Mordred

not sure what you mean by actual cause, the term arrow of time is simply a descriptive of entropy change to measure time. pretty much an analogy. Time itself is not controlled by entropy. Time also doesn't control entropy. The two are unrelated. The arrow of time is simply a model of time like a clock or measuring a second via beta reactions. Change in entropy follows the ideal gas laws in cosmology in the same principles as a gas in a tank. Time being a measure of rate of change of events. its value as a vector only means it has a forward or backward mathematical relation. In the real universe outside of mathematics time can only flow one direction forwards. No process can reverse time. Or another similar usage the use of the Hubble flow aka scale factor in cosmological time. In this case we use the expansion history as our clock. However that does not mean that if the universe is contracting time is running backwards.. Sounds to me that your under a misunderstanding of a multimedia misconception. I recommend you study what entropy really is.. http://en.wikipedia.org/wiki/Entropy a key note is that entropy is a function of state http://en.wikipedia.org/wiki/Function_of_state now I particularly want you to read this article, as it describes how a decrease in entropy is performed and its relations http://www.physics.ohio-state.edu/p670/textbook/Chap_6.pdf now after you read how to decrease the entropy in a tank, does it make sense to say time flowed backward in that tank? while time flows normally outside of it?? Now apply that same scenario to your contracting universe.

the thermodynamic arrow has been used in numerous arguments and models, its a consequence of the 2nd law of thermodynamics. Its been around as long as the concept of entropy has. Just about every famous physicist has contemplated its consequences to just about every model that describes cosmology or any other thermodymamic process. Some physicist have even written entire books just on the arrow of time. In and of itself however isn't a model. Sholman tried to portray a universe inside a black hole using this consequence. Though hes certainly not the only one. Numerous articles discusses its consequence in dealing with black holes. Sean Caroll uses it in terms of a multiverse hypothesis (cyclic universes). The list is endless. One of the mysteries in cosmology has always been explaining why the universe started at a low entropy beginning. Every cosmology model must have a low entropy beginning to match up with observational data. A couple of details to keep in mind, any thermodynamic system must start out at a lower entropy, lower being a relative value. Entropy either has to stay constant or increase, it can never decrease (hence arrow of time ) Here is one article describing it http://edge.org/response-detail/25538 here is one that uses inflation to explain it http://arxiv.org/abs/1212.1087 here is one using Branes http://cds.cern.ch/record/539984/files/0202104.pdf here is a decent paper discussing it http://philsci-archive.pitt.edu/4744/1/gravent_archive.pdf

your welcome and by the way welcome to the forum

yes many of the inflationary models do, particularly after the development of the slow roll inflationary model. Coincidentally the slow roll approximation, is still one of the better fits AFAIK. Its used as a benchmark model to compare the other models in the Encyclopaedia Inflationaris. you need to be careful here, there is two contributions to a particles energy, there is an contribution arising from the particles mass and an energy contribution arising from its momentum. Hence you cannot rely on a particles rest mass in terms of your statement. You must consider both the particles rest mass and momentum, in terms of its total energy. for the total energy of a particle is see equation 7.2 which is derived by a full relativistic treatment. http://www.maths.qmul.ac.uk/~jel/ASTM108lecture7.pdf here is how the total energy is derived http://galileo.phys.virginia.edu/classes/252/energy_p_reln.html for a relativistic particle its rest mass is meaningless, as its mass is dominated by its kinetic energy, hence for a photon its rest mass is treated as zero now consider this in terms of the 4 bosons and GUT theories. Photons are the force carriers of the electromagnetic field. W and Z bosons are the force carriers which mediate the weak force. Gluons are the fundamental force carriers underlying the strong force. Higg's boson imparts mass graviton? for simplicity we will use this table http://en.wikipedia.org/wiki/Graphical_timeline_of_the_Big_Bang planck epoch the forces except gravity as its said to separate at this time and all particles are in thermal equilibrium, Higg's drops out here as well to impart mass for gravity to work. possibly....The Higg's inflation models times it with the gravity phase transition. (depends on which theory) GUT epoch the strong force separates, so Gluons drop out of equilibrium electroweak epoch you need the electromagnetic mediator, so photons have dropped out of equilibrium, at the end of the electroweak epoch the weak force separates so you have your w and z bosons. keep in mind there is a lot of steps missed and inflation reheating can cause certain particle species previously dropped out of equilibrium to go back into thermal equilibrium. I've yet to come across an up to date break down in terms of GUT that includes the effects of inflation lol

