Mordred

A Newton is defined as " One newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in direction of the applied force" https://en.m.wikipedia.org/wiki/Newton_(unit) compare the SI unit of force to the SI unit of acceleration. The only difference is the addition of mass via unit kg.

same here, its a bit slower on the mobile compared to my laptop.

There isn't much available on the Madala boson, however this paper has the theoretical cross scatterings with the Higgs and DM. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1709.09419&ved=0ahUKEwjDpp-EzNnWAhVK3GMKHaAODukQFggwMAU&usg=AOvVaw3vW_v56hM2WFWxe_zCePMQ

edit forget last post forgot to reread your context. The aspect to recall is we are using a coordinate basis. So certain relations are treated as rotations under symmetry. This can alter how quadratic expressions are handled, in particular under a "Coordinate Basis" this is an important distiction to constantly be aware of. So for example a quadradic parabola will be in essence divided by the quadratic geometry treatment under your covariant and contravariant rotations. So the two real or imaginary values that arise from quadradic expressions ie the plus/minus is treated under coordinate rotation symmetry relations.

Night its also late here. See section V on macroscopic gravity correlated with Dirac and the U(1) gauge group application. You should notice immediately the connection to particle/antiparticles. Charge,Helicity, parity. Ie as per Pati-Salam for left/right handedness. As applied to gravity. https://www.google.ca/url?sa=t&source=web&rct=j&url=http://cds.cern.ch/record/274210/files/9412052.pdf&ved=0ahUKEwiMq6fjudjWAhUQHGMKHUgjA7UQFggdMAA&usg=AOvVaw3p6cz8xKi30t-IfqnSSBjO

Fair enough let me put the outer product details later on when I have more time. I will try to get the Shannon treatments applied and its correlations to other metrics. (will take some time, most papers tend to gloss over outer products and focus on the inner products.

I'm not worried about how Shannon handles it. I am interested in how your model handles [latex]u_iv_j[/latex] which is the outer product of the Minkowskii metric with inner products uv=vu

Its a key component. Most of your work involves the inner products. What about the outer products ?

It is the U(1) gauge that gives the hint lol. Think about the Pati-Salam reference and the [latex]\mathbb{Z}[/latex] you find in LQG for example. Under Clifford what is the purpose of the [latex]\mathbb{Z}[/latex] why does LQG require it?

Ok You have a huge body of various metrics to put together into one post if possible. It is getting extremely tricky to correlate the numerous posts as they are all closely related. I'm hoping that your arriving at something similar to [latex]SU(2)\otimes U(1)[/latex] a little research will show that numerous treatments commonly arrive at this from SO(1,3). Including a huge series of papers oft called 2+1 gravity Anyways under one post will make this much easier to identify any missing relations etc.

Try using that equation and determine the acceleration at the radius provided for 21. You don't require a dummy mass for part 1. You should be able to find the accereration at any radius by applying the equation you provided. As you are already given the mass of Mars.

Excellent quality post, well thought out and written.

In essence. The covariant and contravariant scripts denote objects that would be identical if one flips the axis involved 180 degrees. So in the case of positive pressure you have a vector with a magnitude and direction. You flip the direction of the vector but the scalar quantity remains unchanged. It is the same object just under a 180 degree rotation.

