Mordred

Nothing Its still an important point to mention as this is also commonly misunderstood. It's more an FYI, as the universe can be infinite its singularity cannot be accurately thought of as a BH style point like singularity if you include the universe beyond our observable universe. We still don't know if the universe is finite or infinite. Though our observable universe is finite You'd be amazed how often this is misunderstood.

You might want to study which type of singularity. 1.the state of being singular, distinct, peculiar, uncommon or unusual 2.a point where all parallel lines meet 3 a point where a measured variable reaches unmeasurable or infinite value 4. the value or range of values of a function for which a derivative does not exist 5 a point or region in spacetime in which gravitational forces cause matter to have an infinite density; associated with Black Holes. The universe singularity case is number 3 as opposed to 5. As mentioned though this depends on the metrics used. Some examples that avoid or solve number 3 have been mentioned. A notable one being the bounce of LQC.

An explosion regardless of when you measure it has a point of origin. As well as a preferred direction. It is inhomogeneos and isotropic. So when you measure how an explosion expands. It will be nothing like the balloon analogy. You will measure an increase in volume change with a preferred direction and location. All objects are moving from the center outward. However if you measure expansion you will not measure a preferred direction and location. That is precisely the point of the cosmological principle. The distance between all objects are increasing in all directions not an outward direction. Here Ned Wright's tutorial has some good visuals. http://www.astro.ucla.edu/~wright/balloon0.html Beaz has a decent write-up. http://math.ucr.edu/home/baez/physics/Relativity/GR/centre.html Metrics expansion of space shows one decent image. http://en.m.wikipedia.org/wiki/Metric_expansion_of_space http://oneminuteastronomer.com/6949/where-is-the-center-of-the-universe/ http://csep10.phys.utk.edu/ojta/c2c/largescale/cosmology/geometry_tl.html Granted the balloon analogy is 2d, the raisin bread is 3d. http://fundamentalweirdness.blogspot.ca/2010/03/raisin-bread-universe.html?m=1 Here is a decent YouTube video 11 minutes long. https://www.khanacademy.org/science/cosmology-and-astronomy/universe-scale-topic/big-bang-expansion-topic/v/hubble-s-law

Excellent question. To answer this detail we need to clarify one key aspect. "What is the size of the entire universe" Well pop media shows and programs will almost always show this explosion like origin, starting from a volume less than an atom in size. This is entirely wrong. In point of detail we do not know the size of the entire universe.... We only know the size of our observable universe. http://en.m.wikipedia.org/wiki/Observable_universe The big bang model starts at [latex]10^{-49}[/latex] forward in time. Prior to that we cannot accurately describe due to the conditions prior to that point. We call this a singularity conditions, but not a point like singularity such as a BH. Our entire universe could be either finite or infinite in size. The big bang model only describes how our Observable universe evolves in volume since [latex]10^{-49}[/latex] forward. This is the detail missed in pop media literature. The other detail is that at all times the universe surrounds us. No matter what direction you look in, the further you look, the further back in time you look. However you will see not see a particular direction look any different from any other direction. So assuming you could directly see 10^-49 seconds forward you will still see the observable universe in every direction and the same thermodynamic conditions at a given distance in every observation direction. However you will never be able to see the entire universe. You will only ever be able to measure how our Observable portion evolves.

Here is something to consider. Take a telescope pick a star, now you have the problem. How far away is that star. So to determine that one technique is redshift. However for redshift you need an original frequency. So you look at known elements. Hydrogen spectral lines are handy. Already you have to use calculated values. The cosmological redshift formula. One cannot use visual data to measure the universe directly. You always have to find ways to calculate and determine distance.

Didn't I also state you account for age? I did mention the scale factor and post the distance formula in 4d. All datasets must account for observer influences. This includes time "You calculate the proper distance between two or more measurement points. Any time you take any measurements you must account for observer influences. [latex]d{s^2}=-{c^2}d{t^2}+a({t^2})d{r^2}+{S,k}{r^2}d\Omega^2[/latex]" This was posted in a previous post this thread.

Why do I think your still misunderstanding? The cosmological principle has nothing to do with how the universe evolves over time. It is specifically describing the distribution of thermodynamic processes and distribution of matter at specific moments in time. We can directly measure today's temperature. It's the temperature of our local group. We can also confirm the universe expands by taking measurements further and further back in time. Just as we can measure the change in distance measurements and redshift.

