{"arxiv_id":"hep-th/0005032","incoming":{"papers":9,"sentences":13,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":3,"sentences":3,"quotes":[{"arxiv_id":"1009.4200","title":"A Breathing Mode for Warped Compactifications","url":"/paper/1009.4200","section":"Warped Perturbation Theory","sentence":"Inspired by the similarities between perturbations in cosmological and warped backgrounds, in this section we will develop a similar formalism for warped perturbation theory, following [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2604.09925","title":"How to deal with conformal and pure scale-invariant theories of gravity in d dimensions?","url":"/paper/2604.09925","section":"The ghosts in five dimensions","sentence":"In particular, we can apply the scalar-vector-tensor decomposition [ref] for the metric perturbations $δg_μν$ around the anisotropic background $g_μν= g_μν^(0)+δg_μν$: [equation] with $i$ accounting for the $x,y,$ and $z$ coordinates.","intent_p":1.0,"contests_p":null},{"arxiv_id":"2506.18775","title":"Conformal and pure scale-invariant gravities in d dimensions","url":"/paper/2506.18775","section":"Perturbations","sentence":"Let us now consider the perturbations around the previous background, similarly to the formalism developed in [ref] : [equation] where [equation] Here, $i$ runs over $x,y,$ and $z$ coordinates.","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1012.1199","title":"Density perturbations in braneworld cosmology and primordial black holes","url":"/paper/1012.1199","section":"Introduction","sentence":"Cosmological perturbation theory in braneworld cosmology also has some distinct features [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1009.4200","title":"A Breathing Mode for Warped Compactifications","url":"/paper/1009.4200","section":"Introduction","sentence":"The study of dynamics and fluctuations on warped compactifications is much more complicated than the standard Kaluza-Klein (KK) reduction on direct product spaces, and has been studied extensively by a number of authors [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2501.13581","title":"Analysis of inflationary models in higher-dimensional uniform inflation","url":"/paper/2501.13581","section":"Cosmological perturbation in $D+4$ dimensions","sentence":"As mentioned in [ref] , the general formalism for the cosmological perturbations in brane world theories has been studied [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"1004.3962","title":"Brane-World Gravity","url":"/paper/1004.3962","section":"Brane-World Cosmology: Perturbations","sentence":"The theory of gauge-invariant perturbations in brane-world cosmology has been extensively investigated and developed [ref] and is qualitatively well understood.","intent_p":0.91,"contests_p":null},{"arxiv_id":"2311.17680","title":"Cosmological perturbations from five-dimensional inflation","url":"/paper/2311.17680","section":"The scalar perturbations","sentence":"The general formalism for the study of cosmological perturbations in brane world theories has been studied extensively (see for instance [ref] and reference therein).","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":5},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-th/0005032"}}