Anytime you see [latex] T^{\alpha\beta}[/latex] think specifically under the Newton approximation. The above superscript denotes a particular class of solutions comparable to Newtons gravity. Lets detail this further. Start with a" perfect fluid" which has two conditions. No heat induction and no viscosity... So [latex]T^{\alpha\beta}[/latex] is the flux of the [latex]\alpha[/latex]th component across a constant surface [latex]x^\beta[/latex] [latex]T^{00}=[/latex] flux of O'th component energy across time surface N^0= energy density. For null pc^2. (time-time component) [latex]T^{0i}=T^{i0}=0[/latex] energy flux of constant x^i (heat induction statement} [latex] T^{ij}[/latex] flux of i momentum across j surface= stress.... in this case i does not equal j so [latex]T^{\alpha\beta}=\rho_0+\frac{p_0}{c^2}U^\alpha U^\beta-p_0\eta^{\alpha\beta}[/latex] So check your references, see if they are describing a) perfect fluid b) pressureless dust c) Newton approximation including vacuum solutions. Conservation of energy momentum of the above (as per many textbooks,see previous post and article) [latex]T^{\alpha\beta}=\frac{\partial T^{\alpha\beta}}{\partial x^\beta}=0[/latex] note we use partial derivitaves in the above where [latex]T^{\mu\nu}[/latex] uses covarient derivitaves... Reference to above equations etc https://www.google.ca/url?sa=t&source=web&rct=j&url=https://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px436/notes/lecture6.pdf&ved=0ahUKEwjOyKGD-dXWAhVfImMKHQd9CNcQFgggMAE&usg=AOvVaw352GUmErn2XX3x4cVR1l98 I was looking to see if there is a specific named identity to the tensor above. Some papers call it the dust stress tensor, others the matter stress tensor. I find the above treatment more specific to the nature of the above tensor. So decided to post, it is good info to be aware of (the above is from the reference but is also described in numerous GR textbooks. ) Unfortunately dummy indices are arbitrary choices, so they can be interchanged. Really just breaks down to conventions. So unfortunately there is no golden rule but alpha beta is too easy to confuse with Eulers change of basis forms.

That is assuming one can even make any sense of the OP's post. Reads as sheer garbly goop to me.

String theory to properly describe would require serious math skills to understand degree of freedom reductions. Lets see how well you do with quantum mechanics from Vmedvil's well thought out summary.

Personally though this is strictly a personal opinion. I feel out of the theories I have studied for DM the most likely contender is right handed neutrinos via Higgs instability. However there is no confirmational evidence, save one possible xray study that I am aware of.

Anyways errors aside from that site you used. You may want to read the following. "Most writers on General Relativity fail to acknowledge that Eq. (1) is not so much a conservation law, as a law for energy transfer." Equation 1 is the standard form you usually see the stress tensor applied to. https://arxiv.org/abs/1010.5557 Which bring us back to my original point that the EFE equation you posted doesn't provide a detail on the conservation law as equation 1 only applies for strictly freefall. (article includes this detail)

You might try posting the correct tensor. The energy/monentum tensor is [latex]T^{\mu\nu}[/latex] Not [latex]T^{\alpha\beta}[/latex] The conservation element to the stress tensor is the continuity equation [latex]\partial_\nu T^{\mu\nu}=0[/latex] You posted the electromagnetic stress tensor which is not the same as the stress tensor under the EFE. Different tensor elements

Well there is a ton about Star Trek that has very little to do with science. Some of the list above for instance. Attempting to apply physics to their shields etc is pretty much impossible. Too many inconsistencies to even try

