Adiabatic Modes in Cosmology

By S. Weinberg. 2003

327 citations recorded by the source corpus.

We show that the field equations for cosmological perturbations in the Newtonian gauge always have an adiabatic solution, for which a quantity $\mathcal{R}$ is nonzero and constant in all eras in the limit of large wavelength, so that it can be used to connect observed cosmological fluctuations in this mode with those at very early times. There is also a second adiabatic mode, for which $\mathcal{R}$ vanishes for a large wavelength, and in general there may be nonadiabatic modes as well. These conclusions apply in all eras and whatever the constituents of the universe, under only a mild technical assumption about the wavelength dependence of the field equations for a large wavelength. In the absence of anisotropic inertia, the perturbations in the adiabatic modes are given for a large wavelength by universal formulas in terms of the Robertson-Walker scale factor. We discuss an apparent discrepancy between these results and what appears to be a conservation law in all modes found for a large wavelength in the synchronous gauge: it turns out that, although equivalent, the synchronous and Newtonian gauges suggest inequivalent assumptions about the behavior of the perturbations for a large wavelength.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bc8cc88153f7e12fb00d604aee3561c0b6cc4e8d

How researchers see this paper

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In Astronomy and Astrophysics

1. D. Baumann
2. F. Vernizzi
3. D. Green
4. E. Pajer
5. Tsutomu Kobayashi
6. L. Senatore
7. J. Khoury
8. P. Creminelli

In Nuclear and High Energy Physics

1. D. Baumann
2. F. Vernizzi
3. D. Green
4. E. Pajer
5. P. Creminelli
6. Liam McAllister
7. D. Langlois
8. J. Khoury

Citations in the corpus

• Conformal consistency relations for single-field inflation (2012, methodology): “An adiabatic mode is locally a coordinate redefinition of the unperturbed solution: we thus parallel what Weinberg [14] does in Newtonian gauge and look for the most general transformation of the unperturbed FRW that leaves the metric in ζ-gauge.”
• A unifying description of dark energy (2014, methodology): “However, for the solutions (149) and (150) to be physical we must require that these equations are satisfied for finite k in the k → 0 limit [47], which implies vm = −π , (152) and (M2ǫ)· +HM(2)ǫ− σm =M(2)(1 + αT )λ , (153) with solution ǫ = 1 M2a ∫ t a [ M(2)(1 + αT )λ+ σm ] dt .”
• An infinite set of Ward identities for adiabatic modes in cosmology (2013, methodology): “3 we will generalize Weinberg’s argument [37] to show that certain linear combinations of these transformations can be smoothly extended to physical (4)This does not contradict the usual notion that “comoving gauge completely fixes the gauge,” since this statement assumes that gauge transformations ”
• Cosmology and Fundamental Physics with the Euclid Satellite (2012, unknown): “Perturbations are purely adiabatic when for each component α the quantity ζα ≡ −3Hδρα/ρ̇α is the same (Weinberg 2003; Malik et al. 2003).”
• Equilateral Non-Gaussianity and New Physics on the Horizon (2011, background): “During single-field inflation, the curvature perturbation freezes on superhorizon scales, ζ̇ → 0 [25].”
• Galilean Genesis: An Alternative to inflation (2010, background): “Notice that the constant λ is the value of ζ for the constant solution [7]: indeed it parameterizes a rescaling of the spatial coordinates.”
• FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2008, unknown): “For a recent discussion on this topic, see, e.g., Weinberg (2003). and photons, as axion density fluctuations could be produced during inflation independent of curvature perturbations (which were generated from inflaton fields, and responsible for CMB anisotropies that we observe today), and were…”
• Symmetries and loops in inflation (2012, methodology): “For our purposes, it will be useful to state Weinberg’s proof in a quantum mechanical language using the Ward identity (2.10).”
• Inflation and String Theory (2014, methodology): “This links the comoving curvature perturbation R with the Goldstone boson π of spontaneous symmetry breaking during inflation [55,56].”
• Solid Inflation (2012, background): “In fact, Weinberg proved a no-go theorem stating that all FRW cosmological models—inflationary or not—feature two adiabatic modes of fluctuation, one of which has constant and identical ζ and R on large scales, while the other has ζ = R = 0 [17, 19].”
• Phases of new physics in the CMB (2015, background): “By definition, for adiabatic initial conditions, any long-wavelength mode is locally generated by a diffeomorphism [46].”
• Single-field consistency relations of large scale structure part II: resummation and redshift space (2013, methodology): “This was used by Weinberg [26] to give a general procedure to write adiabatic modes in the limit in which they are space independent.”
• On soft limits of inflationary correlation functions (2012, methodology): “For constant transformation parameters λ and ~b this gauge mode is the k → 0 limit of a physical solution [11, 12], a la Weinberg [45], with suitable fall-off at spatial infinity.”
• Galileon as a local modification of gravity (2008, background): “[24]); on the other hand our potentials are supported at ~k = 0 exclusively, |~x|2 ∼ ∇(2)k δ((3))(k).”
• Conformal Symmetries of Adiabatic Modes in Cosmology (2012, methodology): “8) to have consequences on correlation functions involving physical modes, the non-linear part of the transformations should be extendable to physical perturbations (adiabatic modes) with suitable fall-off behavior at infinity [23,24].”