Any good model needs to be able to make predictions, if it can't then its useless as a model. One thing to keep in mind when studying different models. Oft times a different model is merely a different mathematical way of describing the same process. Both models can be correct and make the same predictions. They simply have different metrics to describe the same thing. Though sometimes conflicts do occur. For example you can describe the universe according to the FLRW metric, Einstein field equations or LQC. For the majority of cosmology those three work equally in all situations. The FLRW metric and Einstien field equations are in 100% agreement with each other, however LQC handles the singularity problem differently (bounce). Otherwise they essentially describe the remainder of the universe in the same manner. However then you also have models that try to define an influence differently, good example would be replacing dark matter with modifying Newtons gravity. MOND. Or replacing dark energy with spin and torsion, Poplowskiis, universe inside a black hole, These types of models inherently run into conflicts with LCDM. However other than replacing one or two influences they use the same metrics. Ie FLRW and Einstein field equations. Now take this a step further. say you wish to represent the FLRW metric specifically on a computer and use it to simulate the universe? If you tried to run the formulas directly to a computer you will quickly run into problems on a particle to particle basis. The types of calculations would bog down the processing power and th simulations would take forever to run. To deal with that mathematicians and programmers developed whats called N-body simulations. N-body simulations take a metric and finds another mathematical metric that is easier on the processing done via a computer. I'll use a simple example. A computer is primarily a binary machine. so if I wish to do the calculation 4*2. I have three options. I can directly multiply, I can add 4 two time, or I can do a bit shift right in binary. the bit shift is a faster process. Now N-body is more complex than this. However the codes finds ways to say describe gravity interactions not by the regular GR formulas, but mathematical formulas with the same relations, but done with processing power in mind. Here is a pdf showing some of the N-body code for gravity. note also the use of Matrices and tree codes, this is essentially a visualization of memory stack operations. http://www.cs.hut.fi/~ctl/NBody.pdf Now how does this apply to the quantum information theory? Well simply put if you can relate the metrics used in cosmology or more specifically in the quantum information theory, QM directly to Boolean algebra, You've just found another way to directly define the universe and quantum processes in terms of Binary directly. So in many ways its similar to N-body simulations except for QM applications. Hope this helps. Oh time in a metric system can often be defined differently, the universe doesn't care how we define it. If it allows the mathematics to work and still fit observation data, then its simply a mathematical methodology. Unless it offers a different understanding to observational data

gotcha, just wasn't sure which frequency method you were referring to.

I take it your using the doppler shift in this method?

First off what your describing isn't the universe. However what you described is why the universe isn't rotating, or have a center. There is two key terms to learn Homogeneous (no preferred location) and isotropic (no preferred direction) collectively these terms describe the cosmological principle. Now observations have shown that galaxies appear to be moving away from each other due to expansion uniformly. In other words it doesn't matter which galaxy you use to observe from any galaxy you look at will recede at the same rate. visualize the surface of a balloon. Forget the inside and outside. for this analogy there is no inside our outside. Draw on the balloon various dots. Now blow up the balloon and measure the change in distance from any points regardless of angle or location the rate of change in distance will be equal. albiet with the proper trigonometry lol. This observation of measurements of the rate of expansion (via Galaxies) tells us there is no preferred location or direction. A homogeneous and isotropic universe is a uniform universe, at sufficient scales. roughly 100 Mpc. now here is some recommended reading material, the ballon analogy is of particular importance to your question. 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 the second link of my signature has more material under misconceptions heading. feel free to look at any of the articles there, they will help bring you up to speed on current cosmology now as far as how Cosmology defines geometry the universe geometry article under the site links section (second link of my signature) will help, its based on the FLRW metric

