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\section*{de Sitter spacetime}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{riemannian_geometry}{}\paragraph*{{Riemannian geometry}}\label{riemannian_geometry}

[[!include Riemannian geometry - contents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{definition}{Definition}\dotfill \pageref*{definition} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{References}{References}\dotfill \pageref*{References} \linebreak
\noindent\hyperlink{in_classical_gravity}{In classical gravity}\dotfill \pageref*{in_classical_gravity} \linebreak
\noindent\hyperlink{InPerturbativeQuantumGravity}{In perturbative quantum gravity}\dotfill \pageref*{InPerturbativeQuantumGravity} \linebreak
\noindent\hyperlink{ReferencesInStringTheory}{In string/M-theory}\dotfill \pageref*{ReferencesInStringTheory} \linebreak


\hypertarget{definition}{}\subsection*{{Definition}}\label{definition}

Full de Sitter spacetime is the [[Lorentzian manifold]] which is the [[coset space]] of [[Lorentz groups]]

\begin{displaymath}
dS^d \simeq O(d,1)/O(d-1,1)
\end{displaymath}
This models a cosmology [[FRW model]] for positive [[cosmological constant]]/[[dark energy]].

Similarly [[anti de Sitter spacetime]] is

\begin{displaymath}
adS^d \simeq O(d-1,2)/O(d-1,1)
\end{displaymath}
(e.g )

This admits different spatial slicings of relevance:



\begin{quote}%
graphics grabbed from \href{https://physics.stackexchange.com/a/353157/5603}{this Physics.SE comment}


\end{quote}
\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

[[!include local and global geometry - table]]

\hypertarget{References}{}\subsection*{{References}}\label{References}

\hypertarget{in_classical_gravity}{}\subsubsection*{{In classical gravity}}\label{in_classical_gravity}

\begin{itemize}%
\item [[Leonardo Castellani]], [[Riccardo D'Auria]], [[Pietro Fré]], volume 1, chapter I.3.8 of \emph{[[Supergravity and Superstrings - A Geometric Perspective]]}, World Scientific (1991)


\item [[Matthias Blau]], chapter 38 of \emph{Lecture notes on general relativity} (\href{http://www.blau.itp.unibe.ch/GRLecturenotes.html}{web})


\item Thomas Hartman, \emph{Lecture Notes on Classical de Sitter Space} (\href{http://www.hartmanhep.net/GR2017/desitter-lectures-v2.pdf}{pdf}, [[HartmanDeSitterSpacetime.pdf:file]])


\item Marcus Spradlin, [[Andrew Strominger]], Anastasia Volovich, \emph{Les Houches Lectures on De Sitter Space} (\href{https://arxiv.org/abs/hep-th/0110007}{arXiv:hep-th/0110007})



\end{itemize}
See also

\begin{itemize}%
\item Wikipedia, \emph{\href{http://en.wikipedia.org/wiki/De_Sitter_space}{de Sitter space}}

\end{itemize}
\hypertarget{InPerturbativeQuantumGravity}{}\subsubsection*{{In perturbative quantum gravity}}\label{InPerturbativeQuantumGravity}

Discussion of de Sitter spacetime in [[perturbative quantum gravity]] and its infrared instability, includes the following:

\begin{itemize}%
\item [[Emil Mottola]], \emph{Particle creation in de Sitter space}, Phys. Rev. D 31, 754 – Published 15 February 1985 (\href{https://doi.org/10.1103/PhysRevD.31.754}{doi:10.1103/PhysRevD.31.754})


\item [[Edward Witten]], \emph{Quantum Gravity In De Sitter Space}, talk at \href{http://theory.tifr.res.in/strings/}{Strings 2001}, (\href{https://arxiv.org/abs/hep-th/0106109}{arXiv:hep-th/0106109})


\item Dietmar Klemm, Luciano Vanzo, \emph{Aspects of Quantum Gravity in de Sitter Spaces}, Journal of Cosmology and Astroparticle Physics, Volume 2004, November 2004 (\href{https://arxiv.org/abs/hep-th/0407255}{arXiv:hep-th/0407255})


\item [[Richard Woodard]], \emph{De Sitter Breaking in Field Theory} (\href{https://arxiv.org/abs/gr-qc/0408002}{arXiv:gr-qc/0408002})


\item [[Alexander Polyakov]], \emph{De Sitter Space and Eternity}, Nucl.Phys.B797:199-217, 2008 (\href{https://arxiv.org/abs/0709.2899}{arXiv:0709.2899})