Not really that negligable. Try to understand a key detail. If you look further and further away, your naturally looking further back in time. In this context one can state there is a preferred direction but this isn't entirely accurate. The further you look back in time the denser the universe will appear. This isn't what the Cosmological Principle is really stating. One way to think of it is, " At any specific moment in time, the universe is homogeneous and isotropic." This includes key dynamics such as those involved in thermodynamic processes, or the ideal gas laws. Pressure, temperature, energy density and expansion. The CMB is one such moment. However any point in time will have a uniform density throughout the universe. Today that critical density is roughly 10^29 grams/cubic metre with average blackbody temperature of 2.73 Kelvin. Using the equations of the FLRW metric one can use density as our clock. Fundamentally cosmic time does just that.

Lol oops, evidently I hadn't completely woken up lol

Lol if you didn't understand or follow that article portion. Regardless of notation or otherwise. Then that portion definetely needs a major revamp and rethink.

Not quite, light takes roughly 326 light years to travel 100 Mpc. The changes in that time period is negligible compared to the age of the universe. So one can say roughly the same age. However when you take your measurements. You calculate the proper distance between two or more measurement points. Any time you take any measurements you must account for observer influences. [latex]d{s^2}=-{c^2}d{t^2}+a({t^2})d{r^2}+{S,k}{r^2}d\Omega^2[/latex] Here is the 4d Freidmann equation for distance measures. K is the curvature constant. a(t^2) is the scale factor which takes expansion at a point in time into account. http://en.m.wikipedia.org/wiki/Scale_factor_(cosmology) Note the scale factor also accounts for cosmological redshift. Any specific point in time will have the thermodynamic properties. The universe will be roughly the same temperature throughout. (Though the temperature variations isn't significant in 326 years, except in the early universe) You cannot directly see the same point in time throughout the universe. So you must calculate where objects will be at that point in time. I really wish I could post the charts from the lightcone calculator in my signature. However one can use that tool to see the changes in 326 years. For some reason this site doesn't like the latex the calc uses. You can refine the time period being calculated via the S_upper and S_lower values.

I incorporated some of the suggested changes. In the opening post. Please review. Any suggestions welcome including syntax and writing style. Don't worry I don't bite, I fully expect a site forum FAQ article to undergo numerous adjustments.

