of the cosmic background radiation. Attacking inflation as unproven is futile, because it is well-known to be just that. But interpreting “unproven” as fanciful or unlikely is simply a demonstration of ignorance.

http://web.mit.edu/p...2_cosmology.pdf

Thus, modern cosmology rests on a solid foundation of empirical data and well-formulated theory. That does not make it immutable. Any physical theory is subject to refinement and extension. But any revision must meet equal standards of rigor.

Anyone who rejects modern cosmology must meet the obligation of providing the basis for an alternative . That means providing a theory of gravity to replace GR, and the empirical data to support it. Further, that data must include ALL valid data, including that which currently provides evidence for the validity of GR itself.


Addendum: useful references for the serious (these are NOT popularizations)

Gravitation -- Misner, Thorne, Wheeler

Gravitation and cosmology : principles and applications of the general theory of relativity -- Weinberg

Cosmology -- Weinberg

General Relativity -- Wald

Principles of Physical Cosmology -- Peebles

The large scale structure of space-time -- Hawking and Ellis

General Relativity and the Einstein Equations -- Choquet-Bruhat



Good popularizations include:

A Brief History of Time -- Stephen Hawking

The Big Bang -- Joseph Silk

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Last edited by DrRocket on Fri Jul 06, 2012 1:29 am, edited 1 time in total.


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iNow
Post  Post subject: Re: Foundations of modern cosmology  |  Posted: Thu Oct 13, 2011 1:52 am
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Adding to the superb content above, below are some lectures from CERN in 2005 where Sean Carroll expounds on a few of the key pieces.

The interested reader should consider opening them in a new window and watching full screen with a delicious beverage in a comfortable chair.

Enjoy.


http://blogs.discovermagazine.com/cosmi ... e-physics/

Lecture One: Introduction to Cosmology




Lecture Two: Dark Matter




Lecture Three: Dark Energy




Lecture Four: Thermodynamics and the Early Universe




Lecture Five: Inflation and Beyond


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"[Time] is one of those concepts that is profoundly resistant to a simple definition." ~C. Sagan


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ToddFelico
Post  Post subject: Re: Foundations of modern cosmology  |  Posted: Wed Jun 27, 2012 8:53 am

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Thanks for sharing.


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SkinWalker
Post  Post subject: Re: Foundations of modern cosmology  |  Posted: Mon Jul 09, 2012 8:16 am
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Thank you DrRocket. For sharing that valuable information.


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Benjamin
Post  Post subject: Re: Foundations of modern cosmology  |  Posted: Thu Sep 12, 2013 1:56 am
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This information is going to help me greatly in my astronomy class. This site is a treasure trove of information.


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Osmium
Post  Post subject: Re: Foundations of modern cosmology  |  Posted: Fri Sep 01, 2017 12:16 pm

Joined: Fri May 05, 2017 7:25 pm
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Thanks for sharing, it's very interesting!


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