Correct, the hot big bang model only explains the history of our observable universe or rather shared causality/lightcone. We do not know if the universe is finite or infinite. We can only measure our observable portion and assume that the regions outside our observable portion follows the same understanding. This is unfortunately often misrepresented by multi-media programs and article. They often show the universe as starting from some infinitely small and superdense point. This is not predicted by the hot big bang model. Now speaking of observational limits, we cannot make any observations prior to the dark ages http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang#Dark_Ages so how did we determine the chronology of the epochs represented by this list? http://en.wikipedia.org/wiki/Chronology_of_the_universe The answer to that is based on studies at nuclear reactors and the LHC. In other words our understanding of particle physics. However be warned the list represented by that wiki page is based on an older symmetry breaking understanding, SU(5). I haven't seen any correlation for say SU(32). Most current textbooks and early universe particle physics textbooks no longer include the epochs. Putting that aside the BB model starts at 10-43 seconds, prior to that our understanding of physics cannot describe the conditions at this point in time. However due to our understanding of thermodynamics, the universe must have been expanding prior to inflation. No one knows for sure the rate of expansion at this time but you can calculate the rate of expansion via the radiation equation of state corresponding the temperature and energy-density. as shown on page 41, equation 4.0.1 of this article. http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis however you must keep in mind we have no means of knowing the exact temperature, we cannot observe this period, so we apply our understanding of particle physics,ideal gas laws and cosmology to calculate an approximation. inflation is said to occur at roughly 10-36 sec however this depends on which inflation model is correct (there is over 60 still viable observational fit models). However the recent Planck favors the single scalar models with slow roll. This however does not discount the multi scalar models. A full list of viable models is here Encyclopaedia Inflationaris http://arxiv.org/abs/1303.3787 hope this helps the second link of my signature has a site which is a compiled list of articles I have found useful to teach cosmology over the years. None of the material there is conjectural and is all based on textbook concordance model of the LCDM. However I did include some loop quantum cosmology articles, as it has the same predictable ability as LCDM. (LCDM's closest competitor)

whether you use radio waves, microwaves or other forms of electro magnetic waves will work, radio waves is after all how radar works, sonar is sound waves, infra red or ultrasonic sensors use light waves. Your calculations is the speed of light or sound traveling through a medium. This is particularly important in sound waves. Its time based, between time of emission, time of receive with the corresponding rate of travel through the medium.

first off Hawking radiation will only occur, when the surrounding black body temperature is less than the black body temperature of the black hole. If the surrounding temperature is higher then the black hole will gain mass. Secondly the time it takes for a black hole to radiate away via Hawking radiation is incredible, however the smaller a black hole is the faster it would radiate, with the exception above. a one solar mass for a non rotating, uncharged Kerr black hole would take roughly 6.6*1074 seconds to evaporate. see http://en.wikipedia.org/wiki/Hawking_radiation now the other problem is getting the anti- matter into the black hole. anti matter would react with the normal medium of space long before you could get it past the EH. The volume of space is not empty of matter. Also black holes have an accretion disk to contend with. In the accretion disk thermodynamic processes there is also virtual particle matter and antimatter generation. The anti-matter in this process according to this paper can influence the black holes rotation. However is long destroyed before it reaches the EH http://arxiv.org/abs/1104.5499 :''Black hole Accretion Disk'' -Handy article on accretion disk measurements provides a technical compilation of measurements involving the disk itself. a black hole that loses enough mass would be more like a whimper than an explosion due to the amount of mass you need to lose before this occurs.

ultrasonic/infrared distance sensors are good for this, Banner engineering has a good product line http://www.bannerengineering.com/en-US/search?k=distance+sensors&search_type=all&x=0&y=0 there manuals also include the related distance/time measurements including the electronic reaction times