that statement should have read a property of particles not mass lol oops. Missed that. I am working on this aspect, originally I had planned on including the metric and curvature tensor as defined in an arbitrary coordinate system of a point (test particle). The problem I've run into is simplifying the metric for the average reader. True, again the problem is keeping the article simple yet accurate. I agree more detail on the coordinate aspects of GR is needed for the article, which may be best to apply the Lorentz transformation from two examples from flat and in the Schwartchild metric. On the quantum foam aspects, it's looking like a link to a separate thread may be best. On note on the metric section here is what I have thus far and I'm reconsidering how to go about this section. GR matrix transformations In General Relativity the metric is seemingly complex. One must understand that GR is a coordinate system. When one describes bodies in motion such as planets and stars the metric of a sphere is useful. However at some point one must use an arbitrary coordinate metric. Recalling that GR has the time component as a coordinate as well. Coordinates in GR take the form (ct,x,y,z) this leads to a 4x4 matrix. For the moment we are ignoring everything but the exact specific real numbers the components of the metric take at a single point. Lets define a point as [math]x^\alpha[/math] and our new coordinate as [math]y^{\mu}[/math] these simple coordinates leads to [math]g_{\mu\nu}=g_{\alpha\beta}=\frac{dx^{\alpha}}{dy^{\mu}}\frac{dx^{\beta}}{dy^{\nu}}[/math] What exactly is a matrix. The wiki definition is useful. "In mathematics, a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns that is treated in certain prescribed ways. The individual items in a matrix are called its elements or entries. " http://en.m.wikipedia.org/wiki/Matrix_(mathematics) One example is below. Which is a 4*4 matrix Note the numeric organization. [math] A_{m,n} =\begin{pmatrix}a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\\vdots & \vdots & \ddots & \vdots \\a_{m,1} & a_{m,2} & \cdots a_{m,n}\end{pmatrix}[/math] In GR it is common to replace m and n with [math]\mu[/math] and [math]\nu[/math] respectively. As one can see [math]\mu[/math] denotes the row and [math]\nu[/math] denotes the column. Both [math]\mu[/math] and [math]\nu[/math] are vectors. Matrix transformation examples can be found here http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch9.pdf A more detailed 63 page article on matrix mathematics can be studied in this pdf. http://www.google.ca/url?sa=t&source=web&cd=1&ved=0CBsQFjAA&url=http%3A%2F%2Fwww.mheducation.ca%2Fcollege%2Folcsupport%2Fnicholson4%2Fnicholson4_sample_chap2.pdf&rct=j&q=matrix%20mathematics%20pdf&ei=WaBmVbjaCrDfsASK4YGwAQ&usg=AFQjCNFLoGWucTsDoKqVhBhrLWIaPeIHbw&sig2=P6W5USwrpu7eDNGAbRf4SQ. Einstein field equation Metric tensor In general relativity, the metric tensor below may loosely be thought of as a generalization of the gravitational potential familiar from Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as distance, volume, curvature, angle, future and past. [math]dx^2=(dx^0)^2+(dx^1)^2+(dx^3)^2[/math] [math]g_{\mu\nu}=\begin{pmatrix}g_{0,0}&g_{0,1}&g_{0,2}&g_{0,3}\\g_{1,0}&g_{1,1}&g_{1,2}&g_{1,3}\\g_{2,0}&g_{2,1}&g_{2,2}&g_{2,3}\\g_{3,0}&g_{3,1}&g_{3,2}&g_{3,3}\end{pmatrix}=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] Which corresponds to [math]\frac{dx^\alpha}{dy^{\mu}}=\frac{dx^\beta}{dy^{\nu}}=\begin{pmatrix}\frac{dx^0}{dy^0}&\frac{dx^1}{dy^0}&\frac{dx^2}{dy^0}&\frac{dx^3}{dy^0}\\\frac{dx^0}{dy^1}&\frac{dx^1}{dy^1}&\frac{dx^2}{dy^1}&\frac{dx^3}{dy^1}\\\frac{dx^0}{dy^2}&\frac{dx^1}{dy^2}&\frac{dx^2}{dy^2}&\frac{dx^3}{dy^2}\\\frac{dx^0}{dy^3}&\frac{dx^1}{dy^3}&\frac{dx^2}{dy^3}&\frac{dx^3}{dy^3}\end{pmatrix}[/math] The simplest transform is the Minkowskii metric, Euclidean space or flat space. This is denoted by [math]\eta[[/math] Flat space [math]\mathbb{R}^4 [/math] with Coordinates (t,x,y,z) or alternatively (ct,x,y,z) flat space is done in Cartesian coordinates. In this metric space time is defined as [math] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/math] [math]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] In an effort to keep this article to a manageable length I will refer to the wiki article on Lorentz transformations and its connection to SR. http://en.m.wikipedia.org/wiki/Lorentz_transformation A free textbook (open source) can be found here http://www.lightandmatter.com/sr/ (For the Schwartzchild Metric I was thinking of using Kruskal Szekeres coordinates.) Though it may better to stick to the Schwartzchild Metric) and just link other coordinate systems of note.

Quantum foam is also a mathematical descriptive. When you get into the details. I think it may be best to place that under the QM forum. Then provide a link to each article. Still deciding on that. Atm the curvature and stress energy tensors is giving me headaches trying to simplify them.

FAQ article development, feel free to ask questions or make suggestions. (I'm still working on the Einstein field equation section. Probably keep that portion seperate to minimize length) This question is amongst one of the most commonly asked questions in relativity. Numerous articles both in pop media and peer reviewed articles refer to terms such as space time fabric, space time curvature. This leads the new learners with a common misconception that space has some mysterious fabric or material like property. To answer this properly we need to describe a few principles. A) gravity influences mass B) energy is a property of particles, or physical configurations such as feilds. Energy does not exist on its own. C) space is defined as a volume only. That volume contains the standard model particles and feilds. It is not something form of ether. In GR space is mapped in an arbitrary coordinate system. Without the time component the coordinates are in 3d. D) spacetime is any metric that includes the time component as a vector. This is the 4th dimension, in GR the time component is treated in coordinate form. E) General relativity is a coordinate system metric. This coordinate system makes use of manifolds. Which is a topological space that is resembles Euclidean space at beach point. For example a Euclidean space (flat space), can undergo a homeomorphism to curved space via relativistic effects such as inertia and mass to an observer. The rubber sheet example is one such homeomorphism. http://theory.uwinnipeg.ca/users/gabor/black_holes/slide5.html A good YouTube video is http://m.youtube.com/watch?v=MTY1Kje0yLg Keep in mind the rubber sheet analogy is just that. An analogy, it was never intended to state that space time is a materialistic fabric or ether. A classical example of a homeomorphism is the coordinate change from Cartesian coordinates (Euclidean flat space) to polar coordinates. (Curved, spherical geometry) https://www.mathsisfun.com/polar-cartesian-coordinates.html http://en.m.wikipedia.org/wiki/Manifold http://en.m.wikipedia.org/wiki/Homeomorphic Now with those in mind, we find that spacetime curvature is a geometric coordinate relation of how the strength of gravity influences the particles that reside in the volume of space. In short it is a geometric description of how gravity influences particles not the volume of space. The terms fabric, curvature, sretches are misleading. They are analogies used to explain the change in geometric relations. 2) How is space time created? The volume of space simply increases, space itself is just volume filled with the standard model particles.

