Theory of Cosmological Perturbations  

General Theory > s.a. perturbations in general relativity [gauge-invariant, gravitational waves].
* Idea: Perturbations are almost always done by expanding the metric around FLRW spacetimes as background.
* Motivation: The evolution of cosmological perturbations of an averaged FLRW model allows us to make predictions for structure formation and cosmological radiation backgrounds, that can be checked against observation; The linearized theory can be trusted because the perturbations of interest are currently of order 1, so they must have been small in the past (gravity enhances them in time).
* Weinberg theorem: There always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales.
@ Reviews: Mukhanov et al PRP(92); Tsagas LNP(02)ap; Brandenberger LNP(04)ht/03, ht/05-ln; Straumann AdP(06)hp/05-ln; Tsagas et al PRP(08)-a0705; Malik & Matravers CQG(08)-a0804 [concise intro]; Malik & Wands PRP(09)-a0809; Gorbunov & Rubakov 10 [and inflation]; Lesgourgues a1302-ln.
@ Parametric resonance / amplification: Finelli & Gruppuso PLB(01)hp/00 [electromagnetic].
@ Correlation functions: Marcori & Pereira JCAP(17)-a1612 [from isometries of the background metric].
@ Related topics: Couch & Torrence CJP(96) [gauging]; Lukash PU(06)ap [tensor and scalar perturbations]; Capozziello et al PS(09)-a0905 [tomographic description]; Allen & Rendall a0906 [initial singularity and late-time asymptotics]; Christopherson PhD-a1106 [applications, higher-order]; Eingorn et al EPJC(15)-a1407 [need for vanishing average perturbations]; Akhshik et al JCAP(15)-a1508 [Weinberg theorem, loopholes].
blue bullet Related topics: see averaging; quantum cosmological perturbations.

Higher-Order Perturbations > s.a. gravitating many-body systems.
@ Non-Gaussianity: Bartolo et al JCAP(04); Cabass et al JCAP(17)-a1612.
@ Second-order: Malik & Wands CQG(04)ap/03; Nakamura PRD(06)gq, PTP(07)gq/06, PTP(09)-a0812 [gauge-invariant], a0901-proc [consistency conditions]; Hwang & Noh PRD(07); Senatore et al JCAP(09)-a0812; Noh et al PRL(09) [infrared divergence of Einstein contribution to density power spectrum]; Nakamura PRD(09) [matter fields], AiA(10)-a1001 [status], a1001-proc [with scalar field]; Appignani et al JCAP(10), a1002-MG12 [non-canonical scalars, ambiguities]; Hamazaki PRD(11)-a1107 [gradient expansion, leading order]; Anselmi et al JCAP(11) [next-to-leading-order resummations]; Uggla & Wainwright GRG(13)-a1203 [minimal approach], CQG(14)-a1312 [simple expressions]; Domènech & Sasaki PRD(18)-a1709 [Hamiltonian approach]; Uggla & Wainwright CQG(19)-a1801 [better formulation], PRD(18)-a1808 [minimal, dynamics]; Wang & Zhang PRD(19)-a1905; Nakamura a1912-ch [gauge-invariant, rev].
@ Second-order, curvature perturbations: Dias et al JCAP(15)-a1410; Carrilho & Malik JCAP(16)-a1507 [vector and tensor contributions].
@ Third and higher-order: Hwang & Noh JCAP(07)-a0704 [pressureless fluids]; Christopherson & Malik JCAP(09)-a0909 [gauge transformations]; Prokopec & Weenink JCAP(13)-a1304 [third-order gauge invariant action for scalar-graviton interactions in the Jordan frame]; Nakamura CQG(14)-a1403 [recursive structure]; Nandi & Shankaranarayanan JCAP(15)-a1502 [constraint consistency between two approaches], JCAP(16)-a1512, JCAP(16)-a1606, Nandi a1707-PhD [Hamiltonian analysis].
@ Non-linear effects: Matarrese & Pietroni MPLA(08)ap/07, JCAP(07)ap, comment Rosten JCAP(08)-a0711 [renormalization group and structure]; Pietroni JCAP(08)-a0806; Juszkiewicz et al JCAP(10)-a0901; Langlois & Vernizzi CQG(10)-a1003 [geometrical approach]; Christopherson CTP(12)-a1111-GRF [signatures of non-linear perturbation theory]; Christopherson et al CQG(11) [comparing two approaches]; Macpherson et al PRD(17)-a1611 [numerical approach].

Approaches and Types
@ Effective field theory: Piazza & Vernizzi CQG(13)-a1307; Senatore JCAP(15)-a1406 [bias]; Burgess et al JHEP-a1408 [open systems, and the quantum-to-classical transition]; Vlah et al JCAP(15)-a1506 [Lagrangian framework].
@ Gauge-invariant variables: Malik & Matravers GRG(13)-a1206; Giesel et al CQG(18)-a1801 [using geometrical clocks], CQG(19)-a1811 [dynamics of Dirac observables].
@ Other approaches: Bertschinger ap/01-proc; Bartolo et al PRD(04)ap/03 [scalar + fluid]; Bashinsky PRD(06)ap/04 [cmb and matter]; Carbone & Matarrese PRD(05)ap/04 [evolution framework]; Casadio et al PRD(05)gq/04 [WKB analysis]; Strokov AR(07)ap/06 [hydrodynamical and field approaches]; Enqvist et al PRD(07)gq [covariant]; Carlson et al PRD(09)-a0905 [assessment]; Green & Wald PRD(11)-a1011 [mathematically precise framework]; Uggla & Wainwright CQG(11)-a1102 [simple and concise form]; Matsumoto PRD(11)-a1105 [ΛCDM model]; Miedema a1106 [and the evolution of small-scale inhomogeneities]; Szapudi & Czinner CQG(12)-a1111 [based on Lie-group representations]; Pietroni et al JCAP(12) [coarse-grained]; Hortua & Castañeda a1407-proc [equivalence between formulations]; Rostworowski a1902 [Regge-Wheeler formalism].
@ Long-wavelength perturbations: Unruh ap/98 [exact solutions]; Carroll et al PRD(14)-a1310 [consistent effective theory].
@ Other types: Afshordi & Johnson PRD(18)-a1708 [cosmological zero modes].
> Specific spacetimes and theories: see cosmological models; models and phenomenology [including other theories]; types of black holes [primordial].

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