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Q1 How does the stretching of space-time affect gravity? In general relativity the “stretching” (or, better, the curvature) of spacetime is gravity. Both dark matter and ordinary matter/energy curve spacetime and so create gravitational fields. Q2 What effect of dark matter is assisting in the decoupling? By “decoupling” I assume you mean the clumping ...


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Yes but... Many of the "laws" of classical physics are actually rather conditional - they work OK in normal environments, but they tend to break down in extreme cases, like in black holes. As a result, physics has developed a Standard Model of subatomic particles, which interact in non-intuitive ways to produce the classical physics we know. As an ...


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Aristotle argued that one of the major goals of physics was the study of change. If the laws of physics that we knew of changed with time, then we can ask for the reason behind this change and call that a law of physics instead. If that in turn appeared to change then again we can ask for the reason behind this change. One does not expect this to go on, ad ...


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As far as we know, the laws of nature have not changed in the 13.7 billion years since the big bang. That is the laws of gravity, E&M, quantum mechanics, and so on applied then as they do now. Furthermore, the strength of the constants that describe the strength of interactions and such, like G, e, and so on, have not changed. Conditions have changed ...


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Galaxies and clusters of galaxies are held together by gravity. They do not expand as the universe expands. Therefore they are not closer together and not denser as time passes.


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Two points. (1) The current best estimate for the current size of the radius R of the observable universe (OU) is 45.7 billion light-years. See https://en.wikipedia.org/wiki/Observable_universe . (2) R is calculated by integrating the time T of a photon's traveling from the circumference of OU to the center (where Earth is) taking into account that the OU ...


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There are two approaches to time dependence in physical laws. One is to say that there could be different laws at different times. Another is to say that there is one "true" unchanging law, which might happen to include a dependence on time (or temperature/energy, or some other parameter). With either approach you get the same outcome - the ...


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This subject is not in my area of expertise, but for what it's worth, in the following article titled "Eras of the Big Bang" (https://web.njit.edu/~gary/202/Lecture26.html#:~:text=The%20Planck%20Era%20is%20prior,a%20single%20%22super%22%20force.) the following statement is made: "The first few eras are when the laws of physics were ...


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Yes, the laws of nature are independent of time. That is, when and if we have the 'correct laws' of physics. It's quite subjective and philosophical as physical laws can't be proved right, only falsified, or proved wrong. However most scientists would think that if we had a 'law of physics' and it was found to vary with time - then it had been falsified and ...


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At high energies the laws of nature become different than in lower energies so as we go back in time some laws must have been different.


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There were no matter particles at all "before", or at the exact time of the Big Bang. Particles formed a short time after the Big Bang. The laws of physics (quantum mechanics and general relativity) as we know them currently, are not properly applicable before about $10^{-12}$ seconds after the Big Bang. So talking about particles and curvature ...


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The status is that the prediction must be wrong and that this is an unsolved problem of QFT.


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Brane cosmology could solve this issue. Here, an effective de Sitter brane is included in an Anti-de Sitter space-time. With an effective Friedmann equation from brane cosmology (see below) one can realize a small effective cosmological constant within the effective Friedmann equation a large cosmological constant as a solution of the covariant energy ...


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You can take a finite spherical region of a closed, dust-dominated FLRW universe and embed it in a Schwarzschild background. The combination describes a sphere of matter that expands from an initial singularity (the white-hole singularity of the full Schwarzschild geometry) and recollapses to a final singularity (the black-hole singularity), and is ...


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We normally say, a balloon expands. If we were being more expansive, we would say it expands into the air. Note that the air is larger than the balloon. And that both are a small part of eveythimg, but with, of course, the latter small thing larger than the preceding small thing. Thus a thing expands when the thing, a small part of everything, expands into a ...


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I think the main reason not to consider an embedding space is Occam's razor. The data are perfectly well fit with a 4-dimensional manifold, which does not require an embedding space. If you were to introduce the embedding space, you would then need some theory which explained how the embedding came about, and what the dynamics are of the extra dimensions. Or,...


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In an ideal FLRW recollapsing universe, the collapse is just the time reversal of the expansion. The Doppler shift factor at all times is $a(t_\text{emission})/a(t_\text{detection})$, and during the collapse, that's a blueshift instead of a redshift. Realistically, the big crunch would be much more chaotic than the big bang, because entropy would continue to ...


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Here are some comments on the physics. (i) the origin of the different peaks, The peaks are remnants of sound waves in the primordial at the time of recombination. The size of the peak at a given angular scale is predominantly determined by modes of a corresponding wavenumber. The phase is determined by the initial conditions of the Universe; some modes ...


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The statement that the speed of light in a vacuum is observed the same in all free-falling frames of reference is axiomatic in general relativity. Einstein took that as a postulate, but you could also develop the theory in other ways. You can have a Lorentz-symmetric physics in which only sublight speeds exist; you don't need anything to move at exactly $c$ ...