If measurement and observations are found that disagree with the Cosmological principle then yes it would need to be dropped. Thus far all the best datasets and measurements still find the principle accurate. These datasets are not limitted to WMAP and Planck, those two are merely the more popularly known. Correct. This is the value also provided in numerous textbooks as well. Afaik cosmology papers are still currently using this value. The metrics of the BB model accounts for the aspects of time vs distance. There is several different types of time used in cosmology. Cosmic, conformal and proper time. There is also different categories of distance measure. Proper conformal and commoving distance. Think of it this way. At any specific moment in time. The average universe density and thus rate of expansion is uniform. So at any moment of time. The Cosmological principle applies. The FLRW metrics accounts for this via the scale factor. It is a good point to raise in regards to time. One of the articles provided by Brian Powell that I included goes into this detail.

In my spare time I will be writing a series of useful articles to help answer common questions. As these are being designed for forum reference I feel strongly on cooperative review. Here is the first. Please look over and feel free to make suggestions. Any solid contributions will be accorded credit at the end of the final product. (Key note all articles MUST comply with textbook descriptives, they are being designed as teaching aids) [latex]\textbf{The Cosmological principle}[/latex] is defined as "at sufficiently large scales, the universe appears as homogeneous and isotropic." [latex]\underline{Homogenous}[/latex] is oft defined as " no preferred location" [latex]\underline{Isotropic}[/latex] is oft defined as "no preferred direction" Obviously at smaller localized scales we can see numerous examples of systems that are inhomogeneous and anisotropic (planets, stars galaxies and large scale structures). However if you increase the radius of measurements sufficient enough those non uniform regions essentially become negligible or more accurately averages out. A good analogy is look at the surface of a lake. At small scales you can discern waves and ripples. As you increase in height or distance from the lake those non uniform regions become a uniform appearing surface. The cosmological principle works the same way. The scale commonly used is 100 Mpc mega parsecs. Speed of light in a vacuum: [latex]c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}[/latex] The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometers (19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×1013 kilometers The cosmological principle has an added reward in that complex systems can be modelled as good approximations with far less complicated mathematics. However it should be noted that if measurements and observations disagree with the cosmological principle those metrics become invalid. We're lucky though as the body of evidence fully support the cosmological principle. A commonly referred to example being the CMB. Cosmic microwave background. Although the temperature images look chaotic, the difference in temperature of the blue regions and red regions are roughly 1/1000 of a degree. Certainly supports the cosmological principle. The cosmological principle is of importance in telling us that the Universe did not have an origin point nor is the result of an explosion. This is of primary importance in regards to expansion and inflation. Lets detail this a bit further. Take any number of points, three or more. As the volume of space increases, the same ratio of change will occur between any two points and the angles between those points also do not change. This mathematically is only possible via a uniform change regardless of location. A good analogy is the balloon analogy or the raisin bread analogy. http://www.phinds.com/balloonanalogy/: A thorough write up on the balloon analogy used to describe expansion http://tangentspace.info/docs/horizon.pdf:Inflation and the Cosmological Horizon by Brian Powell The other consequence of the cosmological principle is that the universe cannot have a rotation. All rotating bodies have a center of rotation and rotation imparts a preferred direction.

