A general proof of the conservation of the curvature perturbation

By D. Lyth, Karim A. Malik, Misao Sasaki. 2004

853 citations recorded by the source corpus.

Without invoking a perturbative expansion, we define the cosmological curvature perturbation, and consider its behaviour assuming that the universe is smooth over a sufficiently large comoving scale. The equations are simple, resembling closely the first-order equations, and they lead to results which generalize those already proven in linear perturbation theory and (in part) in second-order perturbation theory. In particular, the curvature perturbation is conserved provided that the pressure is a unique function of the energy density.

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Citations in the corpus

Rapidly-Varying Speed of Sound, Scale Invariance and Non-Gaussian Signatures (2008, background): “= a(˝)( d˝2 + ed~x2): (3.5) From = v=qand the explicit solution (2.5), we see that the growing mode is ˘1=qy. In Case I, which includes standard in ation, q˘1=y, and !const:on super-Hubble scales [34, 35]. Thus these backgrounds are stable. In Case II, however, q˘y2, and the growth of as k!0 indicat”
Non-linear isocurvature perturbations and non-Gaussianities (2008, background): “On scales larger than the Hubble radius, the above definitions are equivalent to the non-linear curvature perturbation on uniform density hypersurfaces as defined in [22, 23],”
The (not so) squeezed limit of the primordial 3-point function (2011, background): “Indeed, the δN formalism [30] relates, locally in space, (3)There is a typo in the published version of the paper of their expression A (I) ǫ2 , which has been corrected in the latest preprint version.”
Phenomenology of a pseudo-scalar inflaton: naturally large nongaussianity (2011, methodology): “Beyond linear order, the relationship between ζ and δφ is simplest to derive using the δN -formalism [46].”
Primordial non-Gaussianities in single-field inflation (2005, unknown): “ilt of this spectrum is given by n− 1 = dln∆2(k) dlnk ≈ −2ε− η. (39) The quantity R is conserved outside the horizon [20, 45], which is the analogous result to that of conventional slow-roll inﬂation [42, 46]. 4. The third-order action 4.1. General form of the action We now turn to the central calcu”
On the consistency relation of the three-point function in single-field inflation (2007, background): “This assumption is not necessary for the proof of the consistency relation, as it was previously noted in [1, 18], and more general fluctuations can be easily included.”
Primordial bispectrum from multifield inflation with nonminimal couplings (2012, background): “[49] D.”
Inflation, Cosmic Perturbations and Non-Gaussianities (2013, methodology): “There are a few ways to do this and here we follow the method of [78].”
Inflationary trispectrum from graviton exchange (2008, methodology): “Our eventual aim is to compute the four-point function of the comoving curvature perturbation, R, which on super-Hubble scales is equal to the curvature perturbation on uniform density slices, ζ [37, 38, 39].”