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An interesting question! This can be answered in two ways. Answer #1: there is no conceptual gap You note that the light clock argument is used to motivate a lot of results in special relativity, but dark matter doesn't interact with light. But the light clock argument is not really that important within special relativity, and neither is light itself. In ...


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You may really be surprised, but you do create both electric and magnetic fields when you move a metal rod. But, here is a simple and intuitive example: An electric generator. It is made of solid metals, but it has bearings and the rotor can rotate. Rotate it fast enough and you get both magnetic fields (inside) and electric fields (at the wires). The Earth'...


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Using the Friedmann equation (in terms of $H$) and the respective scale-factor dependence of energy densities ($\rho_i$, where $i = M, R, \Lambda$), we can obtain the scale-factor dependence of density parameters as follows: $$ \begin{align*} \Omega_M(a) &= \frac{8\pi G}{3 (H(a))^2}\left(\rho_M(a)\right)^{-3} \\ &= \frac{8\pi G}{3 H_0^2}\...


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You can! Here's how I did it. We're going to need the following: The Einstein field equations: \begin{equation} R_{ab} - \Lambda g_{ab} = 8 \pi G \Big(T_{ab} - \frac{1}{2} T g_{ab} \Big) \end{equation} The energy-momentum tensor for a perfect fluid with four-velocity $u^a$: \begin{equation} T_{ab} = (\rho + P) u_a u_b + P g_{ab} \end{equation} The geodesic ...


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First, the universe is believed to be spatially flat (or close to it); that's not the same as spacetime being flat. The two-dimensional surface of the Earth is curved even though it's a part of a three-dimensional space that is flat (well, close to flat). In a similar way, it's geometrically possible for the three-dimensional surfaces that are called "...


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It looks like you’re mistake is in what a flat universe really means. While the universe is generally believed to be flat as a large scale structure this does not suggest at all that that it behaves in a Euclidean geometric way. Spacetime by its definition is non-Euclidean; even a special relativistic treatment of spacetime shows that pretty quickly. One ...


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You would be better to conflate your first two questions and define time as a continuum of non-spatial change, as the question 'what does time look like?' is literally meaningless-we cannot see time. Your statement about the arrow of time is false. High entropy does not rule out change over time. The idea of time having a direction is unnecessary- one can ...


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What is time? A state that changes. There are a couple of problems here. You have to define what you allow to be a "state" and what you allow to vary when the state "changes" i.e. what is it changing with respect to. To illustrate these problems, suppose we define a state as "the average temperature at a given location on the ...


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Great and thorough technical answers here already. But I'd like to mention, the best illustration I've seen of how the Big Bang happened is in this video https://youtu.be/q3MWRvLndzs


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Coordinates The $x^{a}$ you're asking about is a coordinate system, a way of labeling points on a spacetime manifold. As such, it does not really belong to anybody. You need to modify the way of thinking that was possible in Special Relativity - where inertial frames with an observer at their origin could provide us with coordinates as well. We can use ...


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If by "cosmological constant dominated universe" you mean $Ω_Λ=1$, i.e., de Sitter space, then this is pretty easy to solve. You can use de Sitter static coordinates, $$ds^2 = (1-r^2/R^2)\,dt^2 - (1-r^2/R^2)^{-1}dr^2$$ in which there is a natural notion of constant distance, namely, both galaxies being at some constant $r$ independent of $t$. (This ...


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You seem to refer to in your question to quantum foam/quantum gas models which posit that QFT is an epiphenomenon of an underlying physics which is discrete and/or statistical-mechanical at the Planck scale, or below. In such models the foam/gas is usually assumed to be randomly distributed (e.g. Poisson distributed), because Poisson distribution provides ...


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It is not trivial to see this from the description given by Sean Carroll. The FRW metric, as you have mentioned, can have a simple solution $a = t^p$ for $(0<q<1)$. (The metric you have given only have a(t) instead of $a^2(t)$) We see that, for $t\rightarrow 0$, the scale factor vanishes. But this does not answer your question of why the light cones do ...


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We are working in Newton gauge which is also called longitudinal gauge. The perturbed metric can be written as $g_{\mu\nu} = g_{\mu\nu}^{(0)} + g_{\mu\nu}^{(1)}$ with, \begin{equation} g_{\mu\nu}^{(1)} = \left(\begin{matrix} 2\psi & v_i \\ v_i & 2\phi \delta_{ij}+h_{ij} \end{matrix}\right) \end{equation} Unlike in synchronous gauge, here, due to ...


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I think that the diagrams are technically correct if interpreted in a certain unintuitive way, namely if you take Distance to be the present-day metric distance to the galaxy, and Velocity to be its recessional velocity when it emitted the light, i.e. the cosmological-time derivative of its past metric distance. If $t$ is the time of emission of the light, ...


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In both of your graphs, the y-axis is the distance modulus defined below ($d_L$ is the luminosity distance). \begin{equation} \mu = m-M = 25 + 5\log d_L ; \ d_L = c(1+z)\int_0^z \frac{dz'}{H(z')} \end{equation} This explains why the slope changes as you go to the right in the second plot. This is not the case in the first one because for small redshifts, we ...


