Physics 480/581

The discovery of the dimming of distant supernovae, in the late 1990's, has caused many to ascribe this to the influence of a mysterious "dark energy" component of our universe. This occurs because this data is being put into a picture of the universe which requires that we believe the universe is homogeneous and isotropic, at sufficiently large scales, and therefore the FLRW model of the universe should be viewed as accurate, at least to within first-order perturbations, but of course only when the actual matter content is averaged over those sufficiently large scales.

George Ellis, a very long-time researcher in both cosmology and general relativity, has been very active in attempting to keep these "debates" on an even keel, and related to actual measurements---on our past light cone---that we make or infer.
One of his most important articles is probably Inhomogeneity effects in cosmology, Class. Qu. Grav. 28 (2011) 164001.
An earlier, more brief one is Patchy solutions, Nature, 452, 158-161 (2008).

Below I give some additional references to try to help readers understand this field which is generating a great many papers these days.

1. Buchert equations: the temporal evolution of spatial averages is not the same as the average of evolved spatial metrics.\br The difference causes terms referred to as backreaction, which are geometrical terms that could, or could not, be moved to the side of the equation where matter terms occur.
   • Is Dark Energy Simulated by Structure Formation in the Universe?,by Thomas Buchert. ArXiv:1810.09188v2 [gr-qc] 14 Nov 2018. Thoughtful comments about how the positing of dark energy may preclude more serious ways to model the universe.
   • Cosmological backreaction and its dependence on spacetime foliation, by Thomas Buchert, Pierre Mourier and Xavier Roy, arXiv:1805.10455v2 [gr-qc] 14 Nov 2018. New, and therefore somewhat difficult to understand without some reading of earlier work.
   • On the covariance of scalar averaging and backreaction in relativistic inhomogeneous cosmology, by A. Heinesen, P. Mourier, and T. Buchert, arXiv:1811.01374v1 [gr-qc] 4 Nov 2018. Works at putting his backreaction terms into a completely covariant formalism, so that they can simply be added as additional terms in the Friedmann equations.
   • Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects, Thomas Buchert, Class. Qu. Grav., 28 (2011) 164007.
   • On the relation between the isotropy of the CMB and the geometry of the universe, Syksy Räsänen, arXiv:0903.3013 [astro-ph.CO] (2009). Very nice general derivation of constraints between "good" observers, imperfect, possibly anisotropic fluids, and more general cosmologies. Shows that almost isotropic is not necessarily anywhere near isotropic.
   • Structure formation as an alternative to dark energy and modified gravity, Syksy Räsänen, arXiv:0811.2364 [astro-ph] (2008).
   • On the curvature of the present day universe, Thomas Buchert and Mauro Carfora, Class. Qu. Grav. 25, 195001-195036 (2008)---very interesting, detailed discussion of how prior assumptions about models affect the interpretation of measured data.
   • Dark Energy from structure: a status report, Thomas Buchert (Université de Lyon), Gen. Rel. Gravit. 40, 467-527 (2008).
   • On Average Properties of Inhomogeneous Fluids in General Relativity: Dust Cosmologies, Thomas Buchert, Gen. Rel. Gravit. 32, 105-125 (2000). His first (actually second) step into the foray.
   • On Average Properties of Inhomogeneous Fluids in General Relativity: Perfect Fluid Cosmologies, Thomas Buchert, Gen. Rel. Gravit. 33, 1381-1405 (2001).
   • Towards a theory of macroscopic gravity, R.M. Zalaletdinov, Gen. Rel. Grav. 25, 673-696 (1993). This is quite a different approach to averaging. He has a couple of other references on this approach; however, their references are most easily found via the next, much more recent, article listed just below.
   • Spatial averaging limit of covariant macroscoic gravity: Scalar corrections to the cosmological equations, Aseem Paranjape and T.P. Singh, Phys. Rev. D 76, 044006 (2007). These authors push forward with Zalaletdinov's averaging approach, where they show that his equations are basically the same as those of Buchert, even though they began from rather different starting places.
