End of cosmology paper
Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
This commit is contained in:
		| @@ -55,6 +55,7 @@ | |||||||
| \providecommand{\qed}{\textsc{QED}\xspace} | \providecommand{\qed}{\textsc{QED}\xspace} | ||||||
| \providecommand{\qcd}{\textsc{QCD}\xspace} | \providecommand{\qcd}{\textsc{QCD}\xspace} | ||||||
| \providecommand{\ope}{\textsc{o.p.e.}\xspace} | \providecommand{\ope}{\textsc{o.p.e.}\xspace} | ||||||
|  | \providecommand{\ode}{\textsc{o.d.e.}\xspace} | ||||||
| \providecommand{\dof}{\textsc{d.o.f.}\xspace} | \providecommand{\dof}{\textsc{d.o.f.}\xspace} | ||||||
| \providecommand{\cy}{\textsc{CY}\xspace} | \providecommand{\cy}{\textsc{CY}\xspace} | ||||||
| \providecommand{\lhs}{\textsc{lhs}\xspace} | \providecommand{\lhs}{\textsc{lhs}\xspace} | ||||||
| @@ -91,6 +92,7 @@ | |||||||
| \renewcommand{\vartheta}{\ensuremath{\upvartheta}\xspace} | \renewcommand{\vartheta}{\ensuremath{\upvartheta}\xspace} | ||||||
| \renewcommand{\varpi}{\ensuremath{\upvarpi}\xspace} | \renewcommand{\varpi}{\ensuremath{\upvarpi}\xspace} | ||||||
| \renewcommand{\varphi}{\ensuremath{\upvarphi}\xspace} | \renewcommand{\varphi}{\ensuremath{\upvarphi}\xspace} | ||||||
|  | \renewcommand{\varsigma}{\ensuremath{\upvarsigma}\xspace} | ||||||
| \renewcommand{\Gamma}{\ensuremath{\Upgamma}\xspace} | \renewcommand{\Gamma}{\ensuremath{\Upgamma}\xspace} | ||||||
| \renewcommand{\Delta}{\ensuremath{\Updelta}\xspace} | \renewcommand{\Delta}{\ensuremath{\Updelta}\xspace} | ||||||
| \renewcommand{\Theta}{\ensuremath{\Uptheta}\xspace} | \renewcommand{\Theta}{\ensuremath{\Uptheta}\xspace} | ||||||
| @@ -130,6 +132,7 @@ | |||||||
| \providecommand{\dvartheta}{\ensuremath{\dot{\upvartheta}}\xspace} | \providecommand{\dvartheta}{\ensuremath{\dot{\upvartheta}}\xspace} | ||||||
| \providecommand{\dvarpi}{\ensuremath{\dot{\upvarpi}}\xspace} | \providecommand{\dvarpi}{\ensuremath{\dot{\upvarpi}}\xspace} | ||||||
| \providecommand{\dvarphi}{\ensuremath{\dot{\upvarphi}}\xspace} | \providecommand{\dvarphi}{\ensuremath{\dot{\upvarphi}}\xspace} | ||||||
|  | \providecommand{\dvarsigma}{\ensuremath{\dot{\upvarsigma}}\xspace} | ||||||
| \providecommand{\dGamma}{\ensuremath{\dot{\Upgamma}}\xspace} | \providecommand{\dGamma}{\ensuremath{\dot{\Upgamma}}\xspace} | ||||||
| \providecommand{\dDelta}{\ensuremath{\dot{\Updelta}}\xspace} | \providecommand{\dDelta}{\ensuremath{\dot{\Updelta}}\xspace} | ||||||
| \providecommand{\dTheta}{\ensuremath{\dot{\Uptheta}}\xspace} | \providecommand{\dTheta}{\ensuremath{\dot{\Uptheta}}\xspace} | ||||||
| @@ -169,6 +172,7 @@ | |||||||
| \providecommand{\bvartheta}{\ensuremath{\overline{\upvartheta}}\xspace} | \providecommand{\bvartheta}{\ensuremath{\overline{\upvartheta}}\xspace} | ||||||
| \providecommand{\bvarpi}{\ensuremath{\overline{\upvarpi}}\xspace} | \providecommand{\bvarpi}{\ensuremath{\overline{\upvarpi}}\xspace} | ||||||
| \providecommand{\bvarphi}{\ensuremath{\overline{\upvarphi}}\xspace} | \providecommand{\bvarphi}{\ensuremath{\overline{\upvarphi}}\xspace} | ||||||
|  | \providecommand{\bvarsigma}{\ensuremath{\overline{\upvarsigma}}\xspace} | ||||||