I do a lot of work with robotics in plant automation applications. The ones I deal with typically use ladder logic, ie Allen Bradley RS5000, and SLC 500. The other big names is Siemens. You would find SLC500 easier to learn. Keep in mind many robotic applications also incorporate data collection, so having C++ is also a good skill. Some industrial applications uses SCADA. (I've worked with well over 20 programming laquages, mostly relay/ladder logic, here is the thing. Choose one to learn. Once you can program in one laquage adapting to other lanquages is fairly straightforward. If you want a cheap method to learn ladder logic, but a low cost zelio smart relay or for AB, a picosoft relay. It will include the programming cable and software. Cost of under 200.00. SLC500 is around 2k, controllogix is roughly 3 to 4 k. (Wouldnt recommend the expensive ones to start) Good textbook on Automation systems is http://www.amazon.ca/Automating-Manufacturing-Systems-Plcs-Hugh/dp/0557344255 (Key note for robotics you will need a strong electrical, hydraulic and pneumatic understanding.) As well as calculus.

Cosmological principle the universe has no preferred location or direction Comprises two principle terms. Homogeneous no preferred location Isotropic no preferred direction. What this means is uniformity in overall energy density/mass distribution. Now the Einstein field equations and the FLRW metric are both interchangeable. They both involve the ideal gas laws. Cosmology describes the universe as a perfect fluid. pv=nRt Each contributor (particle etc) has an equation of state. http://en.m.wikipedia.org/wiki/Equation_of_state_%28cosmology%29 in GR energy density corresponds to pressure via the stress energy tensor. [latex]T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p \eta^{\mu\nu}[/latex] http://www.th.physik.uni-bonn.de/nilles/exercises/ss04/gr05.pdf http://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor for the metric tensor portion above. http://en.m.wikipedia.org/wiki/Metric_tensor_(general_relativity) The full subject is too lengthy to post all the relationships. http://en.m.wikipedia.org/wiki/Metric_tensor_(general_relativity) I have numerous articles covering this under my signature for direct GR to cosmology chapter 9 covers this. http://www.blau.itp.unibe.ch/newlecturesGR.pdf"Lecture Notes on General Relativity" Matthias Blau However this book is rather advanced. I have some simplifications in these two articles. Site Articles (Articles written by PF and Site members) http://cosmology101.wikidot.com/redshift-and-expansion http://cosmology101.wikidot.com/universe-geometry page 2 FLRW distance to FLRW metric http://cosmology101.wikidot.com/geometry-flrw-metric/ these articles all cover the above the beginning chapters covering the Cosmological principle. Unfortunately the range of your questions require individual threads to properly answer each one even in narrative form Cosmological principle covered, Mass is resistance to inetia, you can have particles that are not matter with mass aka bosons. Elementary Matter particles are fermionic Google Pauli exclusion principle. Matter particles of the same state occupies space only one fermionic particle of the same state can occupy the same space. Any number of bosons can occupy a given volume. The entire universe is not being sucked into blackholes. Electrons go around the nucleus due to electromagnetic charge. Planets and moons is due to gravity. No one knows for sure past the event horizon. We can't measure it directly

You don't one essential detail. The research for a preferred location (center) has been done. None is found. More models than I can count tried having a inhomogeneous and anisotropic universe. As such this has been extensively looked into by BOSS. Planck,WMAP etc. The cosmological principle is extremely well tested.

Cosmology is based on observational evidence. Not believability. All observational data shows a strong agreement with no center, no preferred direction and no preferred location. The latest Planck dataset places this to near 100% accuracy, or as close as any model gets to that accuracy they always allow for some % of error. Read this particular article as well, it was written by Brain Powell who has a PH.D in Cosmology. http://tangentspace....ocs/horizon.pdf:Inflationand the Cosmological Horizon by Brian Powell You'll note the same details in the Lineweaver and Davies articles

The universe BB model was not an explosion nor does the universe has a center. It is a rapid expansion of space. Not a kinetic type explosion. Here is some material please read the misconceptions of the big bang Lineweaver and Davies in particular. Misconceptions (Useful articles to answer various Cosmology Misconceptions) http://www.phinds.com/balloonanalogy/: A thorough write up on the balloon analogy used to describe expansion http://tangentspace.info/docs/horizon.pdf:Inflation and the Cosmological Horizon by Brian Powell http://arxiv.org/abs/1304.4446:"What we have leaned from Observational Cosmology." -A handy write up on observational cosmology in accordance with the LambdaCDM model. http://arxiv.org/abs/astro-ph/0310808:"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf:"Misconceptions about the Big bang" also Lineweaver and Davies The balloon analogy is also handy

