\documentclass[12pt,titlepage]{article}

\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{color}
\usepackage{ucs}
\usepackage[utf8x]{inputenc}
\usepackage{xparse}
\usepackage{hyperref}

%----Macros----------
%
% Unresolved issues:
%
%  \righttoleftarrow
%  \lefttorightarrow
%
%  \color{} with HTML colorspec
%  \bgcolor
%  \array with options (without options, it's equivalent to the matrix environment)

% Of the standard HTML named colors, white, black, red, green, blue and yellow
% are predefined in the color package. Here are the rest.
\definecolor{aqua}{rgb}{0, 1.0, 1.0}
\definecolor{fuschia}{rgb}{1.0, 0, 1.0}
\definecolor{gray}{rgb}{0.502, 0.502, 0.502}
\definecolor{lime}{rgb}{0, 1.0, 0}
\definecolor{maroon}{rgb}{0.502, 0, 0}
\definecolor{navy}{rgb}{0, 0, 0.502}
\definecolor{olive}{rgb}{0.502, 0.502, 0}
\definecolor{purple}{rgb}{0.502, 0, 0.502}
\definecolor{silver}{rgb}{0.753, 0.753, 0.753}
\definecolor{teal}{rgb}{0, 0.502, 0.502}

% Because of conflicts, \space and \mathop are converted to
% \itexspace and \operatorname during preprocessing.

% itex: \space{ht}{dp}{wd}
%
% Height and baseline depth measurements are in units of tenths of an ex while
% the width is measured in tenths of an em.
\makeatletter
\newdimen\itex@wd%
\newdimen\itex@dp%
\newdimen\itex@thd%
\def\itexspace#1#2#3{\itex@wd=#3em%
\itex@wd=0.1\itex@wd%
\itex@dp=#2ex%
\itex@dp=0.1\itex@dp%
\itex@thd=#1ex%
\itex@thd=0.1\itex@thd%
\advance\itex@thd\the\itex@dp%
\makebox[\the\itex@wd]{\rule[-\the\itex@dp]{0cm}{\the\itex@thd}}}
\makeatother

% \tensor and \multiscript
\makeatletter
\newif\if@sup
\newtoks\@sups
\def\append@sup#1{\edef\act{\noexpand\@sups={\the\@sups #1}}\act}%
\def\reset@sup{\@supfalse\@sups={}}%
\def\mk@scripts#1#2{\if #2/ \if@sup ^{\the\@sups}\fi \else%
  \ifx #1_ \if@sup ^{\the\@sups}\reset@sup \fi {}_{#2}%
  \else \append@sup#2 \@suptrue \fi%
  \expandafter\mk@scripts\fi}
\def\tensor#1#2{\reset@sup#1\mk@scripts#2_/}
\def\multiscripts#1#2#3{\reset@sup{}\mk@scripts#1_/#2%
  \reset@sup\mk@scripts#3_/}
\makeatother

% \slash
\makeatletter
\newbox\slashbox \setbox\slashbox=\hbox{$/$}
\def\itex@pslash#1{\setbox\@tempboxa=\hbox{$#1$}
  \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa
  \copy\slashbox \kern-\@tempdima \box\@tempboxa}
\def\slash{\protect\itex@pslash}
\makeatother

% math-mode versions of \rlap, etc
% from Alexander Perlis, "A complement to \smash, \llap, and lap"
%   http://math.arizona.edu/~aprl/publications/mathclap/
\def\clap#1{\hbox to 0pt{\hss#1\hss}}
\def\mathllap{\mathpalette\mathllapinternal}
\def\mathrlap{\mathpalette\mathrlapinternal}
\def\mathclap{\mathpalette\mathclapinternal}
\def\mathllapinternal#1#2{\llap{$\mathsurround=0pt#1{#2}$}}
\def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}}
\def\mathclapinternal#1#2{\clap{$\mathsurround=0pt#1{#2}$}}

% Renames \sqrt as \oldsqrt and redefine root to result in \sqrt[#1]{#2}
\let\oldroot\root
\def\root#1#2{\oldroot #1 \of{#2}}
\renewcommand{\sqrt}[2][]{\oldroot #1 \of{#2}}

% Manually declare the txfonts symbolsC font
\DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n}
\SetSymbolFont{symbolsC}{bold}{U}{txsyc}{bx}{n}
\DeclareFontSubstitution{U}{txsyc}{m}{n}

% Manually declare the stmaryrd font
\DeclareSymbolFont{stmry}{U}{stmry}{m}{n}
\SetSymbolFont{stmry}{bold}{U}{stmry}{b}{n}