Evidently your misunderstanding what I am saying, so yes better clarity is needed. For one thing I chose not to break down when or what temperatures particles drop out of thermal equilibrium. I chose instead to let the OP use the article as a reference for those details. " One point I'd clarify is that production of massive particles actually starts earlier, but thermal equilibrium quickly ensures that just as many are destroyed as are created. It is only after they drop out of equilibrium due to cooling that that the reverse order of lighter to heavier takes over." correct some older textbooks cover pre-inflationary particle productions, such as the various epochs, planck epoch, electroweak epoch, lepton epoch, etc... The listing of epochs depend on which form of symmetry breaking is describing the process, super-symmetry vs symmetry for example. As we cannot observe this time period, much of our understanding of these era's depend on which model is being looked at. textbook examples include Weinberg's first 3 minutes, Any processes prior to inflation however is effectively washed out, or rather the energy density of any pre-inflationary particles would be so miniscule as to be negligable. Or as Liddle describes it in the first link I posted, "Inflation comes to an end when H begins to decrease rapidly. The energy stored in the vacuum-like state is then transformed into thermal energy, and the universe becomes extremely hot. From that point onward, its evolution is described by the standard hot universe theory, with the important refinement that the initial conditions for the expansion stage of the hot universe are determined by processes which occurred at the inflationary stage, and are practically unaffected by the structure of the universe prior to inflation" Now here is where things get interesting, I mentioned that inflation did not reheat the universe with uniformity. This is fairly new research after the time of Liddle's article and most textbooks and is showing that pre-inflationary thermodynamics may in fact affect post inflationary thermodynamics. The work was pointed out by a friend of mine named Brian Powell. I am in regular contact with him. The pre-inflationary vacuum in the cosmic microwave background. http://arxiv.org/pdf/astro-ph/0612006v3.pdf his work is working on the degeneracy problems in canonical/non-canonical inflation. " In the simple case of single field canonical inflation, the amplitudes of the scalar and tensor power spectra on CMB scales uniquely map to the parameters of the inflationary Lagrangian. However, the inflaton need not be canonically normalized, nor need it be the primary source of primordial perturbations." http://arxiv.org/pdf/1212.4154v2.pdf anyways he has numerous articles now on www.arxiv.com so you can follow his work,for these reasons I did not specify timelines or temperatures when particles drop out of thermal equilibrium. I prefer to leave that to the OP to discover for himself. For one thing it also depends on which inflationary model is correct. Planck data shows a better fit to the single scalar models, however that does not rule out the multi scalar models, currently there is still 60+ inflationary models that are decent observational fit, the Planch data fits 17 of them. Which one you prefer is up to you Encyclopaedia Inflationaris http://arxiv.org/abs/1303.3787 as far as the sequence goes I could have posted this article http://www.maths.qmul.ac.uk/~jel/ASTM108lecture7.pdf however as I described above it depends on which inflation model, which form of symmetry breaking etc that occurs. Out of numerous searches online and dozens of articles I've seen including textbooks you will rarely see any two articles or textbooks that 100% agree with each other, when it comes to the temperature they drop out at, or the timeline/epoch. So I prefer to go with the textbooks as opposed to any other form of article. on that note the particle physics of the early universe, matches up to Scott Dodelsons Modern Cosmology 2nd edition.

your close, Ads/Cft isn't particularly my area of expertise, so I'll try to provide you some direction best I can. Now that you have narrowed out what your after these are far more related than my previous articles lol. Keep in mind ADS/CFT involves M-theory as well as conformal field theory. Keep in mind there is no easy way to explain this. I wish I could simplify the metrics for you on it however I'm not up to par on it, so the best I can do is supply some research direction. For one thing my string theory isn't great lol http://en.wikipedia.org/wiki/AdS/CFT_correspondence http://en.wikipedia.org/wiki/Anti_de_Sitter_space This portion is described by m-theory rather than the Einstein field equations. (if I understand it correctly) http://en.wikipedia.org/wiki/Conformal_field_theory An Introduction to Conformal Field Theory http://arxiv.org/pdf/hep-th/9910156v2.pdf Introducing Conformal Field Theory http://www.damtp.cam.ac.uk/user/tong/string/four.pdf Applied Conformal Field Theory http://arxiv.org/pdf/hep-th/9108028.pdf http://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory An Introduction to Generalized Yang-Mills Theories http://arxiv.org/pdf/hep-th/0102055.pdf?origin=publication_detail putting these together you have below Introduction to ADS/CFT http://arxiv.org/pdf/0712.0689v2.pdf this particular article is over 800 pages long, however has QFT,CFT,String and ADS/CFT in it http://arxiv.org/abs/hepth/9912205 : "Fields" - A free lengthy technical training manual on classical and quantum fields

OK lets clarify a few aspects here, first off the hot big bang model does not describe the beginning of the universe..... It only describes that the universe was in a hot dense state near its beginning. Now this is not to mean a singularity such as that found within a black hole. The singularity of the BB model is simply a point in time prior to 10-43 seconds, we simply do not have the physics to accurately describe conditions at this extreme temperature, and density. Clearing that up, there is so many models of the beginning of the universe, I cannot possibly describe them all. However they all break down into 3 essential categories. Universe from nothing, due to quantum fluctuations (Leanard Susskind supports this model) Although there is a couple of variations. A cyclic universe, one in which our universe is one in a long line of universes that collapsed and restarted. Bounce universe, similar to the cyclic universe however the BB portion temperatures etc is the result of the bounce (from collapsing) Loop quantum Cosmology is a prime example of this model. Now there is also numerous models which describe our universe as being the result of a black hole/white hole in another universe and we are residing within the EH. There is numerous problems with this model, first it does not account for early large scale structure formation. Two any universe inside a BH would be rotating, no matter how slow a rotation is this universe would not be homogenous and isotropic. It would inherently have a preferred direction an location. Our universe is homogenous and isotropic. The universe in a BH model has numerous different purporters, however one of the more prominant ones is Poplowskii with his spin and torsion model. Then there is the many worlds universe, which is based of the quantum many worlds interpretation. Essentially every decision in a wave function starts a new universe. In this there would be an infinite number of universes created every second lol. Not too practical. Chaotic eternal inflation also has a process that describes bubble universes, the essential nature of this model is that small anistropies in a parent universe, will expand to form causally separate universes. Via the same inflation mechanism as the inflation in our universe. The main problem is we have no direct evidence of any other universe even existing, every multiverse model is conjecture only. We can only gather data within our observable portion of the universe. Our universe could be finite or infinite, we still do not know which. Due to that limitation science cannot answer how our universe started as we simply do not know with certainty. We can only model possibilities based on our understanding and observations.. Though some of the models are more likely than others. However unless we can disprove a particular model, then it is equally valid as an other model. That is simply the scientific way. Hope this helps edit forgot to mention time, lol most multiverse models depend on time continuing between the parent universe to the birth of the new universe. However this may or may not be the case. Rather than explain that I recommend reading "Time before time" http://arxiv.org/ftp/physics/papers/0408/0408111.pdf

