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\section*{standard model of cosmology}

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

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\hypertarget{gravity}{}\paragraph*{{Gravity}}\label{gravity}

[[!include gravity contents]]

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

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{properties}{Properties}\dotfill \pageref*{properties} \linebreak
\noindent\hyperlink{structure_formation}{Structure formation}\dotfill \pageref*{structure_formation} \linebreak
\noindent\hyperlink{vacuum_energy_and_cosmological_constant}{Vacuum energy and Cosmological constant}\dotfill \pageref*{vacuum_energy_and_cosmological_constant} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak
\noindent\hyperlink{possible_tension_with_observation}{Possible tension with observation}\dotfill \pageref*{possible_tension_with_observation} \linebreak
\noindent\hyperlink{in_aqft_on_curved_spacetimes}{In AQFT on Curved spacetimes}\dotfill \pageref*{in_aqft_on_curved_spacetimes} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

The standard [[model (in theoretical physics)]] for the [[observable universe]] on the largest length scales of [[cosmology]]:

it is an [[cosmic inflation|inflationary]] [[FRW spacetime]] with [[cosmological constant]] (``[[dark energy]]'') and cold [[dark matter]]. The technical term for this is the \emph{$\Lambda$ CDM concordance model} (where ``$\Lambda$'' is the standard symbol for the [[cosmological constant]] and ``CDM'' is for ``cold dark matter'').

The current model assumes that the energy density of the [[observable universe]] consists of

\begin{itemize}%
\item 4.9\% [[baryon|baryonic]] (visible) [[matter]]


\item 26.8\% [[dark matter]]


\item 68.3\% [[dark energy]].



\end{itemize}


(e.g. \hyperlink{Einasto09}{Einasto 09, fig 17}, \href{https://ned.ipac.caltech.edu/level5/Sept09/Einasto/Einasto6.html}{here})

\hypertarget{properties}{}\subsection*{{Properties}}\label{properties}

\hypertarget{structure_formation}{}\subsubsection*{{Structure formation}}\label{structure_formation}

Computer simulation of [[cosmic structure formation]] on scales larger than that of [[galaxies]] had always shown very good agreement of the $\Lambda CDM$ [[standard model of cosmology]] and observation.

There used to be various discrepancies of [[cold dark matter]]-[[model (in theoretical physics)|models]] on the scale of [[galaxies]]

\begin{itemize}%
\item \href{dark+matter#CuspCoreProblem}{core-cusp behaviour}.


\item [[galaxy rotation curves]]


\item [[Tully-Fisher relation]]



\end{itemize}
But recent analysis seems to show that more fine-grained analysis shows that [[cold dark matter]]-[[model (in theoretical physics)|models]] match all of these observations well. See behind the above links for more.

\hypertarget{vacuum_energy_and_cosmological_constant}{}\subsubsection*{{Vacuum energy and Cosmological constant}}\label{vacuum_energy_and_cosmological_constant}

The [[renormalization]] freedom in [[perturbative QFT|perturbative]] [[quantization]] of [[gravity]] ([[perturbative quantum gravity]]) induces freedom in the choice of [[vacuum expectation value]] of the [[stress-energy tensor]] and hence in the [[cosmological constant]].

For review see \hyperlink{Hack15}{Hack 15, section 3.2.1}

For more see at [[cosmological constant]] \href{cosmological+constant#InPerturbativeQuantumGravity}{here}.

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

\begin{itemize}%
\item [[dark energy]], [[dark matter]], [[MOND]]


\item [[structure formation]], [[inhomogeneous cosmology]]


\item [[baryogenesis]]


\item [[standard model of particle physics]]


\item [[Randall-Sundrum model]]


\item [[theory of everything]]


\item \href{string+theory+FAQ#InsightsIntoCosmology}{string theory FAQ -- Does string theory tell us anything about cosmology, such as the Big bang or cosmic inflation?}



\end{itemize}
[[!include standard model of fundamental physics - table]]

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

\hypertarget{general}{}\subsubsection*{{General}}\label{general}

Lecture notes include

\begin{itemize}%
\item [[Matthias Blau]], chapter 37 of \emph{Lecture notes on general relativity} (\href{http://www.blau.itp.unibe.ch/GRLecturenotes.html}{web})