The old forum software never could accept the latex structure of the cosmo calculator in my signature. So I was never able to introduce its sheer usefulness. Here is a 100 step history of Cosmology. [latex]{\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/latex] [latex]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&z&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&V_{gen}/c&V_{now}/c&V_{then}/c&H/Ho \\ \hline 0.001&1090.000&1089.000&0.000373&0.000628&45.331596&0.041589&0.056714&0.000856&21.023&3.148&66.182&22915.263\\ \hline 0.001&970.069&969.069&0.000454&0.000759&45.248813&0.046645&0.063641&0.001047&19.566&3.142&61.483&18980.740\\ \hline 0.001&863.334&862.334&0.000551&0.000915&45.159913&0.052309&0.071406&0.001279&18.232&3.136&57.177&15740.128\\ \hline 0.001&768.343&767.343&0.000668&0.001102&45.064558&0.058652&0.080109&0.001561&17.007&3.129&53.223&13067.118\\ \hline 0.001&683.804&682.804&0.000810&0.001326&44.962398&0.065753&0.089864&0.001904&15.881&3.122&49.585&10859.192\\ \hline 0.002&608.566&607.566&0.000979&0.001594&44.853035&0.073703&0.100794&0.002319&14.843&3.115&46.232&9032.833\\ \hline 0.002&541.606&540.606&0.001183&0.001915&44.736079&0.082599&0.113040&0.002822&13.885&3.107&43.136&7520.218\\ \hline 0.002&482.014&481.014&0.001428&0.002298&44.611118&0.092551&0.126756&0.003430&13.000&3.098&40.273&6265.981\\ \hline 0.002&428.979&427.979&0.001722&0.002756&44.477683&0.103683&0.142116&0.004165&12.180&3.089&37.619&5224.758\\ \hline 0.003&381.779&380.779&0.002074&0.003303&44.335327&0.116128&0.159313&0.005052&11.419&3.079&35.157&4359.526\\ \hline 0.003&339.773&338.773&0.002496&0.003956&44.183524&0.130038&0.178562&0.006124&10.712&3.068&32.869&3639.803\\ \hline 0.003&302.388&301.388&0.003001&0.004736&44.021755&0.145580&0.200103&0.007416&10.055&3.057&30.740&3040.607\\ \hline 0.004&269.117&268.117&0.003606&0.005666&43.849475&0.162938&0.224202&0.008973&9.443&3.045&28.756&2541.361\\ \hline 0.004&239.507&238.507&0.004329&0.006776&43.666058&0.182317&0.251154&0.010848&8.873&3.032&26.905&2125.058\\ \hline 0.005&213.154&212.154&0.005194&0.008100&43.470902&0.203941&0.281289&0.013105&8.340&3.019&25.177&1777.702\\ \hline 0.005&189.701&188.701&0.006228&0.009680&43.263304&0.228060&0.314971&0.015819&7.842&3.004&23.561&1487.678\\ \hline 0.006&168.829&167.829&0.007463&0.011563&43.042568&0.254948&0.352603&0.019082&7.377&2.989&22.049&1245.393\\ \hline 0.007&150.253&149.253&0.008937&0.013808&42.807958&0.284906&0.394635&0.023003&6.941&2.973&20.634&1042.892\\ \hline 0.007&133.721&132.721&0.010698&0.016484&42.558633&0.318265&0.441559&0.027712&6.533&2.955&19.307&873.554\\ \hline 0.008&119.008&118.008&0.012800&0.019675&42.293784&0.355387&0.493924&0.033363&6.150&2.937&18.063&731.896\\ \hline 0.009&105.913&104.913&0.015309&0.023478&42.012463&0.396668&0.552333&0.040144&5.791&2.918&16.895&613.344\\ \hline 0.011&94.260&93.260&0.018302&0.028010&41.713731&0.442539&0.617449&0.048276&5.454&2.897&15.799&514.097\\ \hline 0.012&83.889&82.889&0.021873&0.033412&41.396601&0.493471&0.690005&0.058025&5.138&2.875&14.769&430.988\\ \hline 0.013&74.659&73.659&0.026132&0.039848&41.059938&0.549970&0.770801&0.069708&4.840&2.851&13.802&361.371\\ \hline 0.015&66.444&65.444&0.031211&0.047518&40.702622&0.612585&0.860719&0.083704&4.561&2.827&12.892&303.042\\ \hline 0.017&59.133&58.133&0.037266&0.056657&40.323472&0.681908&0.960718&0.100464&4.298&2.800&12.036&254.163\\ \hline 0.019&52.627&51.627&0.044487&0.067545&39.921133&0.758568&1.071848&0.120530&4.051&2.772&11.231&213.190\\ \hline 0.021&46.837&45.837&0.053094&0.080518&39.494307&0.843238&1.195249&0.144544&3.818&2.743&10.473&178.842\\ \hline 0.024&41.683&40.683&0.063355&0.095974&39.041469&0.936624&1.332155&0.173278&3.600&2.711&9.759&150.041\\ \hline 0.027&37.097&36.097&0.075584&0.114387&38.561117&1.039471&1.483902&0.207649&3.394&2.678&9.087&125.889\\ \hline 0.030&33.015&32.015&0.090158&0.136321&38.051665&1.152552&1.651928&0.248752&3.200&2.642&8.455&105.633\\ \hline 0.034&29.383&28.383&0.107528&0.162452&37.511295&1.276652&1.837767&0.297896&3.017&2.605&7.859&88.642\\ \hline 0.038&26.150&25.150&0.128224&0.193578&36.938267&1.412573&2.043059&0.356639&2.845&2.565&7.297&74.389\\ \hline 0.043&23.272&22.272&0.152887&0.230655&36.330540&1.561097&2.269531&0.426844&2.683&2.523&6.768&62.431\\ \hline 0.048&20.712&19.712&0.182274&0.274818&35.686105&1.722983&2.519001&0.510729&2.530&2.478&6.270&52.398\\ \hline 0.054&18.433&17.433&0.217283&0.327417&35.002842&1.898930&2.793361&0.610939&2.386&2.431&5.800&43.981\\ \hline 0.061&16.405&15.405&0.258995&0.390062&34.278330&2.089532&3.094542&0.730635&2.250&2.380&5.357&36.917\\ \hline 0.068&14.600&13.600&0.308686&0.464664&33.510190&2.295250&3.424511&0.873577&2.123&2.327&4.940&30.990\\ \hline 0.077&12.993&11.993&0.367873&0.553490&32.695921&2.516347&3.785220&1.044246&2.002&2.271&4.546&26.017\\ \hline 0.086&11.564&10.564&0.438378&0.659241&31.832675&2.752795&4.178540&1.247998&1.889&2.211&4.176&21.843\\ \hline 0.097&10.291&9.291&0.522342&0.785104&30.917756&3.004225&4.606237&1.491191&1.782&2.147&3.827&18.342\\ \hline 0.109&9.159&8.159&0.622337&0.934864&29.948028&3.269765&5.069835&1.781425&1.682&2.080&3.498&15.403\\ \hline 0.123&8.151&7.151&0.741396&1.112970&28.920472&3.547949&5.570564&2.127725&1.587&2.008&3.188&12.938\\ \hline 0.138&7.254&6.254&0.883106&1.324642&27.831986&3.836543&6.109216&2.540822&1.499&1.933&2.896&10.871\\ \hline 0.155&6.456&5.456&1.051751&1.575989&26.679131&4.132295&6.685941&3.033511&1.415&1.853&2.622&9.137\\ \hline 0.174&5.746&4.746&1.252327&1.874042&25.458852&4.430801&7.300157&3.620922&1.337&1.768&2.364&7.684\\ \hline 0.196&5.114&4.114&1.490772&2.226851&24.167785&4.726112&7.950210&4.321054&1.265&1.678&2.122&6.467\\ \hline 0.220&4.551&3.551&1.773969&2.643393&22.803119&5.010547&8.633245&5.155130&1.197&1.584&1.895&5.448\\ \hline 0.247&4.050&3.050&2.109877&3.133394&21.362526&5.274330&9.344906&6.148142&1.135&1.484&1.683&4.596\\ \hline 0.277&3.605&2.605&2.507705&3.706949&19.844072&5.505151&10.078977&7.329494&1.078&1.378&1.485&3.885\\ \hline 0.312&3.208&2.208&2.977691&4.373615&18.247534&5.688090&10.827382&8.733318&1.026&1.267&1.301&3.292\\ \hline 0.350&2.855&1.855&3.531250&5.141190&16.573938&5.805127&11.579797&10.399216&0.981&1.151&1.129&2.801\\ \hline 0.394&2.541&1.541&4.180384&6.013592&14.827243&5.835394&12.323993&12.372310&0.942&1.030&0.970&2.395\\ \hline 0.442&2.261&1.261&4.937174&6.988248&13.014812&5.755347&13.046138&14.703398&0.911&0.904&0.824&2.061\\ \hline 0.497&2.013&1.013&5.813076&8.053192&11.147771&5.539179&13.731340&17.448904&0.888&0.774&0.688&1.788\\ \hline 0.558&1.791&0.791&6.817286&9.184553&9.242569&5.160286&14.365254&20.669840&0.875&0.642&0.562&1.568\\ \hline 0.627&1.594&0.594&7.955449&10.346218&7.320583&4.592515&14.935503&24.431020&0.873&0.508&0.444&1.392\\ \hline 0.705&1.419&0.419&9.228712&11.492781&5.406771&3.811243&15.432947&28.800505&0.883&0.375&0.332&1.253\\ \hline 0.792&1.263&0.263&10.632280&12.576261&3.528946&2.795101&15.853609&33.848476&0.907&0.245&0.222&1.145\\ \hline 0.890&1.124&0.124&12.156498&13.554725&1.713811&1.525243&16.198190&39.648621&0.945&0.119&0.113&1.062\\ \hline 1.000&1.000&-0.000&13.787206&14.399932&0.000000&0.000000&16.472274&46.278944&1.000&0.000&0.000&1.000\\ \hline 1.122&0.891&-0.109&15.486308&15.092847&1.618903&1.816439&16.682257&53.725767&1.071&0.112&0.120&0.954\\ \hline 1.259&0.794&-0.206&17.257193&15.648602&3.109203&3.914254&16.841624&62.157478&1.158&0.216&0.250&0.920\\ \hline 1.413&0.708&-0.292&19.084811&16.081339&4.480102&6.328312&16.960166&71.678284&1.265&0.311&0.394&0.895\\ \hline 1.585&0.631&-0.369&20.956083&16.410335&5.731185&9.083316&17.046787&82.407190&1.391&0.398&0.554&0.877\\ \hline 1.778&0.562&-0.438&22.860235&16.655836&6.865865&12.209426&17.109031&94.480167&1.537&0.477&0.733&0.865\\ \hline 1.995&0.501&-0.499&24.788750&16.836447&7.890128&15.742876&17.152975&108.052165&1.707&0.548&0.935&0.855\\ \hline 2.239&0.447&-0.553&26.735095&16.967918&8.811470&19.726424&17.183327&123.299150&1.900&0.612&1.163&0.849\\ \hline 2.512&0.398&-0.602&28.694196&17.063037&9.638020&24.209612&17.203810&140.420122&2.120&0.669&1.419&0.844\\ \hline 