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Questions tagged [de-sitter-spacetime]

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How is deSitter group tranformations different from poincare group transformations

In QFT, we have studies Poincare group of massive and massless particles. Is the deSitter group also useful to study such things? What exactly is the main role of this group in QFT? I just know the ...
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4answers
142 views

What would happen to de Sitter universe if the cosmological constant disappears?

De sitter universe is dominated by a cosmological constant (devoid of matter and radiation), corresponding to dark energy in the far future or the inflaton field in the early universe, leading to an ...
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2D deSitter conserved charges

For $1+1$-dimensional dS spacetime, the metric takes the form (in comoving coordinates) $$\mathrm{d}s^2=\left(\mathrm{d}x^0\right)^2-e^{2Hx^0}\left(\mathrm{d}x^1\right)^2.$$ I want to find the ...
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deSitter spacetime metric and curvature

I have to compute the metric of an hyperboloid given by $-(X^0)^2+(X^1)^2+(X^2)^2+(X^3)^2=H^{-2}$ in 5D Minkowski spacetime using the following coordinates: $$X^0=H^{-1}\sinh(Ht)\sqrt{1-H^2r^2}$$ $$X^...
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1answer
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$dS^d$ and $AdS^d$ are conformally equivalent

I have seen in the book by Zee (Einstein Gravity in a Nutshell) the following metric for $dS^4$: $ds^2 = \frac{1}{\cos^2 \tau} \big( - d\tau^2 + d\psi^2 + \sin^2 \psi \, d\Omega_2^2 \big) $, (Eq. IX....
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1answer
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Why $dS^d \cong SO(d,1)/SO(d-1,1)$?

I have found a similar question, but there they give a seemingly rigorous proof, and what I am looking for is just an intuition. I understand that $S^2 \cong SO(3)/SO(2)$: for every point in $S^2$ ...
3
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1answer
196 views

Metric for 2D de Sitter?

What is the correct metric to use for two dimensional de Sitter? If one starts with the following metric, which looks similar to de Sitter in 4 dimensions: $$ds^2 = -dt^2 + e^{2H t} dx^2,$$ one can ...
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1answer
76 views

Lorentz transformations in non-Euclidean geometries

I have an assessment/investigation coming up in my math class and I plan to investigate Lorentz transformations in geometries other than Euclidean such as spherical or hyperbolic. For spherical/polar, ...
3
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0answers
86 views

Strings 2018 takeaways [closed]

What are the main takeaways from the Strings 2018 conference? What are the main announcements, discoveries or directions emerging from this event? To my knowledge, one is the result by Vafa and ...
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0answers
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If the Schwarzschild radius of the universe is bigger than the universe, how come the universe didn't collapse into a black hole? [duplicate]

According to this answer, the Schwarzschild radius of the universe is about 3 times the radius of the universe. According to the Newtonian theory of gravity, inside any sphere of a given density, the ...
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2answers
566 views

Why is our physical Universe a de Sitter space?

Wikipedia says, When $n=4$ (3 space dimensions plus time), it is (the de Sitter space) a cosmological model for the physical universe; see de Sitter universe. It appears to me that the statement ...
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1answer
154 views

Maximally symmetric spaces

In GR, what is the most precise definition of a maximally symmetric spacetime? Also, we study about the temporal boundary of dS space, and a spatial boundary of AdS space, but aren't these spaces ...
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47 views

De sitter spacetime and co-ordinates

I was recently looking at de - Sitter spacetime and I relaized that there are many different parameterizations possible, each of which has it's own advantages. Can someone help me out and list the ...
4
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2answers
407 views

Can String Theory really fail to contain a de Sitter vacua?

I was reading a post earlier from Peter Woit's Not Even Wrong blog and came across the following reference to the paper "What if string theory has no de Sitter vacua?" by Ulf H. Danielsson, Thomas Van ...
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1answer
35 views

Can a De Sitter universe have a detectable rotation?

In De Sitter relativity, the cosmological constant becomes a geometric term with the dimensions of radius, and the universe becomes a pseudo-sphere. Is it meaningful to speak of intrinsic rotation of ...
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2answers
213 views

Is the dynamics of spacetime observer-dependent?