% Manually declare the MnSymbolE font
\DeclareFontFamily{OMX}{MnSymbolE}{}
\DeclareSymbolFont{mnomx}{OMX}{MnSymbolE}{m}{n}
\SetSymbolFont{mnomx}{bold}{OMX}{MnSymbolE}{b}{n}
\DeclareFontShape{OMX}{MnSymbolE}{m}{n}{
    <-6>  MnSymbolE5
   <6-7>  MnSymbolE6
   <7-8>  MnSymbolE7
   <8-9>  MnSymbolE8
   <9-10> MnSymbolE9
  <10-12> MnSymbolE10
  <12->   MnSymbolE12}{}

% Declare specific arrows from txfonts without loading the full package
\makeatletter
\def\re@DeclareMathSymbol#1#2#3#4{%
    \let#1=\undefined
    \DeclareMathSymbol{#1}{#2}{#3}{#4}}
\re@DeclareMathSymbol{\neArrow}{\mathrel}{symbolsC}{116}
\re@DeclareMathSymbol{\neArr}{\mathrel}{symbolsC}{116}
\re@DeclareMathSymbol{\seArrow}{\mathrel}{symbolsC}{117}
\re@DeclareMathSymbol{\seArr}{\mathrel}{symbolsC}{117}
\re@DeclareMathSymbol{\nwArrow}{\mathrel}{symbolsC}{118}
\re@DeclareMathSymbol{\nwArr}{\mathrel}{symbolsC}{118}
\re@DeclareMathSymbol{\swArrow}{\mathrel}{symbolsC}{119}
\re@DeclareMathSymbol{\swArr}{\mathrel}{symbolsC}{119}
\re@DeclareMathSymbol{\nequiv}{\mathrel}{symbolsC}{46}
\re@DeclareMathSymbol{\Perp}{\mathrel}{symbolsC}{121}
\re@DeclareMathSymbol{\Vbar}{\mathrel}{symbolsC}{121}
\re@DeclareMathSymbol{\sslash}{\mathrel}{stmry}{12}
\re@DeclareMathSymbol{\bigsqcap}{\mathop}{stmry}{"64}
\re@DeclareMathSymbol{\biginterleave}{\mathop}{stmry}{"6}
\re@DeclareMathSymbol{\invamp}{\mathrel}{symbolsC}{77}
\re@DeclareMathSymbol{\parr}{\mathrel}{symbolsC}{77}
\makeatother

% \llangle, \rrangle, \lmoustache and \rmoustache from MnSymbolE
\makeatletter
\def\Decl@Mn@Delim#1#2#3#4{%
  \if\relax\noexpand#1%
    \let#1\undefined
  \fi
  \DeclareMathDelimiter{#1}{#2}{#3}{#4}{#3}{#4}}
\def\Decl@Mn@Open#1#2#3{\Decl@Mn@Delim{#1}{\mathopen}{#2}{#3}}
\def\Decl@Mn@Close#1#2#3{\Decl@Mn@Delim{#1}{\mathclose}{#2}{#3}}
\Decl@Mn@Open{\llangle}{mnomx}{'164}
\Decl@Mn@Close{\rrangle}{mnomx}{'171}
\Decl@Mn@Open{\lmoustache}{mnomx}{'245}
\Decl@Mn@Close{\rmoustache}{mnomx}{'244}
\makeatother

% Widecheck
\makeatletter
\DeclareRobustCommand\widecheck[1]{{\mathpalette\@widecheck{#1}}}
\def\@widecheck#1#2{%
    \setbox\z@\hbox{\m@th$#1#2$}%
    \setbox\tw@\hbox{\m@th$#1%
       \widehat{%
          \vrule\@width\z@\@height\ht\z@
          \vrule\@height\z@\@width\wd\z@}$}%
    \dp\tw@-\ht\z@
    \@tempdima\ht\z@ \advance\@tempdima2\ht\tw@ \divide\@tempdima\thr@@
    \setbox\tw@\hbox{%
       \raise\@tempdima\hbox{\scalebox{1}[-1]{\lower\@tempdima\box
\tw@}}}%
    {\ooalign{\box\tw@ \cr \box\z@}}}
\makeatother

% \mathraisebox{voffset}[height][depth]{something}
\makeatletter
\NewDocumentCommand\mathraisebox{moom}{%
\IfNoValueTF{#2}{\def\@temp##1##2{\raisebox{#1}{$\m@th##1##2$}}}{%
\IfNoValueTF{#3}{\def\@temp##1##2{\raisebox{#1}[#2]{$\m@th##1##2$}}%
}{\def\@temp##1##2{\raisebox{#1}[#2][#3]{$\m@th##1##2$}}}}%
\mathpalette\@temp{#4}}
\makeatletter