Neither time nor space is being created... the geometric volume of space simply increases. One of the most common mistakes is to try and define space with some fabric like property. Space itself has no energy or fabric. It is a geometric volume that is simply filled with the energy-mass from the rest of the universe. That being said the superluminal velocity measurements of expansion is a consequence of the separation distance and the Hubble flow. Hubble's law. The greater the distance the greater the recessive velocity. [latex]V_{recessive}=H_Od[/latex] the subscript o meaning the hubble parameter today, which is constant only in time..meaning at a particular time Its not a constant as per se a consequence of Hubble's law is that when recessive velocity becomes greater than the speed of light, this region is described as the Hubble radius or sphere. However the recessive velocity is not an inertial velocity hence as mentioned, as only the volume is increasing and expansion is not a consequence of inertia, GR and SR do not apply. This recent article written by a physicist friend of mine, covers this in excellent and well written detail. With very little math involved as his target audience is the general public http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell this is another good article http://arxiv.org/abs/astro-ph/0310808 :"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies We This is incorrect we can see farther than the Hubble sphere, Much farther. We can measure recessive velocities at z=1080 at around 3c. See the first article I posted to see why. correct

The terms created, stretched etc is VERY misleading. Space itself has no substance, fabric or energy. Space is simply geometric volume that is simply filled with the contents of the universe. However an important consequence of having a region of volume is that you will have a vacuum energy-density at the very least. This does not mean that the volume has a fabric or energy property. A volume of space is simply a filled region. Space geometry changes due to gravity is simply a descriptive of its energy-density distributions. The term warping of space is also a poor and misleading descriptive.

I've spent a few years collecting good articles to teach online students Cosmology, according to textbook standards. Here is a collection of articles Misconceptions (Useful articles to answer various Cosmology Misconceptions) http://www.phinds.com/balloonanalogy/ : A thorough write up on the balloon analogy used to describe expansion http://arxiv.org/abs/1304.4446 :"What we have leaned from Observational Cosmology." -A handy write up on observational cosmology in accordance with the LambdaCDM model. http://arxiv.org/abs/astro-ph/0310808 :"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" Lineweaver and Davies http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf: "Misconceptions about the Big bang" also Lineweaver and Davies http://arxiv.org/abs/1002.3966 "why the prejudice against a constant" http://arxiv.org/abs/gr-qc/0508052 "In an expanding universe, what doesn't expand? Richard H. Price, Joseph D. Romano http://arxiv.org/abs/1301.0219What's in a Name: History and Meanings of the Term "Big Bang" Helge Kragh http://arxiv.org/pdf/0906.1442v1.pdf Is it possible to see the infinite future of the Universe when falling into a black hole? Training (textbook Style Articles) http://arxiv.org/pdf/hep-ph/0004188v1.pdf :"ASTROPHYSICS AND COSMOLOGY"- A compilation of cosmology by Juan Garcıa-Bellido http://arxiv.org/abs/astro-ph/0409426 An overview of Cosmology Julien Lesgourgues http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis http://www.gutenberg.org/files/30155/30155-pdf.pdf: "Relativity: The Special and General Theory" by Albert Einstein http://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on General Relativity" Matthias Blau http://arxiv.org/abs/1201.4598 "Introduction to Loop Quantum Cosmology by Abhay Ashtekar http://arxiv.org/abs/hepth/9912205 : "Fields" - A free lengthy technical training manual on classical and quantum fields Historical article links http://www.astrosurf.com/luxorion/hubble-law-redshift1929.htm Reprint of one of Hubbles papers. http://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf An authorized reprint of Einsteins Special relativity paper. http://apod.nasa.gov/diamond_jubilee/debate20.html The "Great debate of the 20's" jubilee reprint article available http://www.drchinese.com/Bells_Theorem.htm Good reference site covering Bells theorem. http://www.intechopen.com/download/pdf/41230 good historical coverage of many of the key figures in Cosmology history http://arxiv.org/abs/1302.1498 " “The Waters I am Entering No One yet Has Crossed”: Alexander Friedman and the Origins of Modern Cosmology" written by Ari Belenkiy http://arxiv.org/pdf/1212.5499.pdf "The Contribution of V. M. Slipher to the Discovery of the Expanding Universe" by C. O’Raifeartaigh http://www.gutenberg.org/files/17384/17384-pdf.pdf "foundations of geometry" David Hilbert