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Consider a static closed universe, of the following metric (consider $a$ as a simple constant with units of length) : \begin{equation}\tag{1} ds^2 = dt^2 - a^2 \big( d\chi^2 + \sin^2 {\chi} \; (d\vartheta … In a closed universe, it is important to not confuse length and distance. …

can be expressed exactly as this : $$\tag{3} \mathcal{D}_L(t_0, z) = (1 + z) \, a(t_0) \int_{t_e}^{t_0} \frac{1}{a(t)} \; dt. $$ For the dust universe, this formula gives this : $$\tag{4} \mathcal{D}_ … Equation (2) then gives $\delta t_{\text{max}} = (3 - \sqrt{5}) \, t_0 \approx 0.764 \, t_0$, instead of $\delta t_{\text{max}} = t_0$ for $z \rightarrow \infty$ ($t_0$ is the age of the universe). …

The light sources are uniformly distributed in a general expanding FLRW universe, and comoving with the cosmic fluid. … More specifically, consider a universe with the following standard Robertson-Walker metric : $$\tag{1} ds^2 = dt^2 - a^2(t)\Big( \, \frac{1}{1 - k \, r^2} \; dr^2 + r^2 \, (d\vartheta^2 + \sin^2 {\vartheta …

I'm looking for references on Lemaître's "hesitating" universe models, defined by a long period of stagnation of the cosmological scale factor. … Maybe the name "hesitating universe" isn't appropriate ? EDIT 1 : Here are two papers about Lemaître's work. The first one doesn't describe the "hesitating universes". …

I'm interested in the following question: What could we say about the thermodynamical properties of the Universe, using thermodynamics alone (without using general relativity), assuming that the Universe …

The following is a speculation of what other universes may look like, or what our universe may have been. … Is it plausible to get/define/wathever "parallel" universe in which the night sky isn't black, but aurorae-like green, for example ? …

Consider a spatially closed empty universe ($k = 1$) with a positive cosmological constant $\Lambda$ (closed deSitter universe). … Light may turn around several times in the closed universe before beeing detected by the observer, so this may produce the infinite luminosity if the stars are emitting light since infinity in the past …

(think of that model as a 3D "game-universe" that you launch at some time on your computer, then quit after a while. Poor virtual creatures living in the game !) … Here's a picture I made to represent that simple universe. Distance $\mathcal{D}$ is the proper distance from the stationary observer, shown as a blue vertical word-line on the picture. …