% udots (taken from yhmath)
\makeatletter
\def\udots{\mathinner{\mkern2mu\raise\p@\hbox{.}
\mkern2mu\raise4\p@\hbox{.}\mkern1mu
\raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern1mu}}
\makeatother

%% Fix array
\newcommand{\itexarray}[1]{\begin{matrix}#1\end{matrix}}
%% \itexnum is a noop
\newcommand{\itexnum}[1]{#1}

%% Renaming existing commands
\newcommand{\underoverset}[3]{\underset{#1}{\overset{#2}{#3}}}
\newcommand{\widevec}{\overrightarrow}
\newcommand{\darr}{\downarrow}
\newcommand{\nearr}{\nearrow}
\newcommand{\nwarr}{\nwarrow}
\newcommand{\searr}{\searrow}
\newcommand{\swarr}{\swarrow}
\newcommand{\curvearrowbotright}{\curvearrowright}
\newcommand{\uparr}{\uparrow}
\newcommand{\downuparrow}{\updownarrow}
\newcommand{\duparr}{\updownarrow}
\newcommand{\updarr}{\updownarrow}
\newcommand{\gt}{>}
\newcommand{\lt}{<}
\newcommand{\map}{\mapsto}
\newcommand{\embedsin}{\hookrightarrow}
\newcommand{\Alpha}{A}
\newcommand{\Beta}{B}
\newcommand{\Zeta}{Z}
\newcommand{\Eta}{H}
\newcommand{\Iota}{I}
\newcommand{\Kappa}{K}
\newcommand{\Mu}{M}
\newcommand{\Nu}{N}
\newcommand{\Rho}{P}
\newcommand{\Tau}{T}
\newcommand{\Upsi}{\Upsilon}
\newcommand{\omicron}{o}
\newcommand{\lang}{\langle}
\newcommand{\rang}{\rangle}
\newcommand{\Union}{\bigcup}
\newcommand{\Intersection}{\bigcap}
\newcommand{\Oplus}{\bigoplus}
\newcommand{\Otimes}{\bigotimes}
\newcommand{\Wedge}{\bigwedge}
\newcommand{\Vee}{\bigvee}
\newcommand{\coproduct}{\coprod}
\newcommand{\product}{\prod}
\newcommand{\closure}{\overline}
\newcommand{\integral}{\int}
\newcommand{\doubleintegral}{\iint}
\newcommand{\tripleintegral}{\iiint}
\newcommand{\quadrupleintegral}{\iiiint}
\newcommand{\conint}{\oint}
\newcommand{\contourintegral}{\oint}
\newcommand{\infinity}{\infty}
\newcommand{\bottom}{\bot}
\newcommand{\minusb}{\boxminus}
\newcommand{\plusb}{\boxplus}
\newcommand{\timesb}{\boxtimes}
\newcommand{\intersection}{\cap}
\newcommand{\union}{\cup}
\newcommand{\Del}{\nabla}
\newcommand{\odash}{\circleddash}
\newcommand{\negspace}{\!}
\newcommand{\widebar}{\overline}
\newcommand{\textsize}{\normalsize}
\renewcommand{\scriptsize}{\scriptstyle}
\newcommand{\scriptscriptsize}{\scriptscriptstyle}
\newcommand{\mathfr}{\mathfrak}
\newcommand{\statusline}[2]{#2}
\newcommand{\tooltip}[2]{#2}
\newcommand{\toggle}[2]{#2}

% Theorem Environments
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{cor}{Corollary}
\newtheorem*{utheorem}{Theorem}
\newtheorem*{ulemma}{Lemma}
\newtheorem*{uprop}{Proposition}
\newtheorem*{ucor}{Corollary}
\theoremstyle{definition}
\newtheorem{defn}{Definition}
\newtheorem{example}{Example}
\newtheorem*{udefn}{Definition}
\newtheorem*{uexample}{Example}
\theoremstyle{remark}
\newtheorem{remark}{Remark}
\newtheorem{note}{Note}
\newtheorem*{uremark}{Remark}
\newtheorem*{unote}{Note}