As far as I know this is the finest/affordable resolution obtainable, however it still depends on wavelength as swansont and others are describing, its an intriguing development. As far as I know not yet on market. the related nano equipment is also included. Love to get my hands on these to play around with, in particular the single photon LED (sends a stream) and the quantum dot detector, not to mention the particle entanglement diode. However this is still determined by wavelength. I mentioned them simply to point out some of the latest developments in nanotech applications (Keyword,quantum, as in all the rules mentioned on this thread apply) http://www.toshiba-e...uantumdots.html http://www.toshiba-e...ndetection.html http://www.toshiba-e...generation.html http://www.toshiba-e...otonsource.html http://www.toshiba-e...tangledled.html

here is the arxiv paper on it http://arxiv.org/pdf/1402.6319v2.pdf I seem to be having some trouble getting it to load though found this article as well, I was trying to locate its proper distance http://www.universetoday.com/111609/runaway-star-cluster-breaks-free-from-distant-galaxy/ according to this article and that I couldn't find it in the arxiv article "The star cluster is moving so fast it should soon by sailing into intergalactic space. It may already be, but its distance remains unknown." its still too early to tell as we don't have its proper distance

actually we do have the technology to emit a single photon and detect a single photon, as well as entangle two photons together http://www.toshiba-europe.com/research/crl/qig/quantumdots.html http://www.toshiba-europe.com/research/crl/qig/singlephotondetection.html http://www.toshiba-europe.com/research/crl/qig/singleelectronspingeneration.html http://www.toshiba-europe.com/research/crl/qig/singlephotonsource.html http://www.toshiba-europe.com/research/crl/qig/entangledled.html its pretty obvious just from that alone that photons do exist, in the same way any particle exists with an energy/mass relation. Photons mediate the electromagnetic force. That includes light. Photons are the force carriers of the electromagetic force W and Z bosons are the force carriers which mediate the weak force Gluons are the fundamental force carriers underlying the strong force in other words their interactions with their environment is how the force is carried. with photons their interactions has wave like properties. So it can be treated mathematically as both a particle and a wave

The CMB is particularly useful in the comoving frame. A proper frame, or comoving frame, is a frame of reference that is attached to an object. The object in this frame is stationary within the frame. The CMB is often used for observers that see the universe as isotropic. However an observer moving at relative velocities would not percieve the universe as isotropic. Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time Comoving distance factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space conformal time is similar to having a watch that slows down as the universe expands. You don't see conformal frame used to often nowadays, most articles etc use the comoving or proper frame however this does not qualify the CMB as a perfect frame or an absolute frame, as convenient as it is lol, as you've already pointed out

differential geometry is extremely handy for GR and SR, Calculus of course. Those two subjects are vital in any physics application. this will indicate the need for strong math skills, http://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on General Relativity" Matthias Blau lol be warned its 928 pages long but covers GR and SR in excellent detail. Always handy in any physics reference collection