Consider de Sitter spacetime in static coordinates: $$ ds^2 = \Big(1- (H_\Lambda r)^2 \Big) dt^2 - \frac{dr^2}{1- (H_\Lambda r)^2} -r^2 d\Omega^2, \qquad r\lt H_\Lambda^{-1} \,. $$ This metric ...
5
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1answer
192 views

Holography on non-AdS spacetime

I have a question regarding AdS/CFT and what it teaches about our world. AdS/CFT if often treated as our best tool to explore quantum gravity, and people have worked very hard in trying to understand ...
2
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1answer
149 views

Issues with de Sitter Space and Conformal Field Theory

As a de Sitter universe is more convenient for cosmology, what are the current issues with a dS/CFT type correspondence? Earlier work by Strominger, seemed promising but I haven't heard of additional ...
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2answers
1k views

Is the de Sitter Universe static?

In the book Tolman R.C. Relativity, thermodynamics, and cosmology (3pr., Oxford, 1949) I read that the de Sitter Universe is static as well as the Einstein Universe. But the de Sitter Universe is ...
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1answer
343 views

Is the de Sitter Universe equivalent to the static Einstein Universe?

The de Sitter universe is a flat exponentially expanding universe with a cosmological constant $\Lambda$ and no matter. Einstein's static universe also has a cosmological constant $\Lambda$ but it ...
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What coordinate system produces this particular form of the line element of de Sitter spacetime?

To save space, all the symbols and conventions are adopted from this Wikipedia article. We know that the line element of $n$ dimensional de Sitter space in static coordinates is $$ds^2=-\bigg(1-\...
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1answer
646 views

Is de Sitter space with non-zero curvature an acceptable model for the universe?

On wikipedia I can find that a de Sitter-space has maximal symmetry and a constant curvature. Recently the interest of de Sitter spaces has increased as it could serve as a model for the universe, an ...
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0answers
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Is there a homogeneous $\Lambda$-vacuum spacetime with spatial topology $\mathbb{R}^2\times S^1$?

This question is about homogeneous $\Lambda$-vacuum spacetimes. The unique isotropic solution is de Sitter space, which has the spatial topology of $\mathbb{R}^3$. There is the Kantowski-Sachs metric, ...
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0answers
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Does the curvature parameter $k$ change with coordinate choice (de Sitter spacetime)?

The de Sitter spacetime can be derived from the vacuum Friedmann equations given a choice of $k=0$, where $k$ defines the spatial curvature of the spacetime. The resulting metric in $(t,x,y,z)$ is ...
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85 views

de-Sitter spacetimes

In classical textbooks for GR, Schwarzschild and Kerr spacetimes are adequately described. In which books or articles, it is mostly believed that Reissner-Nordstrom, Kerr-Newman, Schwarzschild-de ...
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3answers
150 views

Large $D$ limit of (Anti) de Sitter Space is Minkowskian Space?

As is well known, the solution of the vacuum Einstein equations with a non-zero cosmological constant, $G_{\mu\nu}+\Lambda g_{\mu\nu}=0$, is an asymptotically (anti) de Sitter space based on the sign ...
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A Universal Upper Limit on Mass Within a Radius $R$?

Since the universe has a positive cosmological constant, there is an upper limit on the mass of the black holes as evident from the so-called Schwarzschild-de Sitter metric: $ds^2 = -f(r)dt^2 + \...
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1answer
118 views

How does one write a three dimensional de Sitter space as the quotient $SL(2, C)/SL(2, R)$?

In arXiv:hep-th/0110108 the $(2+1)-$dimensional de Sitter space is represented as a quotient space of $SL(2, C)/SL(2, \mathbb{R})$. I couldn't understand how, both mathematically and intuitively, is ...
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1answer
130 views

Totally geodesic spacelike surfaces in de Sitter space

Let $S^2_1$ be the de Sitter space $$\{x:\langle x,x\rangle=x_0^2-x_1^2-x_2^2-x_3^2=-1\}$$ in Minkowski space $\mathbb {R}^3_1$ with $ds^2=dx_0^2-dx_1^2-dx_2^2-dx_3^2$. Is it true that for each pair ...
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1answer
507 views

What are the de Sitter Killing vectors?

I'm trying to find the Killing vectors for de Sitter space using global coordinates, i.e. the spherical foliation. In the end, I want to know how to perform a boost on the 1+1 and 3+1 de Sitter ...
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1answer
306 views

Entropy of the de Sitter cosmological horizon

For an eternal dS universe, the entropy of an observer in the static patch goes as the area of the horizon which for 3+1 D goes as $S_H = \frac{Area_{H}}{4} \sim H^{-2}$, as given by Gibbons & ...
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0answers
156 views

Lapse Function and Shift Vector in Minkowski and de Sitter

I'd like to find the lapse function and shift vector in 1+1 Minkowski as well as 1+1 de Sitter (flat foliation) for a region foliated this way: The $y$-axis represents time while the x-axis ...
2
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1answer
150 views

de Sitter reviews?

