Questions tagged [de-sitter-spacetime]
The de-sitter-spacetime tag has no usage guidance.
100
questions
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De Sitter horizon area increase
Black holes increase area when any object falls past the horizon. Note: We define "when" as when the hair from the object falling in becomes undetectable for distant observers. It would also ...
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0answers
41 views
Is there a smooth, spherically symmetric, static, asymptotically de Sitter spacetime of constant scalar curvature?
...other than de Sitter space itself? Two clarifications:
I am not talking about solutions of Einstein's equations, just spacetimes. So, general Lorentzian manifolds.
I am not counting, for example,...
0
votes
1answer
42 views
The contravariant derivative of a substitution for the de Sitter metric
Consider the de Sitter metric:
$$ds^2 = (1-\frac{r^2}{a^2})dt^2 -(1-\frac{r^2}{a^2})^{-1}dr^2-r^2d\Omega^2$$
I know that we rewrite the metric as $(u,r,\theta \phi)$ using the substitution $$u = t-...
0
votes
2answers
130 views
Timelike geodesics of 2-dimensional de Sitter spacetime
The de Sitter spacetime in two dimensions ($\text{dS}_2$) can be spanned by two coordinates : $\tau$ and $\phi$ (can be viewed as a cylinder). The metric is then defined as follows :
$$ds^2=-d\tau^2+\...
2
votes
1answer
66 views
Construction of Carter-Penrose diagram for DeSitter spacetime
The DeSitter spacetime line element in global coordinates is given by
$$ds^2 = -dt^2 + \frac{1}{H^2}\cosh^2(Ht)\left(d\chi^2 + \sin^2(\chi)(d\theta^2 + \sin^2(\theta)d\phi^2 \right).$$
The ranges of ...
2
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0answers
53 views
Bose-Einstein statistics in de Sitter spacetime
The metric in de Sitter spacetime with $(+,-,-,-)$ as metric signature is, in cartesian coordinates:
\begin{equation}
ds^2=dt^2-a^2(t)(dx^2+dy^2+dz^2).
\end{equation}
Where $a(t)=e^{Ht}$. How do I ...
0
votes
0answers
30 views
Question regarding different mode functions in FRW spacetime
I am currently reading Mukhanov's and Winitzki's book with title: "Introduction to Quantum Fields and Classical Backgrounds".
At chapter 6, they argue that in a FRW (Freedman - Robertson - ...
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0answers
24 views
What happens to the information content of the universe in the deSitter phase?
What happens to the information content of the universe when the accelerated expansion enters the empty deSitter phase in the distant future?
3
votes
2answers
280 views
de Sitter Spacetime: Static patch vs Global coordinates
Two well-known coordinate charts on the dS spacetime are the global coordinates and the static patch coordinates. In the global coordinates, the D-dimensional dS metric takes the following form
$$ ds^...
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0answers
45 views
How to check if some metric has a particular type of geodesics?
For instance, we want to know if cylindrically symmetric de Sitter-type spacetime has an axial geodesic.
This is the metric I am interested in
$$ds^2= \cos^{\frac{4}{3}}\left(\frac{\sqrt{3 \Lambda}}{2}...
2
votes
1answer
185 views
Interpretation of horizon in de Sitter
Given the de Sitter metric for spacetime
$$ds^2 = \left( 1 - \frac{\Lambda}{3}r^2\right) dt^2 - \frac{1}{\left( 1 - \frac{\Lambda}{3}r^2 \right)}dr^2 - r^2d\Omega^2 $$
we understand this is a solution ...
3
votes
0answers
119 views
How does $1/r$ gravity change in de Sitter space?
Classical $1/r$ gravity arises from general relativity when curvature is neglected and speeds are small compared to the speed of light.
In de Sitter space with a positive cosmological constant $\...
3
votes
0answers
80 views
Understanding Verlinde: How to get from emergent gravity to MOND
Verlinde ( https://arxiv.org/abs/1611.02269 ) tries to deduce MOND from emergent gravity. Can you help?
Emergent or entropic gravity goes back to Jacobson. He starts with
the entropy-area connection $...
6
votes
2answers
145 views
de-Sitter space as near-horizon limit of Black Holes
We know that we can obtain $AdS_{2}$ x $S_{2}$ spacetime as the near-horizon geometry of an extremal/ near extremal RN (or Kerr) Black Hole in asymptotically flat spacetime. It is also known that we ...
0
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1answer
111 views
Is de Sitter space homogeneous?
Since Minkowski and anti de Sitter are homogeneous Lorentzian manifolds, it is natural to ask if de Sitter is too, but nobody ever discusses this. In Riemannian geometry a globally symmetric complete ...
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0answers
19 views
Jacobi Identity in de Sitter Superalgebra
In the book "Supergravity" (by D. Freedman and A. Van Proeyen) they talk about why $\mathcal{N}=1$ de-sitter superalgebra is impossible to construct (Section 12.6.1).
Basically de-Sitter algebra is a ...
5
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0answers
356 views
Casimir operators of de Sitter space
De-Sitter space can be thought of as a 4 dimensional hyperboloid embedded in 5D Minkowski space. Hence, the symmetry group of dS is $SO(1,4)$ whose generators are,
$J_{AB}=i\left(X_A\frac{\partial}{\...
1
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1answer
158 views
de Sitter vacua in String Theory
I don't quite understand what goes wrong with the de Sitter vacua in string theory. Firstly, how are the vacua calculated (I'm given to understand there is no standard method, so what are the efforts ...
2
votes
1answer
275 views
Does de Sitter space have a preferred frame?