\end{itemize}
Review:

\begin{itemize}%
\item Jorge L. Cervantes-Cota, George Smoot, \emph{Cosmology today -- A brief review} (2011)(\href{http://arxiv.org/abs/1107.1789}{arXiv:1107.1789})


\item [[Viatcheslav Mukhanov]], \emph{Quantum Universe}, Phys.Usp. 59 (2016) no.10, 1021-1027 (\href{http://inspirehep.net/record/1507528}{spire:1507528}, \href{https://iopscience.iop.org/article/10.3367/UFNe.2016.07.037857/meta}{doi:10.3367/UFNe.2016.07.037857}, \href{https://youtu.be/xUIrj_97i0A}{video recording})



\end{itemize}
\begin{quote}%
In March 2013, following an accurate processing of available measurement data, the Planck Scientific Collaboration published the highest-resolution photograph ever of the early Universe when it was only a few hundred thousand years old. The photograph showed galactic seeds in sufficient detail to test some nontrivial theoretical predictions made more than thirty years ago. Most amazing was that all predictions were confirmed to be remarkably accurate. With no exaggeration, we may consider it established experimentally that quantum physics, which is normally assumed to be relevant on the atomic and subatomic scale, also works on the scale of the entire Universe, determining its structure with all its galaxies, stars, and planets.


\end{quote}
A discussion of open problems is in

\begin{itemize}%
\item Benoit Famaey, Stacy McGaugh, \emph{Challenges for Lambda-CDM and MOND} (\href{http://arxiv.org/abs/1301.0623}{arXiv:1301.0623})


\item [[Thomas Buchert]], Alan A. Coley, [[Hagen Kleinert]], Boudewijn F. Roukema, David L. Wiltshire, \emph{Observational Challenges for the Standard FLRW Model}, Int. J. Mod. Phys. D 25, 1630007 (2016) (\href{https://arxiv.org/abs/1512.03313}{arXiv:1512.03313})



\end{itemize}
See also

\begin{itemize}%
\item Wikipedia, \emph{\href{http://en.wikipedia.org/wiki/Lambda-CDM_model}{Lambda-CDM model}}


\item Jaan Einasto, \emph{Dark matter} (\href{https://arxiv.org/abs/0901.0632}{arXiv:0901.0632}) 2009



\end{itemize}
\hypertarget{possible_tension_with_observation}{}\subsubsection*{{Possible tension with observation}}\label{possible_tension_with_observation}

Possible tensions in the model, regarding determination of the [[Hubble constant]] in the early and late universe, apparently observed by various groups, since the late 2010s:

review:

\begin{itemize}%
\item L. Verde T. Treu, A.G. Riess, \emph{Tensions between the Early and the Late Universe} (\href{https://arxiv.org/abs/1907.10625}{arXiv:1907.10625})

\end{itemize}
Indication that the tension is not in the data but in systematic errors:

\begin{itemize}%
\item Freedman et al. \emph{The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch} (\href{https://arxiv.org/abs/1907.05922}{arxiv:1907.05922})

\end{itemize}
\hypertarget{in_aqft_on_curved_spacetimes}{}\subsubsection*{{In AQFT on Curved spacetimes}}\label{in_aqft_on_curved_spacetimes}

Discussion in the rigorous context of[[AQFT on curved spacetimes]] includes

\begin{itemize}%
\item [[Klaus Fredenhagen]], [[Thomas-Paul Hack]], \emph{Quantum field theory on curved spacetime and the standard cosmological model} (\href{http://arxiv.org/abs/1308.6773}{arXiv:1308.6773})


\item [[Thomas-Paul Hack]], \emph{The Lambda CDM-model in quantum field theory on curved spacetime and Dark Radiation} (\href{https://arxiv.org/abs/1306.3074}{arXiv:1306.3074})



\end{itemize}
For review see

\begin{itemize}%
\item [[Thomas-Paul Hack]], section 3.2.1 \emph{Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes}, Springer 2016 (\href{https://arxiv.org/abs/1506.01869}{arXiv:1506.01869}, \href{https://doi.org/10.1007/978-3-319-21894-6}{doi:10.1007/978-3-319-21894-6})

\end{itemize}


\end{document}