%-------------------------------------------------------------------

\begin{document}

%-------------------------------------------------------------------


\section*{Starobinsky model of cosmic inflation}

\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{EmbeddingIntoSupergravity}{Embedding into supergravity}\dotfill \pageref*{EmbeddingIntoSupergravity} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak
\noindent\hyperlink{ReferencesEmbeddingIntoSupergravity}{Embedding into supergravity}\dotfill \pageref*{ReferencesEmbeddingIntoSupergravity} \linebreak
\noindent\hyperlink{ReferencesEmbeddingInto11dSupergravity}{Embedding into 11d supergravity}\dotfill \pageref*{ReferencesEmbeddingInto11dSupergravity} \linebreak
\noindent\hyperlink{ReferencesEmbeddingIntoStringTheory}{Embedding into superstring theory}\dotfill \pageref*{ReferencesEmbeddingIntoStringTheory} \linebreak


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

In [[phenomenology]] of [[cosmology]], the \emph{Starobinsky model} of [[cosmic inflation]] takes into account -- and takes as the very source of the [[inflaton]] field -- [[higher curvature corrections]] to the [[Einstein-Hilbert action]] of [[gravity]], notably the term $R^2$ (square of the [[Ricci curvature]]).

The Starobinsky model stands out among models of inflation as predicting a low value of the scalar-to-tensor ratio $r$, specifically it predicts

\begin{displaymath}
r \sim \frac{12}{N^2}
\end{displaymath}
where $N$ is the number of $e$-foldings during inflation (see e.g. \hyperlink{KehagiasDizgahRiotto13}{Kehagias-Dizgah-Riotto 13 (2.6)}).

Models of this type are favored by [[experiment|experimental]] results (\hyperlink{PlanckCollaboration13}{PlanckCollaboration 13}, \hyperlink{BICEPKeckPlanck15}{BICEP2-Keck-Planck 15}, \hyperlink{PlanckCollaboration15}{PlanckCollaboration 15}) which give a low upper bound on $r$ around $0.1$ (whereas other models like [[chaotic inflation]] are disfavored by these values), see (\hyperlink{PlanckCollaboration13}{PlanckCollaboration 13, page 12}).

 With respect to this data, the Starobinsky model (or ``$R^2$ inflation'') is the model with the highest [[Bayesian reasoning|Bayesian evidence]] (\hyperlink{Rachen15}{Rachen, Feb 15}, \hyperlink{PlanckCollaboration15XX}{PlanckCollaboration 15XX, table 6 on p. 18}) as it is right in the center of the likelihood peak (\hyperlink{PlanckCollaboration13}{PlanckCollaboration 13, figure 1}, also \hyperlink{Linde14}{Linde 14, figure 5}) and at the same time has the lowest number of free parameters :

 

This remains true with the data of (\hyperlink{PlanckCollaboration15}{PlanckCollaboration 15}), see (\hyperlink{PlanckCollaboration15XIII}{PlanckCollaboration 15 XIII, figure 22}) and in the final analysis (\hyperlink{PlanckCollaboration18X}{PlanckCollaboration 18X, Fig 8}), which gives the following (from \href{http://resonaances.blogspot.se/2015/02/weekend-plot-inflation15.html}{here}):

 

\begin{quote}%
$R^2$ inflation has the strongest evidence among the models considered here. However, care must be taken not to overinterpret small differences in likelihood lacking statistical significance. The models closest to $R^2$ in terms of evidence are brane inflation and exponential inflation, which have one more parameter than $R^2$ (\hyperlink{PlanckCollaboration15XX}{PlanckCollaboration 15XX, p. 18})


\end{quote}
See (\hyperlink{Ellis13}{Ellis 13}, \hyperlink{Ketov13}{Ketov 13}, \hyperlink{Efstathiou2019}{Efstathiou 2019, 50:49}) for brief survey and see (\hyperlink{KehagiasDizgahRiotto13}{Kehagias-Dizgah-Riotto 13}) for more details. There it is argued that the other types of models which also fit the data are actually equivalent to the Starobinsky model during inflation.

\hypertarget{EmbeddingIntoSupergravity}{}\subsection*{{Embedding into supergravity}}\label{EmbeddingIntoSupergravity}

Being concerned with pure [[gravity]] (the [[inflaton]] not being an extra [[matter]] field but part of the field of [[gravity]]) the Starobinsky model lends itself to embedding into [[supergravity]] (originally due to \hyperlink{Ceotti87}{Ceotti 87}, see e.g. \hyperlink{FKR13}{Farakos-Kehagias-Riotto 13}). Such embedding has been argued to improve the model further (highlighted e.g. in \hyperlink{Ellis13}{Ellis 13}), for instance by

\begin{itemize}%
\item shrinking the necessary initial homogeneous patch from $\sim 10^3$ [[Planck lengths]] (which would be in need of further explanation) down to just $\sim 10^1$ [[Planck lengths]] (\hyperlink{DalianisFarakos15}{Dalianis-Farakos 15 equations (68), (72) in v1, equations (4.11), (4.17) in v3}, reviewed in \hyperlink{Dalianis16}{Dalianis 16});