\item [[Alexander Polyakov]], \emph{Decay of Vacuum Energy}, Nucl.Phys.B834:316-329, 2010 (\href{https://arxiv.org/abs/0912.5503}{arXiv:0912.5503})


\item Dmitry Krotov, [[Alexander Polyakov]], \emph{Infrared Sensitivity of Unstable Vacua}, Nucl.Phys.B 849 (2011) 410-432 (\href{https://arxiv.org/abs/1012.2107}{arXiv:1012.2107})


\item [[Alexander Polyakov]], \emph{Infrared instability of the de Sitter space} (\href{https://arxiv.org/abs/1209.4135}{arXiv:1209.4135})


\item Paul R. Anderson, [[Emil Mottola]], \emph{On the Instability of Global de Sitter Space to Particle Creation}, Phys. Rev. D 89, 104038 (2014) (\href{https://arxiv.org/abs/1310.0030}{arXiv:1310.0030})


\item Paul Anderson, [[Emil Mottola]], \emph{Quantum Vacuum Instability of `Eternal' de Sitter Space}, Phys. Rev. D 89, 104039 (2014) (\href{https://arxiv.org/abs/1310.1963}{arXiv:1310.1963})


\item [[Arvind Rajaraman]], \emph{de Sitter Space is Unstable in Quantum Gravity}, Phys. Rev. D 94, 125025 (2016) (\href{http://arxiv.org/abs/1608.07237}{arXiv:1608.07237})


\item Paul Anderson, [[Emil Mottola]], Dillon H. Sanders, \emph{Decay of the de Sitter Vacuum}, Phys. Rev. D 97, 065016 (2018) (\href{https://arxiv.org/abs/1712.04522}{arXiv:1712.04522})



\end{itemize}
\hypertarget{ReferencesInStringTheory}{}\subsubsection*{{In string/M-theory}}\label{ReferencesInStringTheory}

A [[no-go theorem]] for [[KK-compactifications]] of [[supergravity]] down to de Sitter spacetime is claimed in

\begin{itemize}%
\item [[Juan Maldacena]], Carlos Nunez, \emph{Supergravity description of field theories on curved manifolds and a no go theorem}, Int.J.Mod.Phys. A16 (2001) 822-855 (\href{https://arxiv.org/abs/hep-th/0007018}{arXiv:hep-th/0007018})

\end{itemize}
Discussion of de Sitter [[perturbative string theory vacua]] and their role in the [[landscape of string theory vacua]] or else in the [[swampland]]:

\begin{itemize}%
\item [[David Kutasov]], Travis Maxfield, Ilarion Melnikov, [[Savdeep Sethi]], \emph{Constraining de Sitter Space in String Theory}, Phys. Rev. Lett. 115, 071305 (2015) (\href{https://arxiv.org/abs/1504.00056}{arXiv:1504.00056})


\item Jakob Moritz, Ander Retolaza, Alexander Westphal, \emph{Towards de Sitter from 10D}, Phys. Rev. D 97, 046010 (2018) (\href{https://arxiv.org/abs/1707.08678}{arXiv:1707.08678})


\item [[Savdeep Sethi]], \emph{Supersymmetry Breaking by Fluxes} (\href{https://arxiv.org/abs/1709.03554}{arXiv:1709.03554})

re-amplified in:

[[Savdeep Sethi]], \emph{Hope or No Hope for a String Landscape?}, talk at \href{https://indico.cern.ch/event/782251/}{StringPheno2019} (\href{https://indico.cern.ch/event/782251/contributions/3441886/attachments/1870138/3076971/3_Sethi.pdf}{pdf} [[SethiLandscape2019.pdf:file]])


\item [[Ulf Danielsson]], [[Thomas Van Riet]], \emph{What if string theory has no de Sitter vacua?}, International Journal of Modern Physics D, Vol. 27, No. 12, 1830007 (2018) (\href{https://arxiv.org/abs/1804.01120}{arXiv:1804.01120}, \href{https://doi.org/10.1142/S0218271818300070}{doi:10.1142/S0218271818300070})

(problems with \href{landscape+of+string+theory+vacua#KKLT03}{KKLT 03})


\item [[Thomas Van Riet]], \emph{Is dS space in the Swampland}, talk at \href{http://sp18.fuw.edu.pl/}{StringPheno18} (\href{http://sp18.fuw.edu.pl/wp-content/uploads/participants-database/thomasvanriet.pdf}{pdf slides})