2.818&0.355&-0.645&30.662778&17.131233&10.378263&29.249920&17.216703&159.640257&2.369&0.721&1.707&0.841\\ \hline 3.162&0.316&-0.684&32.638034&17.180008&11.040250&34.912335&17.224075&181.212698&2.651&0.767&2.032&0.838\\ \hline 3.548&0.282&-0.718&34.618055&17.214789&11.631673&41.270735&17.227279&205.422443&2.968&0.808&2.397&0.836\\ \hline 3.981&0.251&-0.749&36.601471&17.239540&12.159687&48.408586&17.239540&232.589832&3.325&0.844&2.808&0.835\\ \hline 4.467&0.224&-0.776&38.587301&17.257125&12.630854&56.419954&17.257125&263.074711&3.727&0.877&3.269&0.834\\ \hline 5.012&0.200&-0.800&40.574846&17.269607&13.051146&65.410679&17.269607&297.281130&4.179&0.906&3.788&0.834\\ \hline 5.623&0.178&-0.822&42.563607&17.278458&13.425962&75.499732&17.278458&335.662657&4.687&0.932&4.370&0.833\\ \hline 6.310&0.158&-0.842&44.553231&17.284732&13.760162&86.820752&17.284732&378.728355&5.257&0.956&5.023&0.833\\ \hline 7.079&0.141&-0.859&46.543466&17.289176&14.058110&99.523796&17.289176&427.049513&5.896&0.976&5.756&0.833\\ \hline 7.943&0.126&-0.874&48.534134&17.292324&14.323714&113.777305&17.292324&481.267204&6.615&0.995&6.580&0.833\\ \hline 8.913&0.112&-0.888&50.525109&17.294553&14.560471&129.770331&17.294553&542.100779&7.421&1.011&7.504&0.833\\ \hline 10.000&0.100&-0.900&52.516301&17.296130&14.771503&147.715032&17.296130&610.357404&8.326&1.026&8.540&0.833\\ \hline 11.220&0.089&-0.911&54.507647&17.297246&14.959601&167.849482&17.297246&686.942761&9.341&1.039&9.704&0.833\\ \hline 12.589&0.079&-0.921&56.499102&17.298036&15.127252&190.440821&17.298036&772.873059&10.480&1.051&11.009&0.832\\ \hline 14.125&0.071&-0.929&58.490634&17.298594&15.276677&215.788802&17.298594&869.288522&11.758&1.061&12.474&0.832\\ \hline 15.849&0.063&-0.937&60.482221&17.298988&15.409856&244.229762&17.298988&977.468508&13.193&1.070&14.118&0.832\\ \hline 17.783&0.056&-0.944&62.473846&17.299266&15.528554&276.141085&17.299266&1098.848489&14.802&1.078&15.963&0.832\\ \hline 19.953&0.050&-0.950&64.465499&17.299463&15.634346&311.946207&17.299463&1235.039097&16.608&1.086&18.032&0.832\\ \hline 22.387&0.045&-0.955&66.457171&17.299601&15.728633&352.120234&17.299601&1387.847492&18.635&1.092&20.354&0.832\\ \hline 25.119&0.040&-0.960&68.448857&17.299697&15.812667&397.196249&17.299697&1559.301346&20.909&1.098&22.960&0.832\\ \hline 28.184&0.035&-0.965&70.440552&17.299765&15.887564&447.772380&17.299765&1751.675744&23.460&1.103&25.883&0.832\\ \hline 31.623&0.032&-0.968&72.432255&17.299812&15.954315&504.519738&17.299812&1967.523376&26.322&1.108&29.163&0.832\\ \hline 35.481&0.028&-0.972&74.423962&17.299845&16.013807&568.191327&17.299845&2209.708407&29.534&1.112&32.844&0.832\\ \hline 39.811&0.025&-0.975&76.415673&17.299867&16.066830&639.632027&17.299867&2481.444485&33.137&1.116&36.973&0.832\\ \hline 44.668&0.022&-0.978&78.407386&17.299882&16.114087&719.789814&17.299882&2786.337380&37.181&1.119&41.607&0.832\\ \hline 50.119&0.020&-0.980&80.399101&17.299891&16.156204&809.728332&17.299891&3128.432838&41.718&1.122&46.805&0.832\\ \hline 56.234&0.018&-0.982&82.390817&17.299897&16.193742&910.641009&17.299897&3512.270255&46.808&1.125&52.639&0.832\\ \hline 63.096&0.016&-0.984&84.382534&17.299901&16.227197&1023.866895&17.299901&3942.942921&52.519&1.127&59.183&0.832\\ \hline 70.795&0.014&-0.986&86.374252&17.299902&16.257014&1150.908430&17.299902&4426.165600&58.928&1.129&66.527&0.832\\ \hline 79.433&0.013&-0.987&88.365970&17.299902&16.283588&1293.451377&17.299902&4968.350364&66.118&1.131&74.766&0.832\\ \hline 89.125&0.011&-0.989&90.357688&17.299902&16.307273&1453.387193&17.299902&5576.691674&74.185&1.132&84.011&0.832\\ \hline 100.000&0.010&-0.990&92.349407&17.299900&16.328381&1632.838131&17.299900&6259.261851&83.237&1.134&94.384&0.832\\ \hline \end{array}}[/latex] and well into our future. One can select which columns one wishes to use, The WMAP and Planck datasets are selectable and one can fine tune into any time period by selecting the min max stretch values. The resolution being the number of steps. http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

