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\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*{cosmic inflation} \hypertarget{context}{}\subsubsection*{{Context}}\label{context} \hypertarget{physics}{}\paragraph*{{Physics}}\label{physics} [[!include physicscontents]] \hypertarget{contents}{}\section*{{Contents}}\label{contents} \noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak \noindent\hyperlink{variants}{Variants}\dotfill \pageref*{variants} \linebreak \noindent\hyperlink{old_inflation}{Old inflation}\dotfill \pageref*{old_inflation} \linebreak \noindent\hyperlink{new_inflation}{New inflation}\dotfill \pageref*{new_inflation} \linebreak \noindent\hyperlink{eternal_inflation}{Eternal inflation}\dotfill \pageref*{eternal_inflation} \linebreak \noindent\hyperlink{chaotic_inflation}{Chaotic inflation}\dotfill \pageref*{chaotic_inflation} \linebreak \noindent\hyperlink{candidates_for_the_inflaton_field}{Candidates for the inflaton field}\dotfill \pageref*{candidates_for_the_inflaton_field} \linebreak \noindent\hyperlink{HiggsInflation}{Higgs inflation}\dotfill \pageref*{HiggsInflation} \linebreak \noindent\hyperlink{axion_inflation}{Axion inflation}\dotfill \pageref*{axion_inflation} \linebreak \noindent\hyperlink{higher_curvature_inflation_starobinsky_model}{Higher curvature inflation (Starobinsky model)}\dotfill \pageref*{higher_curvature_inflation_starobinsky_model} \linebreak \noindent\hyperlink{ekpyrotic_cosmology}{Ekpyrotic cosmology}\dotfill \pageref*{ekpyrotic_cosmology} \linebreak \noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak \noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak \noindent\hyperlink{reviews}{Reviews}\dotfill \pageref*{reviews} \linebreak \noindent\hyperlink{original_articles}{Original articles}\dotfill \pageref*{original_articles} \linebreak \noindent\hyperlink{ReferencesExperimentalEvidence}{Experimantal evidence}\dotfill \pageref*{ReferencesExperimentalEvidence} \linebreak \noindent\hyperlink{inflation_from_higher_curvature_corrections}{Inflation from higher curvature corrections}\dotfill \pageref*{inflation_from_higher_curvature_corrections} \linebreak \noindent\hyperlink{ReferencesHiggsInflation}{Higgs field inflation}\dotfill \pageref*{ReferencesHiggsInflation} \linebreak \noindent\hyperlink{ReferencesHiggsInflation}{Gauge field inflation}\dotfill \pageref*{ReferencesHiggsInflation} \linebreak \noindent\hyperlink{string_modeled_inflation}{String modeled inflation}\dotfill \pageref*{string_modeled_inflation} \linebreak \hypertarget{idea}{}\subsection*{{Idea}}\label{idea} In the context of [[cosmology]], \emph{cosmic inflation} is a [[model (in theoretical physics)]] that can explain certain large-scale features of the [[observable universe]] (flatness, horizon problem, CMB anisotropy) by assuming a finite period of drastic expansion of the universe shortly after the [[big bang]]. Cosmic inflation is part of the [[standard model of cosmology]]. The typical [[model (physics)|model]] of cosmic inflation adds to a standard [[FRW model]] simply a [[scalar field]] $\phi$ -- then called the \textbf{inflaton field} -- with standard kinetic term and some potential term. If the potential term is chosen suitably one can obtain solutions to [[Einstein's equations]] of this simple homogenous and isotropic model which exhibit ``slow roll behaviour'' for $\phi$, meaning that $\phi$ (homogeneous in space) starts out in the vicinity of the [[big bang]] with some finite value and then slowly ``rolls down'' its potential well (where one speaks in the analogy with the [[model (in theoretical physics)|model]] describing a single [[particle]] on the [[real line]] in the given potential, which has the same kind of [[action functional]]). Therefore in this ``slow roll'' period the contribution of $\phi$ to the [[FRW model]] is essentially that of a [[cosmological constant]] and so this drives