\item naturally subsuming a mechanism for [[supersymmetry breaking]] (\hyperlink{FerrarKehagias14}{Ferrar-Kehagias 14}, \hyperlink{DFKRU14}{DFKRU 14}) notably with a Starobisnky potential naturally induced from [[gravitino condensation]] (\hyperlink{AlexandreHoustonMavromatos14}{Alexandre-Houston-Mavromatos 14}).



\end{itemize}
\begin{quote}%
graphics grabbed from \hyperlink{Dalianis16}{Dalianis 16, p. 8}


\end{quote}
 More concretely, in \hyperlink{HiragaHyakutake18}{Hiraga-Hyakutake 18} a simple model of [[11-dimensional supergravity]] with its $R^4$ [[higher curvature correction]] (see \href{11-dimensional+supergravity#HigherCurvatureCorrection}{there}) is considered and claimed to yield inflation with ``graceful exit'' and dynamical [[KK-compactification]]:

\begin{quote}%
graphics from \hyperlink{HiragaHyakutake18}{Hiraga-Hyakutake 18, p. 8}


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

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

The model is due to

\begin{itemize}%
\item [[Aleksei Starobinsky]], \emph{A new type of isotropic cosmological models without singularity}, Phys. Lett. B 91, 99 (1980); ()

\end{itemize}
and the analysis of its predictions is due to

\begin{itemize}%
\item [[Viatcheslav Mukhanov]] and G. V. Chibisov, JETP Lett. 33, 532 (1981) Pisma Zh. Eksp. Teor. Fiz. 33, 549 (1981);


\item [[Aleksei Starobinsky]], Sov. Astron. Lett. 9, 302 (1983).



\end{itemize}
The experimental data supporting the model is due to

\begin{itemize}%
\item [[Planck Collaboration]], \emph{Planck 2013 results. XXII. Constraints on inflation} (\href{http://arxiv.org/abs/1303.5082}{arXiv:1303.5082})


\item [[Planck Collaboration]], [[BICEP2]] \emph{A Joint Analysis of BICEP2/Keck Array and Planck Data} (\href{http://arxiv.org/abs/1502.00612}{arXiv:1502.00612})


\item [[Planck Collaboration]], \emph{Planck 2015, Overview of results} (\href{http://xxx.lanl.gov/abs/1502.01582}{arXiv:1502.01582})


\item [[Planck Collaboration]], \emph{Planck 2015 results. XIII. Cosmological parameters} (\href{http://xxx.lanl.gov/abs/1502.01589}{arXiv:1502.01589})


\item [[Planck Collaboration]], \emph{Planck 2015 results. XX. Constraints on inflation} (\href{http://arxiv.org/abs/1502.02114}{arXiv:1502.02114})


\item [[Planck Collaboration]], \emph{Planck 2018 results. X. Constraints on inflation} (\href{https://arxiv.org/abs/1807.06211}{arXiv:1807.06211})



\end{itemize}
See also

\begin{itemize}%
\item Debika Chowdhury, Jerome Martin, Christophe Ringeval, Vincent Vennin, \emph{Inflation after Planck: Judgment Day} (\href{https://arxiv.org/abs/1902.03951}{arxiv:1902.03951})

\end{itemize}
Review and exposition includes

\begin{itemize}%
\item [[Alex Kehagias]], Azadeh Moradinezhad Dizgah, Antonio Riotto, \emph{Comments on the Starobinsky Model of Inflation and its Descendants}, Phys. Rev. D 89, 043527 (2014) (\href{http://arxiv.org/abs/1312.1155}{arXiv:1312.1155})


\item [[Sergei Ketov]], \emph{PLANCK mission, Starobinsky inflation and its realization in old-minimal supergravity}, talk at \emph{Kavli IPMU Workshop: SUSY Model Building and Phenomenology}, 2-4 December 2013 (\href{http://indico.ipmu.jp/indico/getFile.py/access?contribId=16&sessionId=7&resId=0&materialId=slides&confId=28}{pdf})


\item [[John Ellis]], \emph{Planck-Compatible Inflationary Models}, talk 2013 (\href{http://londoncosmology.files.wordpress.com/2013/09/lcdm.pptx}{pptx})