   • The universe seen at different scales, by G.F.R.Ellis and T. Buchert, arXiv:gr-qc/0506106v2 5 July, 2005. Very good explanation of how interpretation of measurements can be misleading if an inaccurate model is used.
2. More recently there have been direct debates, in the published literature, between the group of workers in what I am calling the Buchert camp, i.e., those interested in appending backreactions to the standard cosmological model, and the Wald camp,, i.e., those who believe that it's only necessary to introduce small effects, created by perturbation theory, to that standard cosmological model. At least one exemplar of each is given below:
   • Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?, by T. Buchert, M. Carfora, G.F.R.Ellis, E.WS. Kolb, M.A.H. MacCallum, J.J. Ostrowski, S. Räsänen, B.F. Roukema, L. Andersson, A.A. Coley, \& D.L. Wiltshire, arXiv: 1505.07800v2 [gr-qc] 15 Oct. 2015---a very impressive, lengthy list of many of the people working in detailed cosmology. Basic claims that published proofs, by Wald & Green, that backreaction is negligible are erroneous!
   • How well is our universe described by an FLRW model?, by S.R. Green and Robert M. Wald, arXiv:1407.8084v2 [gr-qc] 16 Oct 2014. This is the paper by Wald that Buchert is objecting to, although there are also other responses in this ongoing debate; see the references to learn more.
   • Comments on backreaction, by S.R. Green and R.M. Wald, arXiv:1506.06452v2 [gr-qc] 30 Oct 2015. This is their rebuttal to Buchert's (and others) criticisms.
3. Wiltshire's two-timescale models, for voids and overdense regions:
   • Gravitational energy as dark energy: cosmic structure and apparent acceleration, by David L. Wiltshire, arXiv:1102.2045v1 [astro-ph.CO] 10 Feb 2011
   • Gravitational energy as dark energy: Average observational quantities,, by David L. Wiltshire, arXiv:0912.5236v1 [astro-ph.CO] 29 Dec 2009
   • Average observational quantities in the timescape cosmology, David L. Wiltshire, arXiv:0909.0749 [astro-ph.CO], (2009). {U. Canterbury, New Zealand}
   • Cosmological equivalence principle and the weak-field limit, David L. Wiltshire, Phys. Rev. D 78, 084032 (2008).
   • Gravitational Energy as Dark Energy: Concordance of Cosmological Tests, Ben M. Leith, S.C. Cindy Ng, and David L. Wiltshire, Ap. J. 672, L91-94 (2008). "preliminary quantitative evidence that a new solution to averaging the observed inhomogeneous structure of matter in the universe may lead to an observationally viable cosmology without exotic dark energy."
   • Dark Energy without Dark Energy, David L. Wiltshire, arXiv:0712.3984 (2007). "An overview of a recently-proposed 'radically conservative' solution to the problem of dark energy in cosmology."
   • Exact solution to the averaging problem in cosmology, David L. Wiltshire, arXiv:0709.0732 [gr-qc] (2007). A two-scale solution to the Buchert equations.
   • Cosmic clocks, cosmic variance and cosmic averages, David L. Wiltshire, New Journal of Physics 9, 377-443(2007).
   • Type Ia supernovae tests of fractal bubble universe with no cosmic acceleration, Benedict M.N. Carter, Ben M. Leith, S.C. Cindy Ng, Alex B. Nielsen and David L. Wiltshire, arXiv:astro-ph/0504192 (2005).
   • Viable inhomogeneous model universe without dark energy from primordial inflation, David L. Wiltshire, arXiv:gr-qc/0503099 (2005).
4. Kolb's Phenomenological Background Solutions, "Swiss Cheese Models," again for overdense and underdense regions:
   • Cosmological background solutions and cosmological backreactions, Edward W. Kolb, Valerio Marra, and Sabino Matarrese, arXiv:0901.4566 [astro-ph.CO] (2009), to be published in Gen. Rel. Grav.
   • The Szekeres Swiss Cheese model and the CMB observations, Krzysztof Bolejko, Gen. Rel. Gravit. 41, 173-1755 (2009).