| \providecommand{\bGamma}{\ensuremath{\overline{\Upgamma}}\xspace} | \providecommand{\bGamma}{\ensuremath{\overline{\Upgamma}}\xspace} | ||||||
| \providecommand{\bDelta}{\ensuremath{\overline{\Updelta}}\xspace} | \providecommand{\bDelta}{\ensuremath{\overline{\Updelta}}\xspace} | ||||||
| \providecommand{\bTheta}{\ensuremath{\overline{\Uptheta}}\xspace} | \providecommand{\bTheta}{\ensuremath{\overline{\Uptheta}}\xspace} | ||||||
| @@ -208,6 +212,7 @@ | |||||||
| \providecommand{\tvartheta}{\ensuremath{\widetilde{\upvartheta}}\xspace} | \providecommand{\tvartheta}{\ensuremath{\widetilde{\upvartheta}}\xspace} | ||||||
| \providecommand{\tvarpi}{\ensuremath{\widetilde{\upvarpi}}\xspace} | \providecommand{\tvarpi}{\ensuremath{\widetilde{\upvarpi}}\xspace} | ||||||
| \providecommand{\tvarphi}{\ensuremath{\widetilde{\upvarphi}}\xspace} | \providecommand{\tvarphi}{\ensuremath{\widetilde{\upvarphi}}\xspace} | ||||||
|  | \providecommand{\tvarsigma}{\ensuremath{\widetilde{\upvarsigma}}\xspace} | ||||||
| \providecommand{\tGamma}{\ensuremath{\widetilde{\Upgamma}}\xspace} | \providecommand{\tGamma}{\ensuremath{\widetilde{\Upgamma}}\xspace} | ||||||
| \providecommand{\tDelta}{\ensuremath{\widetilde{\Updelta}}\xspace} | \providecommand{\tDelta}{\ensuremath{\widetilde{\Updelta}}\xspace} | ||||||
| \providecommand{\tTheta}{\ensuremath{\widetilde{\Uptheta}}\xspace} | \providecommand{\tTheta}{\ensuremath{\widetilde{\Uptheta}}\xspace} | ||||||
| @@ -247,6 +252,7 @@ | |||||||
| \providecommand{\hvartheta}{\ensuremath{\widehat{\upvartheta}}\xspace} | \providecommand{\hvartheta}{\ensuremath{\widehat{\upvartheta}}\xspace} | ||||||
| \providecommand{\hvarpi}{\ensuremath{\widehat{\upvarpi}}\xspace} | \providecommand{\hvarpi}{\ensuremath{\widehat{\upvarpi}}\xspace} | ||||||
| \providecommand{\hvarphi}{\ensuremath{\widehat{\upvarphi}}\xspace} | \providecommand{\hvarphi}{\ensuremath{\widehat{\upvarphi}}\xspace} | ||||||
|  | \providecommand{\hvarsigma}{\ensuremath{\widehat{\upvarsigma}}\xspace} | ||||||
| \providecommand{\hGamma}{\ensuremath{\widehat{\Upgamma}}\xspace} | \providecommand{\hGamma}{\ensuremath{\widehat{\Upgamma}}\xspace} | ||||||
| \providecommand{\hDelta}{\ensuremath{\widehat{\Updelta}}\xspace} | \providecommand{\hDelta}{\ensuremath{\widehat{\Updelta}}\xspace} | ||||||
| \providecommand{\hTheta}{\ensuremath{\widehat{\Uptheta}}\xspace} | \providecommand{\hTheta}{\ensuremath{\widehat{\Uptheta}}\xspace} | ||||||
| @@ -286,6 +292,7 @@ | |||||||
| \providecommand{\uvartheta}{\ensuremath{\underline{\upvartheta}}\xspace} | \providecommand{\uvartheta}{\ensuremath{\underline{\upvartheta}}\xspace} | ||||||
| \providecommand{\uvarpi}{\ensuremath{\underline{\upvarpi}}\xspace} | \providecommand{\uvarpi}{\ensuremath{\underline{\upvarpi}}\xspace} | ||||||
| \providecommand{\uvarphi}{\ensuremath{\underline{\upvarphi}}\xspace} | \providecommand{\uvarphi}{\ensuremath{\underline{\upvarphi}}\xspace} | ||||||
|  | \providecommand{\uvarsigma}{\ensuremath{\underline{\upvarsigma}}\xspace} | ||||||
| \providecommand{\uGamma}{\ensuremath{\underline{\Upgamma}}\xspace} | \providecommand{\uGamma}{\ensuremath{\underline{\Upgamma}}\xspace} | ||||||