[latex]{\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/latex] [latex]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{gen}/c&H/Ho \\ \hline 1090.000&0.000373&0.000628&45.331596&0.041589&0.056714&21.023&22915.263\\ \hline 339.773&0.002496&0.003956&44.183524&0.130038&0.178562&10.712&3639.803\\ \hline 105.913&0.015309&0.023478&42.012463&0.396668&0.552333&5.791&613.344\\ \hline 33.015&0.090158&0.136321&38.051665&1.152552&1.651928&3.200&105.633\\ \hline 10.291&0.522342&0.785104&30.917756&3.004225&4.606237&1.782&18.342\\ \hline 3.208&2.977691&4.373615&18.247534&5.688090&10.827382&1.026&3.292\\ \hline 1.000&13.787206&14.399932&0.000000&0.000000&16.472274&1.000&1.000\\ \hline 0.312&32.884943&17.184900&11.117770&35.666086&17.224560&2.688&0.838\\ \hline 0.132&47.725063&17.291127&14.219438&107.785602&17.291127&6.313&0.833\\ \hline 0.056&62.598053&17.299307&15.535514&278.255976&17.299307&14.909&0.832\\ \hline 0.024&77.473722&17.299802&16.092610&681.060881&17.299802&35.227&0.832\\ \hline 0.010&92.349407&17.299900&16.328381&1632.838131&17.299900&83.237&0.832\\ \hline \end{array}}[/latex] Oh my cosmocalc now works on this site