\item [[Andrei Linde]], \emph{Inflationary Cosmology after Planck 2013} (\href{http://arxiv.org/abs/1402.0526}{arXiv:1402.0526})


\item [[Jörg Rachen]], \emph{The Planck 2015 Results: Cosmology and Fundamental Physics from the Polarised CMB and Other Probes}, IMAPP Special Seminar, Nijmegen, Feb.5, 2015


\item [[Ioannis Dalianis]], \emph{Features and implications of the plateau inflationary potentials}, Planck 2015 conference contribution (\href{http://arxiv.org/abs/1602.05026}{arXiv:1602.05026})


\item George P. Efstathiou on behalf of the PLANCK mission, \emph{The PLANCK legacy, inflation and the origin of structure in the universe}, talk at University of Cambridge, January 28, 2019 (\href{https://www.youtube.com/watch?v=16CkVzVK7Wk&feature=youtu.be&t=3049}{recording from 50:49})



\end{itemize}
Discussion with more general [[higher curvature corrections]]:

\begin{itemize}%
\item Gustavo Arciniega, Jose D. Edelstein, Luisa G. Jaime, \emph{Towards purely geometric inflation and late time acceleration} (\href{https://arxiv.org/abs/1810.08166}{arXiv:1810.08166})


\item Gustavo Arciniega, Pablo Bueno, Pablo A. Cano, Jose D. Edelstein, Robie A. Hennigar, Luisa G. Jaimem, \emph{Geometric Inflation} (\href{https://arxiv.org/abs/1812.11187}{arXiv:1812.11187})



\end{itemize}
Discussion of [[eternal inflation]] in Starobinsky-type models

\begin{itemize}%
\item Gabriela Barenboim, [[William Kinney]], Wan-Il Park, \emph{Eternal Hilltop Inflation}, Journal of Cosmology and Astroparticle Physics, Volume 2016, May 2016 (\href{https://arxiv.org/abs/1601.08140}{arXiv:1601.08140})

\end{itemize}
\hypertarget{ReferencesEmbeddingIntoSupergravity}{}\subsubsection*{{Embedding into supergravity}}\label{ReferencesEmbeddingIntoSupergravity}

Discussion of embedding of Starobinsky inflation in [[supergravity]] originates in

\begin{itemize}%
\item S. Cecotti, \emph{Higher derivative supergravity Is equivalent to standard supergravity coupled to matter}, Phys. Lett. B 190, 86 (1987).


\item S. Cecotti, [[Sergio Ferrara]], M. Porrati and S. Sabharwal, Nucl. Phys. B 306, 160 (1988).



\end{itemize}
and is further developed in the following articles:

\begin{itemize}%
\item [[Sergei Ketov]], \emph{Supergravity and Early Universe: the Meeting Point of Cosmology and High-Energy Physics}, Int.J.Mod.Phys. A28 (2013) 1330021 (\href{http://arxiv.org/abs/arXiv:1201.2239}{arXiv:1201.2239})


\item [[John Ellis]], [[Dimitri Nanopoulos]], [[Keith Olive]], \emph{No-Scale Supergravity Realization of the Starobinsky Model of Inflation} Phys. Rev. Lett. 111, 111301 (2013) (\href{http://arxiv.org/abs/1305.1247}{arXiv:1305.1247})


\item [[Renata Kallosh]], [[Andrei Linde]], \emph{Superconformal generalizations of the Starobinsky model} JCAP 1306, 028 (2013) (\href{http://arxiv.org/abs/1306.3214}{arXiv:1306.3214})


\item [[John Ellis]], [[Dimitri Nanopoulos]], [[Keith Olive]], \emph{Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity} JCAP 1310, 009 (2013) (\href{http://arxiv.org/abs/1307.3537}{arXiv:1307.3537})


\item [[Fotis Farakos]], [[Alex Kehagias]], A. Riotto, \emph{On the Starobinsky Model of Inflation from Supergravity}, Nucl. Phys. B 876, 187 (2013) (\href{http://arxiv.org/abs/1307.1137}{arXiv:1307.1137})


\item [[Sergio Ferrara]], [[Renata Kallosh]], [[Andrei Linde]] and M. Porrati, \emph{Minimal Supergravity Models of Inflation} (\href{http://arxiv.org/abs/1307.7696}{arXiv:1307.7696})


\item [[Andrei Linde]] and M. Porrati, \emph{Higher Order Corrections in Minimal Supergravity Models of Inflation} (\href{http://arxiv.org/abs/1309.1085}{arXiv:1309.1085})