the expansion of the ``universe'' in this model. But since $\phi$ is only approximately constant it eventually reaches the minimum of its potential well. Again, if the potential parameters of the model are chosen suitably one can arrange that it stays there (called the ``graceful exit property'' of the inflationary model) and so it stops driving the expansion of the ``universe''. In conclusion this yields variants of the [[FRW model]] that exhibit pronounced expansion shortly after the initial singularity and then asymptote to the behaviour of the plain FRW model. This is what is called \emph{cosmic inflation}. Simple as it is, this model has proven to successfully match the observations that it was designed to match (the large-scale homogeneity of the [[observable universe]], notably). But of course people are trying all kinds of variants, too. A central conceptual problem of most of these models is that it is unclear what the field $\phi$ should be in terms of [[particle physics]] or other known phyisics. In some variants it is identified with the [[Higgs field]], in other it is a scalar moduli field of some [[Kaluza-Klein compactification]], but all of this is speculative. The experimental data (\hyperlink{PlanckCollaboration13}{PlanckCollaboration 13}, \hyperlink{BICEPKeckPlanck15}{BICEP-Keck-Planck 15}, \hyperlink{PlanckCollaboration15}{PlanckCollaboration 15}) strongly favors the [[Starobinsky model of cosmic inflation]]. \hypertarget{variants}{}\subsection*{{Variants}}\label{variants} \hypertarget{old_inflation}{}\subsubsection*{{Old inflation}}\label{old_inflation} (\hyperlink{Guth}{Guth 91}, \hyperlink{Sato}{Sato 81}) \hypertarget{new_inflation}{}\subsubsection*{{New inflation}}\label{new_inflation} (\hyperlink{Linde}{Linde 82}, \hyperlink{AlbrechtSteinhardt}{Albrecht-Steinhardt 82}) \hypertarget{eternal_inflation}{}\subsubsection*{{Eternal inflation}}\label{eternal_inflation} \begin{itemize}% \item [[eternal inflation]] \end{itemize} \hypertarget{chaotic_inflation}{}\subsubsection*{{Chaotic inflation}}\label{chaotic_inflation} [[chaotic inflation]] (\hyperlink{Linde83}{Linde 83}) \hypertarget{candidates_for_the_inflaton_field}{}\subsection*{{Candidates for the inflaton field}}\label{candidates_for_the_inflaton_field} \hypertarget{HiggsInflation}{}\subsubsection*{{Higgs inflation}}\label{HiggsInflation} The idea that the inflaton field in cosmology might be the [[Higgs field]] from the [[standard model of particle physics]] is as old as the idea of inflation itself, but at least in the naive versions it seems to be ruled out by data. However, with the experimental detection of the previously hypothesized Higgs field itself, the topic is gaining interest again and various variations are being proposed to solve the problems with the naive idea, for instance a small non-[[minimal coupling]] of the Higgs field to [[gravity]] (see e.g. \hyperlink{Atkins12}{Atkins 12}, \hyperlink{Kamada12}{Kamada 12}, \hyperlink{Kehagias12}{Kehagias 12}). In particular, the near-criticality of the Higgs potential (see \href{Higgs+field#Curiously}{there}) has been argued to be just the right condition to make Higgs inflation viable (\hyperlink{Jegerlehner13}{Jegerlehner 13}, \hyperlink{Jegerlehner14}{Jegerlehner 14}, \hyperlink{Jegerlehner15}{Jegerlehner 15}, \hyperlink{Jegerlehner18}{Jegerlehner 18}), for review see also \hyperlink{Rubio18}{Rubio 18}. \hypertarget{axion_inflation}{}\subsubsection*{{Axion inflation}}\label{axion_inflation} see \emph{[[axion inflation]]} \hypertarget{higher_curvature_inflation_starobinsky_model}{}\subsubsection*{{Higher curvature inflation (Starobinsky model)}}\label{higher_curvature_inflation_starobinsky_model} It is possible that instead of the inflaton being a fundamental [[scalar field]], it is an effective result of [[higher curvature corrections]] to [[gravity]]. The first such $R^2$ correction leads to the \emph{[[Starobinsky model of cosmic inflation]]}, which sits right in the middle of the parameter space preferred by the PLANCK satellite data. Discussion of inflationary effects of ever higher curvature corrections includes \hyperlink{ArciniegaEdelsteinJaime18}{Arciniega-Edelstein-Jaime 18}, \hyperlink{ABCEHJ18}{ABCEHJ 18}. \hypertarget{ekpyrotic_cosmology}{}\subsubsection*{{Ekpyrotic cosmology}}\label{ekpyrotic_cosmology} See \emph{[[ekpyrotic cosmology]]}. \hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts} \begin{itemize}% \item [[eternal cosmic inflation]] \item [[cosmology]] \item [[FRW model]] \item [[big bang]], [[steady state model]] \end{itemize} [[!include fields and quanta - table]] \hypertarget{references}{}\subsection*{{References}}\label{references} \hypertarget{reviews}{}\subsubsection*{{Reviews}}\label{reviews} \begin{itemize}% \item [[Andrei Linde]], \emph{Particle Physics and Inflationary Cosmology}, Harwood, Chur (1990). \item A. R. Liddle, D. H. Lyth, \emph{Cosmological inflation and large-scale structure}, Cambridge University Press (2000). \item Shinji Tsujikawa, \emph{Introductory review of cosmic inflation}, lecture notes given at The Second Tah Poe School on Cosmology \emph{Modern Cosmology}, Naresuan (2003) (\href{http://arxiv.org/abs/hep-ph/0304257}{arXiv:hep-ph/0304257}). \item Jerome Martin, Christophe Ringeval, Vincent Vennin, \emph{Encyclopaedia Inflationaris} (\href{http://arxiv.org/abs/1303.3787}{arXiv:1303.3787}) \item Jerome Martin, \emph{The Theory of Inflation} (\href{https://arxiv.org/abs/1807.11075}{arXiv:1807.11075}) \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}) \item Wikipedia, \emph{\href{http://en.wikipedia.org/wiki/Inflation_%28cosmology%29}{Inflation (cosmology)}} \end{itemize} \hypertarget{original_articles}{}\subsubsection*{{Original articles}}\label{original_articles} \begin{itemize}% \item Demosthenes Kazanas, \emph{Dynamics of the universe and spontaneous symmetry breaking}, Astrophysical Journal, Part 2 - Letters to the Editor, vol. 241, Oct. 15, 1980, p. L59-L63 (\href{http://adsabs.harvard.edu/doi/10.1086/183361}{web}) \item [[Alan Guth]], Phys. Rev. D 23, 347 (1981). \item K. Sato, Mon. Not. R. Astron. Soc. 195, 467 (1981); Phys. Lett. 99B, 66 (1981) \item [[Andrei Linde]], Phys. Lett. 108B, 389 (1982) \item A. Albrecht and [[Paul Steinhardt]], Phys. Rev. Lett. 48, 1220 (1982) \item [[Andrei Linde]], Phys. Lett. 129B, 177 (1983). \end{itemize} \hypertarget{ReferencesExperimentalEvidence}{}\subsubsection*{{Experimantal evidence}}\label{ReferencesExperimentalEvidence} \begin{itemize}% \item C. L. Bennett et al. \emph{First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results}, Astrophys.J.Suppl.148:1 (2003) (\href{http://arxiv.org/abs/astro-ph/0302207}{arXiv:astro-ph/0302207}) \item H .V. Peiris et al, \emph{First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation}, Astrophys.J.Suppl.148:213,2003 (\href{http://arxiv.org/abs/astro-ph/0302225}{arXiv:astro-ph/0302225}) \item [[Planck Collaboration]], \emph{Planck 2013 results. XXII. Constraints on inflation} (\href{http://arxiv.org/abs/1303.5082}{arXiv:1303.5082}) \begin{itemize}% \item Resonaances, \emph{\href{http://resonaances.blogspot.de/2013/04/planck-about-inflation.html}{Planck about inflation}} \item [[Andrei Linde]], \emph{Inflationary Cosmology after Planck 2013} (\href{http://arxiv.org/abs/1402.0526}{arXiv:1402.0526}) \end{itemize} \item \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://www.cosmos.esa.int/documents/387566/522789/Planck_2015_Results_I_Overview_Products_Results.pdf/14d90465-03c2-4e3c-b8d1-73181248673d}{pdf}) \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} \hypertarget{inflation_from_higher_curvature_corrections}{}\subsubsection*{{Inflation from higher curvature corrections}}\label{inflation_from_higher_curvature_corrections} Besides the references at \emph{[[Starobinsky model of cosmic inflation]]} the following discuss inflation driven by [[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} \hypertarget{ReferencesHiggsInflation}{}\subsubsection*{{Higgs field inflation}}\label{ReferencesHiggsInflation} Literature discussing whether or how the [[Higgs field]] might be identified as the inflaton field includes \begin{itemize}% \item Michael Atkins, \emph{Could the Higgs boson be the inflaton?