| \providecommand{\uDelta}{\ensuremath{\underline{\Updelta}}\xspace} | \providecommand{\uDelta}{\ensuremath{\underline{\Updelta}}\xspace} | ||||||
| \providecommand{\uTheta}{\ensuremath{\underline{\Uptheta}}\xspace} | \providecommand{\uTheta}{\ensuremath{\underline{\Uptheta}}\xspace} | ||||||
|   | |||||||
										
											
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							| @@ -70,12 +70,19 @@ | |||||||
|  |  | ||||||
| %---- coordinates | %---- coordinates | ||||||
| \newcommand{\pX}{\ensuremath{X'}\xspace} | \newcommand{\pX}{\ensuremath{X'}\xspace} | ||||||
| \newcommand{\kmkr}{\ensuremath{\qty{k_+,\, l,\, \vec{k},\, r}}} |  | ||||||
| \newcommand{\kmr}{\ensuremath{\qty{k_+,\, k_-,\, l,\, r}}} | \newcommand{\kmr}{\ensuremath{\qty{k_+,\, k_-,\, l,\, r}}} | ||||||
|  | \newcommand{\kmkr}{\ensuremath{\qty{k_+,\, l,\, \vec{k},\, r}}} | ||||||
| \newcommand{\kmkrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, l_{\qty(#1)},\, \vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}} | \newcommand{\kmkrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, l_{\qty(#1)},\, \vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}} | ||||||
| \newcommand{\kmrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, k_{\qty(#1)\, -},\,l_{\qty(#1)},\, r_{\qty(#1)}}}} | \newcommand{\kmrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, k_{\qty(#1)\, -},\,l_{\qty(#1)},\, r_{\qty(#1)}}}} | ||||||
| \newcommand{\mkmkr}{\ensuremath{\qty{-k_+,\, -l,\, -\vec{k},\, r}}} | \newcommand{\mkmkr}{\ensuremath{\qty{-k_+,\, -l,\, -\vec{k},\, r}}} | ||||||
| \newcommand{\mkmkrN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -l_{\qty(#1)},\, -\vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}} | \newcommand{\mkmkrN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -l_{\qty(#1)},\, -\vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}} | ||||||
|  | \newcommand{\kmkrgen}{\ensuremath{\qty{k_+,\, p,\, l,\, \vec{k},\, r}}} | ||||||
|  | \newcommand{\kmkrgenN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, p_{\qty(#1)},\, l_{\qty(#1)},\, \vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}} | ||||||
|  | \newcommand{\mkmkrgen}{\ensuremath{\qty{-k_+,\, -p,\, -l,\, -\vec{k},\, r}}} | ||||||
|  | \newcommand{\mkmkrgenN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -p_{\qty(#1)},\, -l_{\qty(#1)},\, -\vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}} | ||||||
|  | \newcommand{\lkrsi}{\ensuremath{\qty{l,\, \vec{k},\, r,\, \sigma_-}}} | ||||||
|  | \newcommand{\lsi}{\ensuremath{l\, \hsigma_-}} | ||||||
|  | \newcommand{\lsiN}[1]{\ensuremath{l_{\qty(#1)}\, \hsigma_{-\, \qty(#1)}}} | ||||||
| \newcommand{\pol}[1]{\ensuremath{\mathcal{E}_{\kmkr\, \underline{#1}}}} | \newcommand{\pol}[1]{\ensuremath{\mathcal{E}_{\kmkr\, \underline{#1}}}} | ||||||
| \newcommand{\polN}[2]{\ensuremath{\mathcal{E}_{\kmkrN{#2}\, \underline{#1}}}} | \newcommand{\polN}[2]{\ensuremath{\mathcal{E}_{\kmkrN{#2}\, \underline{#1}}}} | ||||||
| \newcommand{\polabbrN}[2]{\ensuremath{\mathcal{E}_{\qty(#2)\, \underline{#1}}}} | \newcommand{\polabbrN}[2]{\ensuremath{\mathcal{E}_{\qty(#2)\, \underline{#1}}}} | ||||||
|   | |||||||
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