\item [[Sergio Ferrara]], [[Renata Kallosh]], [[Antoine Van Proeyen]], \emph{On the Supersymmetric Completion of R+R2 Gravity and Cosmology} JHEP 1311, 134 (2013) (\href{http://arxiv.org/abs/1309.4052}{arXiv:1309.4052})


\item [[Sergei Ketov]], Takahiro Terada, \emph{Old-minimal supergravity models of inflation}, JHEP12(2013)040 (\href{https://arxiv.org/abs/1309.7494}{arXiv:1309.7494})


\item [[Sergio Ferrara]]], [[Pietro Fre]] and A. S. Sorin, \emph{On the Topology of the Inflaton Field in Minimal Supergravity Models} (\href{http://arxiv.org/abs/1311.5059}{arXiv:1311.5059})


\item Jean Alexandre, Nick Houston, Nick E. Mavromatos, \emph{Starobinsky-type Inflation in Dynamical Supergravity Breaking Scenarios}, Phys. Rev. D 89, 027703 (2014) (\href{https://arxiv.org/abs/1312.5197}{arXiv:1312.5197})

via [[gravitino condensation]], based on

\begin{itemize}%
\item Jean Alexandre, Nick Houston, Nick E. Mavromatos, \emph{Dynamical Supergravity Breaking via the Super-Higgs Effect Revisited}, Phys. Rev. D 88, 125017 (2013) (\href{https://arxiv.org/abs/1310.4122}{arXiv:1310.4122})


\item Jean Alexandre, Nick Houston, Nick E. Mavromatos, \emph{Inflation via Gravitino Condensation in Dynamically Broken Supergravity}, International Journal of Modern Physics D, Volume 24, Issue 04, April 2015 (\href{https://arxiv.org/abs/1409.3183}{arXiv:1409.3183})



\end{itemize}

\item [[Sergei Ketov]], [[Aleksei Starobinsky]], \emph{Inflation and non-minimal scalar-curvature coupling in gravity and supergravity}, JCAP 1208, 022 (2012) (\href{https://arxiv.org/abs/1203.0805}{arXiv:1203.0805})


\item [[Sergei Ketov]], S. Tsujikawa, \emph{Consistency of inflation and preheating in $F(R)$ supergravity}, Phys. Rev. D 86, 023529 (2012) (\href{https://arxiv.org/abs/1205.2918}{arXiv:1205.2918})


\item [[Sergei Ketov]], \emph{On the supersymmetrization of inflation in $f(R)$ gravity},Prog. Theor. Exp. Phys. 2013, 123B04 (\href{https://arxiv.org/abs/1309.0293}{arXiv:1309.0293})


\item [[Sergio Ferrara]], [[Alex Kehagias]], Antonio Riotto, \emph{The Imaginary Starobinsky Model and Higher Curvature Corrections} (\href{http://arxiv.org/abs/1405.2353}{arXiv:1405.2353})


\item [[Sergio Ferrara]], [[Alex Kehagias]], \emph{Higher Curvature Supergravity, Supersymmetry Breaking and Inflation} (\href{http://arxiv.org/abs/1407.5187}{arXiv:1407.5187})


\item [[Ioannis Dalianis]], [[Fotis Farakos]], [[Alex Kehagias]], A. Riotto, [[Rikard von Unge]], \emph{Supersymmetry Breaking and Inflation from Higher Curvature Supergravity} (\href{http://arxiv.org/abs/1409.8299}{arXiv:1409.8299})


\item [[Ioannis Dalianis]], [[Fotis Farakos]], \emph{On the initial conditions for inflation with plateau potentials: the $R + R^2$ (super)gravity case}, \href{http://iopscience.iop.org/article/10.1088/1475-7516/2015/07/044/meta}{Journal of Cosmology and Astroparticle Physics, Volume 2015, July 2015}, (\href{http://arxiv.org/abs/1502.01246}{arXiv:1502.01246})


\item Spyros Basilakos, Nick E. Mavromatos, Joan Sola, \emph{Starobinsky-like inflation and running vacuum in the context of Supergravity} (\href{https://arxiv.org/abs/1505.04434}{arXiv:1505.04434})

\begin{quote}%
In this paper we have shown that SUGRA models with a dynamically induced massive gravitino phase lead to the RVM behavior and therefore provide a strong support for a fundamental description of the cosmic history.