Consider the flat, expanding coordinates for de Sitter space:
$$ds^2=-dt^2+e^{2Ht}d\vec{x}^2\quad .$$
This is clearly not invariant under the ordinary Lorentz transformations. Does this mean that if I ...
0
votes
1answer
114 views
Massive particles in de Sitter space
Can massive particles in de Sitter space move faster than light?
For the radial coordinate (in static coordinates) I have got the hyperbolic expression
$$r(\tau)\propto \sinh\left(\sqrt{\frac{\...
3
votes
0answers
121 views
Supersymmetry in de Sitter space
Is it possible to construct SUSY theories in de Sitter space?
I know statement:
dS superalgebras cannot be constructed unless one constructs actions with matter coupled with
the wrong signs for ...
6
votes
1answer
198 views
Newton's law of gravitation in de Sitter space
Given two masses $M$ and $m$ (with $M\gg m$) in a de Sitter background with cosmological constant $\Lambda>0$ and positive spatial curvature ($k=+1$). What is the corresponding (semiclassical "...
1
vote
1answer
92 views
String Landscape, De Sitter vacua and Broken Supersymmetry
If we assume that the swampland conjectures, etc. regarding de sitter vacuas existence in the string / F-theory landscape turn out to be incorrect (and therefore we can assume the problem is well-...
0
votes
1answer
144 views
How to pick what coordinates transformations to apply in general relativity?
I've been challenged by coordinate transformations lately, as most of you know during solving any problem in GR we have to go through lots of transformations, my question is how we decide the best ...
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0answers
75 views
Why is de Sitter spacetime a better model of our universe than brane world models?
Why is it assumed that we live in a de Sitter space-time? Besides the de Sitter Lambda Cold Dark Matter model, there are Anti de Sitter brane world models, which also generates Friedmann equations ...
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0answers
53 views
AdS/CFT phenomenology and realistic FRW model building
Are there any examples of realistic holography (likely as a de Sitter type Universe: as it approximates FRW / is an FRW solution without baryonic and dark matter). I don’t see why one wouldn’t be ...
2
votes
1answer
182 views
What is the Komar mass of the de-Sitter spacetime?
The Komar mass of some spacetime is defined as an integral (volume or surface, depending on its formulation): https://en.wikipedia.org/wiki/Komar_mass
The de-Sitter metric in static coordinates is ($\...
5
votes
1answer
273 views
Negative temperature of the de-Sitter horizon?
I'm considering the $4D$ de-Sitter spacetime, in static coordinates (I'm using $c = 1$ and $k_{\text{B}} = 1$):
\begin{equation}\tag{1}
ds^2 = (1 - \frac{\Lambda}{3} \, r^2) \, dt^2 - \frac{1}{1 - \...
4
votes
2answers
231 views
Entropy of de-Sitter spacetime and the $10^{120}$ vacuum discrepency
While doing some lazy calculations, I came across a curiosity that I'm unable to interpret. It is well known that the cosmological constant $\Lambda \sim 10^{-52}~\mathrm{m^{-2}}$ is usually ...
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0answers
45 views
dS/CFT in a positive curvature universe
Since Maldacena ground breaking theoretical discovery, have there been any succesfull efforts to try to transpose the AdS/CFT duality to our universe (not an AdS)?
2
votes
1answer
127 views
Symmetry v.s. isometry of Minkowski and AdS or dS spacetime
We know some nice spacetime have a lot of symmetries. It is said that
Minkowski spacetime has
$$ISO(d-1,1)/SO(d-1,1),$$
de Sitter spacetime has
$$SO(d,1)/SO(d-1,1)$$ and
anti-de Sitter spacetime ...
0
votes
1answer
32 views
In de Sitter space, does the cosmic horizon change its shape for fast-moving observer?
If an observer moves at a speed close to the speed of light, will the horizon deviate from spherical shape?
If no, will it be the same horizon as for stationary observer (at the same position)?
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0answers
49 views
Given in de Sitter space time is frozen on the horizon, can we say that in anti-de Sitter space time goes infinitely fast at the space boundary?
Particularly, in de Sitter space everything on the cosmic event horizon is redshifted, while in anti-de Sitter space everything on the horizon is blueshifted.
2
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1answer
437 views
Minkowski space vs De Sitter Space
Can you explain to a layman the differences between the former two?
0
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1answer
97 views
Does an observer inside a black hole experience the de Sitter metric?
My question has emerged, because of the following similarities between the metric an observer experiences in the Schwartzschild space being under the Schwartzschild radius and an observer in the de ...
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0answers
94 views
How accurate is the De Sitter solution of the Einstein field equations of general relativity?
The De sitter solution models the universe as spatially flat, neglecting ordinary matter, such that it is dominated by the cosmological constant. The cosmological constant notion arguably suggests the ...
2
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0answers
34 views
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 ...
2
votes
4answers
279 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 ...
0
votes
0answers
33 views
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.$$ I want to find the ...
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0answers
69 views
deSitter spacetime metric and curvature
I have to compute the metric of an hyperboloid given by $-(X^0)^2+(X^1)^2+(X^2)^2+(X^3)^2=H^{-2}$ in 5D Minkowski spacetime using the following coordinates:
$$X^0=H^{-1}\sinh(Ht)\sqrt{1-H^2r^2}$$
$$X^...
0
votes
1answer
69 views
$dS^d$ 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....
2
votes
1answer
84 views
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
votes
1answer
784 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 ...
1
vote
1answer
111 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
101 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 ...
2
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0answers
142 views
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 ...
3
votes
2answers
2k 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 ...
1
vote
2answers
3k 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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0answers
90 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
votes
2answers
830 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 ...