}, talk (March 2012) (\href{http://indico.cern.ch/getFile.py/access?resId=0&materialId=slides&confId=180122}{pdf}) \item Kohei Kamada, \emph{Generalized Higgs inflation models}, talk at PLANCK 2012 (May 2012)(\href{http://planck12.fuw.edu.pl/talks/kamada.pdf}{pdf}) \item [[Alex Kehagias]], \emph{New Higgs inflation}, talk (September 2012) (\href{http://www.physics.ntua.gr/corfu2010/Talks/kehagias@central_ntua_gr_01.pdf}{pdf}) \item Takehiro Nabeshima, \emph{A model for Higgs inflation and its testability at the ILC}, talk (October 2012) (\href{http://ilcagenda.linearcollider.org/getFile.py/access?contribId=64&sessionId=8&resId=0&materialId=slides&confId=5468}{pdf}) \item Javier Rubio, \emph{Higgs inflation}, Front. Astron. Space Sci. 5:50 (2019) (\href{https://arxiv.org/abs/1807.02376}{arXiv:1807.02376}) \end{itemize} A popular account in the context of the 2013 [[Plack Collaboration]] results is in \begin{itemize}% \item [[Matthew Strassler]], \emph{\href{http://profmattstrassler.com/2013/03/26/cosmic-conflation-the-higgs-the-inflaton-and-spin/}{Cosmic Conflation: The Higgs, The Inflaton, and Spin}} \end{itemize} Discussion of Higgs inflation with emphasis on relation to the \href{Higgs+field#Curiously}{near-criticality of the Higgs field}: \begin{itemize}% \item [[Fred Jegerlehner]], \emph{The hierarchy problem of the electroweak Standard Model revisited} (\href{https://arxiv.org/abs/1305.6652}{arXiv:1305.6652}) \item [[Fred Jegerlehner]], \emph{Higgs inflation and the cosmological constant}, Acta Phys.Polon. B45 (2014) 1215-1254 (\href{https://arxiv.org/abs/1402.3738}{arXiv:1402.3738}) \item [[Fred Jegerlehner]], \emph{About the role of the Higgs boson in the evolution of the early universe} (\href{https://arxiv.org/abs/1406.3658}{arXiv:1406.3658}) \item [[Fred Jegerlehner]], \emph{The hierarchy problem and the cosmological constant problem in the Standard Model} (\href{https://arxiv.org/abs/1503.00809}{arXiv:1503.00809}) \item [[Fred Jegerlehner]], \emph{The Hierarchy Problem and the Cosmological Constant Problem Revisited -- A new view on the SM of particle physics} (\href{https://arxiv.org/abs/1812.03863}{arXiv:1812.03863}) \end{itemize} \hypertarget{ReferencesHiggsInflation}{}\subsubsection*{{Gauge field inflation}}\label{ReferencesHiggsInflation} Literature discussing whether or how [[gauge field]] might be identified as the inflaton field include \begin{itemize}% \item A. Maleknejad, M. M. Sheikh-Jabbari, J. Soda, \emph{Gauge Fields and Inflation} (\href{http://arxiv.org/abs/1212.2921}{arXiv:1212.2921}) \end{itemize} \hypertarget{string_modeled_inflation}{}\subsubsection*{{String modeled inflation}}\label{string_modeled_inflation} In [[string theory]] the [[inflaton]] field can be modeled by various effects, such as \begin{itemize}% \item [[open string]] stretching between [[D-brane]]-[[anti D-brane]] pairs. \end{itemize} For review and further pointers to the literature see \begin{itemize}% \item Cliff Burgess, M. Cicoli, F. Quevedo, \emph{String Inflation After Planck 2013} (\href{http://arxiv.org/abs/1306.3512}{arXiv:1306.3512}) \item [[Daniel Baumann]], Liam McAllister, \emph{Inflation and String Theory} (\href{https://arxiv.org/abs/1404.2601}{arXiv:1404.2601}) \end{itemize} See also at \emph{[[string phenomenology]]}. [[!redirects inflation]] [[!redirects inflaton]] [[!redirects inflatons]] [[!redirects inflaton field]] [[!redirects inflaton fields]] [[!redirects Higgs inflation]] \end{document}