\end{quote}

\item Andrea Addazi, [[Sergei Ketov]], \emph{Energy conditions in Starobinsky supergravity} (\href{https://arxiv.org/abs/1701.02450}{arXiv:1701.02450})


\item [[John Ellis]], Dimitri V. Nanopoulos, [[Keith Olive]], \emph{From $R^2$ Gravity to No-Scale Supergravity}, Phys. Rev. D 97, 043530 (2018) (\href{https://arxiv.org/abs/1711.11051}{arXiv:1711.11051})


\item Hiroyuki Abe, Yermek Aldabergenov, Shuntaro Aoki, [[Sergei Ketov]], \emph{Massive vector multiplet with Dirac-Born-Infeld and new Fayet-Iliopoulos terms in supergravity} (\href{https://arxiv.org/abs/1808.00669}{arXiv:1808.00669})


\item Sergey Ketov, Maxim Khlopov, \emph{Extending Starobinsky inflationary model in gravity and supergravity} (\href{https://arxiv.org/abs/1809.09975}{arXiv:1809.09975})


\item [[John Ellis]], [[Dimitri Nanopoulos]], [[Keith Olive]], Sarunas Verner, \emph{A Unified No-Scale Model of Modulus Fixing, Inflation, Supersymmetry Breaking and Dark Energy}, Phys. Rev. D 100, 025009 (2019) (\href{https://arxiv.org/abs/1903.05267}{arXiv:1903.05267}, \href{https://doi.org/10.1103/PhysRevD.100.025009}{doi:10.1103/PhysRevD.100.025009})



\end{itemize}
\hypertarget{ReferencesEmbeddingInto11dSupergravity}{}\subsubsection*{{Embedding into 11d supergravity}}\label{ReferencesEmbeddingInto11dSupergravity}

Discussion of Starobinsky inflation in [[11-dimensional supergravity]] with its [[higher curvature corrections]] included (see \href{11-dimensional+supergravity#HigherCurvatureCorrection}{there}):

\begin{itemize}%
\item [[Katrin Becker]], [[Melanie Becker]], \emph{Supersymmetry Breaking, M-Theory and Fluxes}, JHEP 0107:038,2001 (\href{https://arxiv.org/abs/hep-th/0107044}{arXiv:hep-th/0107044})


\item Kazuho Hiraga, Yoshifumi Hyakutake, \emph{Inflationary Cosmology via Quantum Corrections in M-theory} (\href{https://arxiv.org/abs/1809.04724}{arXiv:1809.04724})


\item Kazuho Hiraga, Yoshifumi Hyakutake, \emph{Scalar Cosmological Perturbations in M-theory with Higher Derivative Corrections} (\href{https://arxiv.org/abs/1910.12483}{arxiv:1910.12483})



\end{itemize}
\hypertarget{ReferencesEmbeddingIntoStringTheory}{}\subsubsection*{{Embedding into superstring theory}}\label{ReferencesEmbeddingIntoStringTheory}

Embedding of Starobinsky inflation into [[superstring theory]] is discussed in

\begin{itemize}%
\item [[Costas Kounnas]], [[Dieter Luest]], Nicolaos Toumbas, \emph{$\mathcal{R}^2$ inflation from scale invariant supergravity and anomaly free superstrings with fluxes} (\href{http://arxiv.org/abs/1409.7076}{arXiv:1409.7076})


\item [[Ralph Blumenhagen]], Anamaria Font, Michael Fuchs, Daniela Herschmann, Erik Plauschinn, \emph{Towards Axionic Starobinsky-like Inflation in String Theory}, Physics Letters B Volume 746, 30 June 2015, Pages 217--222 (\href{https://arxiv.org/abs/1503.01607}{arXiv:1503.01607})


\item [[John Ellis]], Marcos A. G. Garcia, [[Dimitri Nanopoulos]], [[Keith Olive]], \emph{Phenomenological Aspects of No-Scale Inflation Models} (\href{http://arxiv.org/abs/1503.08867}{arXiv:1503.08867})


\item [[Luis Alvarez-Gaume]], [[Alex Kehagias]], [[Costas Kounnas]], [[Dieter Luest]], Antonio Riotto, \emph{Aspects of Quadratic Gravity} (\href{http://arxiv.org/abs/1505.07657}{arXiv:1505.07657})


\item Benedict Broy, David Ciupke, FranciscoG. Pedro, Alexander Westphal, \emph{Starobinsky-Type Inflation from $\alpha'$-Corrections}, JCAP01(2016)001 (\href{https://arxiv.org/abs/1509.00024}{arXiv:1509.00024})


\item K. Sravan Kumar, \emph{Inflaton candidates: from string theory to particle physics}, PhD thesis (\href{https://arxiv.org/abs/1808.03701}{arXiv:1808.03701})



\end{itemize}
[[!redirects Starobinsky inflation]]



\end{document}