Excellent summary Studiot I would just like to add some essential details without specifying any particular theory. a) Scalar field (magnitude only), there can be tons of smaller movements, but were concerned with the global average mean value. This would be a spin zero, field of value x. There is no inherent direction component of this field. Using relativity as an example the vacuum solutions is one example. In the FRW metric inflation. This is a homogeneous and isotropic field. b) The field now has a direction component mean average, this is no longer a spin zero statistic but the field spin will depend on the quage bosons involved. For the electromagnetic field, spin 1. Gravity best matches spin 2. Any field with an inherent direction is a charged field. Spin will depend on the charges involved. (treat charge as simply attraction/repulsion). there is a handy formula that applies to demonstrate the second post by Studiot. Scalar field equation of state. [latex]w=\frac{\frac{1}{2}\dot{\phi}^2-V\phi}{\frac{1}{2}\dot{\phi}^2+V\phi}[/latex] the numerator is the kinetic energy the denominator is the potential energy. A field with a direction would need additional terms to that equation. Terms mentioned in Studiots last post of flux and vorticity.

There is no membrane to the universe, there is however apparent horizons based on observer limits under GR in terms of the killing vectors under specified metrics of the FRW.. Such as Hubble horizon, particle horizon and Cosmological event horizon. The question on whether or not the conservation of energy/momemtum laws apply on the cosmological scale, however I can quarantee the Einstein field equations does not address that issue. As we don't know what causes Lambda we cannot know if it applies under the conservation laws or not. How can we ? As far as radiation and matter, then yes you are correct. Under an adiabatic and isentropic expansion conservation of energy does apply. Adiabatic meaning no net inflow or outflow of energy. However this does not mean a closed system..... The conservation laws only apply in closed systems... The EFE works equally well for open systems, so why would you think it means the universe is conserved?

You know Schelero perhaps your time will be better used, by learning basic physics. Basic physics 101. Time is the rate of change of events or duration. So in order to have matter, their must FIRST be time for matter to form in the first place. How can anyone think otherwise is 100 percent beyond me, unless they don't know how to think. Quite frankly time must exist for a universe to form in the first place, let alone matter. Not that time is some mysterious pixie dust that requires existence. It is simply a property that emerges with rate of change.