the paper has been released http://arxiv.org/ftp/arxiv/papers/1405/1405.1418.pdf

Its based on the quantum information theory. Though poorly done I might add. There is some validity on the quantum information theory, however this article isn't showing the complete picture. I'm still reading this to understand it better myself. I figure the best place to start is either a textbook or a dissertation I chose the latter http://cds.cern.ch/record/476522/files/0011036.pdf there is one line in this dissertation that struck a cord The theory of quantum computation is an attempt to capture the essential elements of a theory of quantum information processing in a single unifed theory. I say \attempt" because it is not yet clear that the theory of quantum computation provides a complete account of the information processing capabilities afforded by quantum mechanics. right now I would just consider it as a QM alternative in development, the other thing that article mentions is its dependancy upon loop quantum gravity/cosmology. LQC is a strong model but no more or less than LCDM. LQC avoids the information loss of a singularity by having a bounce. In other words once the singularity reaches a planck length it bounces and starts expanding. http://arxiv.org/abs/1108.0893 Planck stars http://arxiv.org/abs/1401.6562 http://arxiv.org/abs/1201.4598 "Introduction to Loop Quantum Cosmology by Abhay Ashtekar The model is gaining weight so make your own judgements

yeah I agree with that. QC isn't a specialty of mine either though I am studying QFT. The paper I posted on LQC is interesting, they use a similar bounce methodology for the BB singularity. Both still doesn't correlate well to this statement "However, because gravity is geometry in general relativity, when the gravitational field becomes singular, the continuum tears and the space-time itself ends. There is no more an arena for other fields to live in. All of physics, as we know it, comes to an abrupt halt" lol I read a good paper on BH accretion disks, they had a metrics that gives a possibility of determining if a BH was in fact a neutron star. Both can have an EH. Its a lengthy article but has some interesting metrics involved.. The dynamics involved in the accretion disk is to say the least amazing. I would say that QC,QFT and string theory each have a chance of solving the singularity problem. Though my thoughts lean towards one of the QM fields of study over string theory. http://arxiv.org/abs/1104.5499 :''Black hole Accretion Disk'' -Handy article on accretion disk measurements provides a technical compilation of measurements involving the disk itself. lol sometimes I read far too much, I have a huge collection of articles and textbooks, from various fields of study. Cosmology, particle physics QM, QFT, LQC, N-Body simulations, that's the list of textbooks I have with numerous textbooks for each field. My article database is somewhere in the realm of 16 gigs worth of PDF's. speaking of BH's and quacky articles you should find this one humerous http://arxiv.org/abs/1304.6592 "Destroying the event horizon of regular black holes" lol maybe then we will know for sure

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.

just figuring out the latex structure. [latex]H=\frac{\dot a}{a}[/latex] [latex]f:\mathbb R\rightarrow\mathbb R[/latex] [latex]x\in\mathbb R[/latex] [latex]a\!b\,c\ d~e\quad f\qquad g\ \ \ \ h~~~~i\hspace{20mm}j[/latex] [latex]\Lambda^\mu_\nu,\ \Lambda_\nu^\mu,\ \Lambda^\mu{}_\nu,\ \Lambda_\nu{}^\mu[/latex] [latex]\lim_{n\rightarrow +\infty} {\frac{\sin(x)}{x}}[/latex] [itex] [latex]x^{10}+x^{whatever value}[/latex] [latex]\lim_n x_n=x_n x_n[/latex] [latex]x_nx_n[/latex] [latex]xe^x = x \Big( \sum_{n=0}^\infty\frac{x^n}{n!} \Big)[/latex] [latex] \left\{ \begin{array}{l} x=r\cos\theta\\ y=r\sin\theta \end{array} \right. ~~\Rightarrow~~ x^2+y^2 =r^2(\underbrace{\cos^2\theta+\sin^2\theta}_{=1})=r^2 [/latex] hrrm doesn't like multilayer lines lol [latex]\left\{\begin{array}{l}x=r\cos\theta\\y=r\sin\theta\end{array}\right.~~\Rightarrow~~ x^2+y^2=r^2(\underbrace{\cos^2\theta+\sin^2\theta}_{=1})=r^2[/latex] [latex]\int_{x-2}^d[/latex] [latex]\iiint_{x-2}^d[/latex] [latex]\begin{pmatrix}1 & 2 & 3 & 4\\a & b & c & d\\x & y & z & w\end{pmatrix}[/latex] kk think I have her some variation in syntax from the latex I used before http://www.tex.ac.uk/tex-archive/info/symbols/comprehensive/symbols-a4.pdf [latex]\leftharpoonup[/latex] [latex]\rho[/latex] [latex]\overbrace{abc}[/latex] [latex] \celsius[/latex] evidently not all the latex form are supported at least according to the forms on that pdf [latex]\Updownarrow[/latex] [latex]\Leftrightarrow[/latex]