\item [[Thomas Van Riet]], \emph{Status of KKLT}, talk at \emph{\href{http://scgp.stonybrook.edu/archives/24870}{Simons summer workshop 2018}} (\href{http://scgp.stonybrook.edu/video_portal/video.php?id=3730}{recording})


\item [[Ulf Danielsson]], \emph{The quantum swampland} (\href{https://arxiv.org/abs/1809.04512}{arXiv:1809.04512})

(argues that the issue with [[string theory|stringy]] de Sitter [[moduli stabilization]] raised in \hyperlink{Sethi17}{Sethi 17} is related to the de Sitter instability seen in QFT, according to the references \hyperlink{InPerturbativeQuantumGravity}{above})


\item Georges Obied, [[Hirosi Ooguri]], Lev Spodyneiko, [[Cumrun Vafa]], \emph{De Sitter Space and the Swampland} (\href{https://arxiv.org/abs/1806.08362}{arXiv:1806.08362})


\item Jakob Moritz, Ander Retolaza, Alexander Westphal, \emph{On uplifts by warped anti-D3-branes} (\href{https://arxiv.org/abs/1809.06618}{arXiv:1809.06618})


\item Iosif Bena, Emilian Dudas, Mariana Graña, Severin Lüst, \emph{Uplifting Runaways} (\href{https://arxiv.org/abs/1809.06861}{arXiv:1809.06861})


\item [[Clay Cordova]], G. Bruno De Luca, [[Alessandro Tomasiello]], \emph{Classical de Sitter Solutions of Ten-Dimensional Supergravity} (\href{https://arxiv.org/abs/1812.04147}{arXiv:1812.04147})



\end{itemize}
On [[de Sitter spacetime]] [[cosmology]] realized in [[brane world models]] in ambient $\sim$[[anti de Sitter spacetime|AdS]]-[[bulk]] [[spacetime]]:

\begin{itemize}%
\item Souvik Banerjee, [[Ulf Danielsson]], Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo, \emph{Emergent de Sitter cosmology from decaying AdS} (\href{https://arxiv.org/abs/1807.01570}{arXiv:1807.01570})


\item Souvik Banerjee, [[Ulf Danielsson]], Giuseppe Dibitetto, Suvendu Giri, Marjorie Schillo, \emph{de Sitter Cosmology on an expanding bubble} (\href{https://arxiv.org/abs/1907.04268}{arXiv:1907.04268})



\end{itemize}
Discussion in the context of [[M-theory on G2-manifolds]]:

\begin{itemize}%
\item Beatriz de Carlos, Andre Lukas, Stephen Morris, \emph{Non-perturbative vacua for M-theory on G2 manifolds}, JHEP 0412:018, 2004 (\href{https://arxiv.org/abs/hep-th/0409255}{arxiv:hep-th/0409255})

which concludes that with taking [[non-perturbative effects]] from [[membrane instantons]] into account one gets 4d vacua with vanishing and negative [[cosmological constant]] ([[Minkowski spacetime]] and [[anti-de Sitter spacetime]]) but not with positive [[cosmological constant]] ([[de Sitter spacetime]]). They close by speculating that [[M5-brane]] instantons might yield [[de Sitter spacetime]].


\item Johan Blåbäck, [[Ulf Danielsson]], Giuseppe Dibitetto, Suvendu Giri, \emph{Constructing stable de Sitter in M-theory from higher curvature corrections} (\href{https://arxiv.org/abs/1902.04053}{arXiv:1902.04053})

which suggests that including [[higher curvature corrections]] makes it work


\item Iosif Bena, Alex Buchel, Severin Lüst, \emph{Throat destabilization (for profit and for fun)} (\href{https://arxiv.org/abs/1910.08094}{arxiv:1910.08094})



\end{itemize}
For analogous discussion of embedding of the [[ekpyrotic cosmology]]-scenario into [[string theory]]/[[type IIA supergravity]]:

\begin{itemize}%
\item [[Kunihito Uzawa]], \emph{No-Go theorems for ekpyrosis from ten-dimensional supergravity}, J. High Energ. Phys. (2018) 2018: 41 (\href{https://arxiv.org/abs/1803.11084}{arXiv:1803.11084}, )

reviewed in:

Kunihito Uzawa, \emph{Ekpyrotic scenario in string theory} (\href{http://www2.yukawa.kyoto-u.ac.jp/~gc2018/slides/4th/Mar2/Uzawa.pdf}{pdf})



\end{itemize}
[[!redirects de Sitter spacetimes]]

[[!redirects de Sitter space]] [[!redirects de Sitter spaces]]



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