CorpInflation.tex

\documentclass[aps, prd, preprint, superscriptaddress, tightenlines, nofootinbib]{revtex4}

\include{header}

%%%%%%%%%%%%%%%%%%%%%%% BEGIN DOCUMENT %%%%%%%%%%%%%%%%
\begin{document}

\title{\bf Generalised Corpuscular Inflation}

\author{Florian K{\"u}hnel}
\email{florian.kuhnel@fysik.su.se}
\affiliation{The Oskar Klein Centre for Cosmoparticle Physics,
	Department of Physics,
	Stockholm University,
	AlbaNova,
	106\.91 Stockholm,
	Sweden}

\author{Marit Sandstad}
\email{marit.sandstad@astro.uio.no}
\affiliation{Institute of Theoretical Astrophysics,
	University of Oslo,
	P.O.~Box 1029 Blindern,
	N-0315 Oslo,
	Norway}

\date{\formatdate{\day}{\month}{\year}, \currenttime}

\begin{abstract}
We extend the corpuscular formulation of inflation from $\phi^2m^2$ to general single field inflation. 
We use these results to obtain the corpuscularly corrected values for $r$ and $n_s$, finally comparing
these to results from current observations. This shows how the constraints on inflation are changed 
when a the graviton condensate view of gravity is employed.
\end{abstract}

\maketitle


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
\label{sec:Introduction}
\setcounter{equation}{0}

\noindent
\input{Introduction.tex}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Corpuscular inflation}
\label{sec:Main-Part}
\setcounter{equation}{0}

\noindent
\input{Main-Part.tex}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Discussion and Outlook}
\label{sec:Discussion-and-Outlook}
\setcounter{equation}{0}

\noindent
\input{Conclusion.tex}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\acknowledgements
\vspace{-4mm}F.~K.~acknowledges support from the Swedish Research Council (VR)
through the Oskar Klein Centre, and thanks the Institute of Theoretical Astrophysics at the University of Oslo where part of this work as been performed. M.S.~thanks ... . It is a pleasure to thank ... for fruitful discussions.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}

\bibitem{Starobinski}
	A.~A.~Starobinsky,
	%``A new Type of Isotropic Cosmological Models without Singularity,''
	Phys. Lett. B 91, 99 (1980).

%\cite{Guth:1980zm}
\bibitem{Guth:1980zm}
	A.~H.~Guth,
	%``The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,''
	Phys.~Rev.~D {\bf 23} 347, (1981).
	%%CITATION = PHRVA,D23,347;
	%5097 citations counted in INSPIRE as of 10 Dec 2014

\bibitem{Planck}
	P.~A.~R.~Ade {\it et al.} [Planck Collaboration],
	%``Planck 2013 results. XXII. Constraints on inflation,''
	Astron.~Astrophys.~{\bf 571}, A22 (2014).
	%[arXiv:1303.5082 [astro-ph.CO]].
	%%CITATION = ARXIV:1303.5082;
	%928 citations counted in INSPIRE as of 23 gen 2015
	P.~A.~R.~Ade {\it et al.}  [BICEP2 and Planck Collaborations],
	``A Joint Analysis of BICEP2/Keck Array and Planck Data,''
	arXiv:1502.00612 [astro-ph.CO].
	%%CITATION = ARXIV:1502.00612;%%

%\cite{Vilenkin:1983xq}
\bibitem{Vilenkin:1983xq} 
	A.~Vilenkin,
	%``The Birth of Inflationary Universes,''
	Phys.~Rev.~D {\bf 27}, 2848 (1983).
	%%CITATION = PHRVA,D27,2848;%%
	%661 citations counted in INSPIRE as of 05 mar 2015

%\cite{Dvali:2013eja}
\bibitem{Dvali:2013eja}
	G.~Dvali and C.~Gomez,
	%``Quantum Compositeness of Gravity: Black Holes, AdS and Inflation,''
	JCAP {\bf 1401} (2014) 01, 023.
	%[arXiv:1312.4795 [hep-th]].
	%%CITATION = ARXIV:1312.4795;
	%19 citations counted in INSPIRE as of 10 Dec 2014

\bibitem{DvaliGomez}
	G.~Dvali and C.~Gomez,
	%``Quantum Compositeness of Gravity: Black Holes, AdS and Inflation,''
	JCAP {\bf 01}, 023 (2014);
	% arXiv:1312.4795 [hep-th];
	%``Black Hole's Information Group,''
	%arXiv:1307.7630;
	%``Black Holes as Critical Point of Quantum Phase Transition,''
	Eur.~Phys.~J.~C {\bf 74}, 2752 (2014);
	%[arXiv:1207.4059 [hep-th]];
	%``Black Hole's 1/N Hair,''
	Phys.~Lett.~B {\bf 719}, 419 (2013);
	%[arXiv:1203.6575 [hep-th]];
	%``Landau-Ginzburg Limit of Black Hole's Quantum Portrait: Self Similarity and Critical Exponent,''
	Phys.~Lett.~B {\bf 716}, 240 (2012);
	%[arXiv:1203.3372 [hep-th]];
	%``Black Hole's Quantum N-Portrait,''
	Fortsch.~Phys.~{\bf 61}, 742 (2013);
	%[arXiv:1112.3359 [hep-th]];
	G.~Dvali, C.~Gomez and S.~Mukhanov,
	``Black Hole Masses are Quantized,''
	arXiv:1106.5894 [hep-ph].