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Let us evolve the Universe in both arguments to a de Sitter end-point so the 'horizon' is then the future cosmic event horizon in both cases. What is then clearly the same in both arguments is that the entropy is: \begin{equation}\tag{A} \ S=S_{Bulk}=S_{dS}\sim \frac{E}{T_{dS}} \end{equation} Also, $T_{dS}\approx 2.4\times10^{-30}K$. The volume of the space ...


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The specific heat of the universe as a whole is the subject of this study titled Cosmographic study of the universe’s specific heat: A landscape for Cosmology? by Orlando Luongo and Hernando Quevedo published in April 2013. A method is proposed for constructing the specific heat for the universe by following standard definitions of classical thermodynamics,...


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This is not a well researched article. Most of the problems at best only contradict early versions of the big bang theory. Grand unified theories, which are appealing models for the early universe, would indeed produce magnetic monopoles. One of the reasons for introducing inflation (which is usually considered an extension of the big bang theory rather ...


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The OP's question is a variation of this question, with a different start point. The answer, therefore, is very similar: Its often conjectured that the observable universe will asymptote to a de Sitter state (dark energy only, no matter, flat universe). It is well known that the de Sitter characteristic length $l_\Lambda$ (i.e. future cosmic event horizon ...


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Although the distance between stars doesn't really change due to the expansion of space over the evolution of the universe, the region of space around our Sun is quite sparse compared to some places in the universe. As such, your desired conditions could exist not in the remote past but today, just in a different location. Here's an article which says "...


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As the universe expands each individual galaxy stays roughly the same size, with stars on orbits of roughly constant diameter, so the stars within any given galaxy were no closer together a long time ago than they are now (at least as far as cosmic expansion effects are concerned). The distances between galaxy clusters were smaller in the past, and a good ...


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Let's say the shape of the balloon is spherical, and has a radius of $R$. Then it's a 2d surface embedded in 3d space satisfying the equation: $$ x^2 + y^2 + z^2 = R^2 $$ It is finite and bounded. Similarly, if you want a finite and bounded 3d space, one way to do it is: $$ w^2 + x^2 + y^2 + z^2 = R^2 $$ Which defines a 3d space embedded in a 4d space. There ...


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It is a paradox of QED. As the paradox is sofar unresolved, it is a real problem. It is not a cosmological problem at all. QED claims a near infinite zero point energy. Such an energy would have enormous impact and it is safe to say that this cannot be a true prediction.


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Consider the Einstein Field Equations [1]: $$G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu}$$ $G_{\mu \nu}$ is the Einstein Tensor $g_{\mu \nu}$ is the metric tensor $T_{\mu \nu}$ is the stress-energy tensor $\Lambda$ is the cosmological constant and $\kappa$ is a constant of nature (that involves the gravitational constant and the speed of light). ...


0

The Friedmann equation for these models can be written $$ \dot{a}^2 = H_0^2(\frac{\Omega_{m}}{a} + 1 - \Omega_{m}) $$ For a universe with both matter and nonzero curvature, we have $$ \frac{\dot{a}^2}{a^2} = H_0^2(\Omega_m a^{-3} + \Omega_k a^{-2}) \implies (\frac{da}{dt})^2 = H_0^2(\Omega_m a^{-1} + \Omega_k) $$ Therefore, $$ H_0dt = \frac{da}{\sqrt{\...


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I'm not sure exactly what point Sabine was trying to make or what her understanding of the cosmological constant is (I didn't watch the video), but one alternative point of view to the "cosmological constant as vacuum energy" picture is that the cosmological constant is a boundary condition. In other words, it's part of the definition of the model ...


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Although we don't know the full details of quantum gravity yet, it will result in $4$-momentum-space integrals that ought to look like $\int_0^\Lambda f(k)d^4k+\int_{\Lambda}^\infty f(k)d^4k$ where we're only confident of the behaviour of $f(k)$ in the first term. In this context, $\Lambda$ is an energy cutoff scale, not the cosmological constant that ...


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There is a nice explanation from John Baez on his page where he comes up with 5 possible values for the vacuum energy density: Very close to zero. Infinite. Enormous but finite. Zero. Not determined. where 1. is based on experiment / observation and conservative assumptions about General Relativity; 2., 3. and 4. are based on naive theoretical calculations ...


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First one is the ratio of baryon asymmetry to photon density, the second is baryon asymmetry to entropy density. According to wiki present-day entropy density $s$ is related to photon density $n_\gamma$ as $s=7.04n_\gamma$. This reconciles the two values more or less.


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A proton in a quark-gluon plasma would be like a water droplet underwater. The idea of a droplet includes a boundary and a surrounding non-water region. The higher the energy density of quark matter, the less likely it is that all of the quarks but three will separate from three of the quarks by enough distance, and for enough time, that you could reasonably ...


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