I'm very interested in learning more about de Sitter and anti-de Sitter spaces and their applications in GR and cosmology. Can anyone recommend favorite review articles -- or, more likely, a series ...
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If the expansion of the Universe accelerates, why its horizon does not shrink?

In de Sitter (expanding) universe to which our universe asymptotically approaches, the higher the rate of space expansion, the smaller the radius of the cosmic horizon. Why then our universe is ...
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2answers
222 views

Are orbits possible in de sitter space?

Since the de sitter space has constant positive curvature does that mean that objects can't orbit around other objects?
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1answer
246 views

Why $C_{abcd}C^{abcd}$ in de Sitter–Schwarzschild metric doesn't depend on $\Lambda$

With the de Sitter–Schwarzschild metric: $$ds^2=-\left(1-\frac{2M}{r}-\frac{\Lambda r^2}{3}\right)dt^2+\left(1-\frac{2M}{r}-\frac{\Lambda r^2}{3}\right)^{-1}dr^2+r^2d\theta+r^2\sin^2\theta d\phi$$ I ...
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1answer
148 views

Why can only asymptotically flat and AdS black hole have the thermodynamics? What's about asymptoticaly dS black hole?

Almost all advanced GR textbooks will have the content of black hole thermodynamics for asymptotically flat black hole. And this paper solve the asymptotically AdS (Anti-de Sitter) black hole http://...
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How to find de Sitter and almost de Sitter solutions in (super)string theory

From Cosmology, we have learned that we live in an almost de Sitter (positively accelerated!) Universe. It seems that dS space solutions in superstring/theory are problematic and there are some no-go ...
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1answer
149 views

Static De Sitter Metric

For static dS metric we have $$x_{0}=\sqrt{H^{-2}-r^{2}}\sinh(Ht)$$$$x_{1}=\sqrt{H^{-2}-r^{2}}\cosh(Ht)$$ and the metric can be written as $$ds^{2}=-dx_{0}^{2}+dx^{2}_{1}+d\bar x$$ where the barred $...
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1answer
372 views

Definition of conformal time in de Sitter spacetime

I'm trying to follow the calculations in http://arxiv.org/abs/hep-th/0201158v2 The aim is to rederive the expressions (2.16), (2.17) for the power spectrum in de Sitter spacetime. In order to do so, ...
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1answer
462 views

Negative energy/mass bounds on de-Sitter spacetime

There exists a Positive Energy theorem for General Relativity in Anti-de Sitter and asymptotically flat spacetimes, but there is no equivalent theorem for de Sitter spacetimes Question: Is there a ...
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1answer
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Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary?

Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, ...
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Observers in (Schwarzschild-) de Sitter spacetime

In (pure) de Sitter spacetime, the cosmological horizon is said to be ‘observer dependent’. I imagine that as the observer always being in the center of that horizon. Another (spacelike separated) ...
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2answers
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What is the gist of the equations on Alejandro Guijarro's “2/14” “Momentum” blackboard?

The artist Alejandro Guijarro has an exhibit of photographs of a variety of blackboards with physics equations, drawings and text on them, as covered at Quantum Chaos on Display in Top Physicists’ ...
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1answer
279 views

Wave equation for de Sitter invariant Green's functions

In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can ...
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Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
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1answer
516 views

Black hole temperature in an asymptotically de Sitter spacetime

I am trying to calculate the Hawking temperature of a Schwarzschild black hole in a spacetime which is asymptotically dS. Ignoring the 2-sphere, the metric is given by $ds^2=\left(1-\frac{2M}{r}-\frac{...
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2answers
130 views

Are the cosmic horizons observer-specific?

It is known that all observers will agree on the position of the black hole event horizon. But what about the cosmic horizon of the de Sitter space? Can one say that the horizon of scientist1 is ...
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Can matter leave the cosmic horizon?

Cosmic horizon in the de Sitter space is a sphere, centered at the observer with finite radius where the red shift due to cosmic expansion becomes infinite. Given that no information can be ...
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2answers
383 views

Can Hubble red shift be interpreted as time dilation?

Can we interpret the de Sitter universe as a spherical cosmic horizon null surface of finite radius, centered at Earth, and containing the Hubble volume of space where time is dilated and radial ...