%\cite{Dvali:2014gua}
\bibitem{Dvali:2014gua}
	G.~Dvali and C.~Gomez,
	``Quantum Exclusion of Positive Cosmological Constant?,''
	arXiv:1412.8077 [hep-th].
	%%CITATION = ARXIV:1412.8077;

%\cite{Flassig:2012re}
\bibitem{Flassig:2012re}
	D.~Flassig, A.~Pritzel and N.~Wintergerst,
	%``Black Holes and Quantumness on Macroscopic Scales,''
	Phys.~Rev.~D {\bf 87} (2013) 084007.
	%[arXiv:1212.3344].
	%%CITATION = ARXIV:1212.3344;
	%9 citations counted in INSPIRE as of 21 Feb 2014

%\cite{Casadio:2015xva}
\bibitem{Casadio:2015xva} 
	R.~Casadio, F.~Kuhnel and A.~Orlandi,
	``Consistent Cosmic Microwave Background Spectra from Quantum Depletion,''
	arXiv:1502.04703 [gr-qc].
	%%CITATION = ARXIV:1502.04703;%%

\bibitem{Kuhnel:2014oja}
	F.~Kuhnel,
	%``Bose-Einstein Condensates with Derivative and Long-Range Interactions as Set-Ups for Analog Black Holes,''
	Phys.~Rev.~D {\bf 90}, no. 8, 084024 (2014);
	%[arXiv:1312.2977 [gr-qc]]
	%%CITATION = ARXIV:1312.2977;
	%4 citations counted in INSPIRE as of 23 Jan 2015
	F.~Kuhnel and B.~Sundborg,
	``Modified Bose-Einstein Condensate Black Holes in d Dimensions,''
	arXiv:1401.6067 [hep-th];
	%%CITATION = ARXIV:1401.6067;
	%2 citations counted in INSPIRE as of 23 Jan 2015
	F.~Kuhnel and B.~Sundborg,
	%``High-Energy Gravitational Scattering and Bose-Einstein Condensates of Gravitons,''
	JHEP {\bf 1412}, 016 (2014);
	%[arXiv:1406.4147 [hep-th]];
	%%CITATION = ARXIV:1406.4147;
	%4 citations counted in INSPIRE as of 23 Jan 2015
	F.~Kuhnel and B.~Sundborg,
	%``Decay of Graviton Condensates and their Generalizations in Arbitrary Dimensions,''
	Phys.~Rev.~D {\bf 90}, no. 6, 064025 (2014).
	%[arXiv:1405.2083 [hep-th]];
	%%CITATION = ARXIV:1405.2083;
	%4 citations counted in INSPIRE as of 23 Jan 2015

\bibitem{mueckPT}
	W.~M{\"u}ck and G.~Pozzo,
	%``Quantum Portrait of a Black Hole with P\"oschl-Teller Potential,''
	JHEP {\bf 1405}, 128 (2014).
	% [arXiv:1403.1422 [hep-th]].
	%%CITATION = ARXIV:1403.1422;%%
	%1 citations counted in INSPIRE as of 04 Feb 2015

%\cite{Hofmann:2014jya}
\bibitem{Hofmann}
	S.~Hofmann and T.~Rug,
	``A Quantum Bound-State Description of Black Holes,''
	arXiv:1403.3224 [hep-th];
	%%CITATION = ARXIV:1403.3224;
	%5 citations counted in INSPIRE as of 15 Dec 2014
	L.~Gruending, S.~Hofmann, S.~M{\"u}ller and T.~Rug,
	``Probing the Constituent Structure of Black Holes,''
	arXiv:1407.1051 [hep-th].
	%%CITATION = ARXIV:1407.1051;%%
	%2 citations counted in INSPIRE as of 05 Mar 2015
  
  %\cite{Binetruy:2012kx}
\bibitem{Binetruy:2012kx}
	P.~Binetruy,
	``Vacuum energy, holography and a quantum portrait of the visible Universe,''
	arXiv:1208.4645 [gr-qc].
	%%CITATION = ARXIV:1208.4645;
	%5 citations counted in INSPIRE as of 21 Feb 2014

%\cite{Kuhnel:2014gja}
\bibitem{Kuhnel:2014gja} 
	F.~Kuhnel,
	``Thoughts on the Vacuum Energy in the Quantum N-Portrait,''
	arXiv:1408.5897 [gr-qc].
	%%CITATION = ARXIV:1408.5897;%%

%\cite{Casadio:2014vja}
\bibitem{Casadio:2014vja}
	R.~Casadio, A.~Giugno, O.~Micu and A.~Orlandi,
	%``Black holes as self-sustained quantum states, and Hawking radiation,''
	Phys.~Rev.~D {\bf 90} (2014) 8, 084040.
	%[arXiv:1405.4192 [hep-th]].
	%%CITATION = ARXIV:1405.4192;
	%4 citations counted in INSPIRE as of 15 Dec 2014

\bibitem{Brustein}
%\bibitem{Brustein:2012jn}
	R.~Brustein,
	%Origin of the blackhole information paradox,
	Fortsch.~Phys.~{\bf 62}, 255 (2014);
	R.~Brustein and A.~J.~M.~Medved,
	%``Horizons of semiclassical black holes are cold,''
	JHEP {\bf 1406}, 057 (2014);
	%%CITATION = ARXIV:1312.0880;%%
	%8 citations counted in INSPIRE as of 05 mar 2015%\bibitem{Brustein:2013ena}
	R.~Brustein and A.~J.~M.~Medved,
	%``Phases of information release during black hole evaporation,''
	JHEP {\bf 1402}, 116 (2014).


\end{thebibliography}

\end{document}