   • Living in a Void: Testing the Copernican Principle with Distant Supernovae, Timothy Clifton, Pedro G. Ferreira, and Kate Land, arXiv:0807.1443 [astro-ph] (2008).
   • On cosmic acceleration without dark energy, E.W. Kolb, S. Matarrese, A. Riotto, arXiv: astro-ph/0506534 (2006).
   • Luminosity distance in "Swiss cheese" cosmology with randomized voids: I. Single void size, R.A. Vanderveld, E.E. Flanagan, I. Wasserman, arXiv:0808.1080 [astro-ph].
   • Effect of inhomogeneities on the expansion rate of the Universe, E.W. Kolb, S. Matarrese, A. Riotto, arXiv: astro-ph/0409038 (2005).
5. Lemaitre-Tolman-Bondi (LTB) metrics as cosmological models, with inhomogeneous densities but only with radial dependencies:
   • Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe, Krzysztof Bolejko and Pedro Ferreira, arXiv:1204.0909 [astro-ph] (2012).
   • The effect of inhomogeneities on the distance to the last scattering surface and the accuracy of the CMB analysis, Krzysztof Bolejko, arXiv:1101.3338[astro-ph] (2011).
   • A new approach for doing theoretical and numeric work with Lemaitre-Tolman-Bondi dust models, Roberto A. Sussman, arXiv:1001.0904 [gr-qc] (2010).
   • "Structures in the Universe by Exact Methods," Krzysztof Bolejko, Andrzej Krasinski, Charles Hellaby and Marie-Noëlle Célérier. A book by Cambridge Univ. Press (2010). [in our dept. library]
   • Imitating accelerated expansion of the Universe by matter inhomogeneities---corrections of some misunderstandings, A. Krasinski, Ch. Hellaby, M.N. Celerier, and K. Bolejko, arXiv:0903.4070 [gr-qc] (2009).
   • Lematire-Toldman-Bondi cosmological models, smoothness, and positivity of the central deceleration parameter, R.A. Vanderveld, E.E. Flanagan, & I. Wasserman, arXiv:0904.4319 [astro-ph] (2009).
6. Articles that simply discuss difficulties with the FLRW approach:
   • An instability of the standard model of cosmology creates the anomalous acceleration without dark energy, by J. Smoller, B. Temple and Z. Vogler, Proceedings of the Royal Society A, 473, 20160887.
   • Universe's missing mass found in the cosmic web, Physics World, 02 Dec., 2015.
   • Dark energy degeneracies in the background dynamics, Renée Hlozek, Marina Cortês, Chris Clarkson, and Bruce Bassett, Gen. Rel. Gravit. 40, 285-300 (2008).
   • Relativistic cosmology: its nature, aims and problems, G.F.R. Ellis, published in the invited papers of the 10th international conference on general relativity and gravitation, 1984. Re-published in Gen. Rel. and Grav., sometime in 2009. This is the underlying reference for notions such as "finite infinity" and the beginning of worrying about how to take averages in general relativity and cosmology.
   • Towards the Limits of Cosmology, by Joseph Silk, Foundations of Physics: 48, 1305-1332 (2018)
     A very well-written historical summary of the last several years, beginning with ``We are at an impasse in cosmology."
   • Dark Energy Survey year 1 results: Cosmological constraints from galaxy clustering and weak lensing, by the Dark Energy Survey Collaboration (lots of names, the first one being T.M.C. Abbott), Phys. Rev. D. 98, 043526 (2018)
7. Articles concerning constraints on cosmological notions caused by recent gravitational wave measurements:
   1. Strong Constraints on Cosmological Gravity from GW170817 and GRB170817A, by T. Baker, E. Bellini, P.G. Ferreira, et al, Phys. Rev. Lett.,119251301 (2017);
   2. Dark Energy after GW170817 and GRB170817A, by P. Creminelli and F. Vernizzi, Phys. Rev. Lett.,119, 251302 (2017);
   3. Dark Energy After GW170817: Dead Ends and the Road Ahead, by J.M. Ezquiaga and M. Zumalacárregui
   4. Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories, by J. Sakstein and Bh. Jain, Phys. Rev.,119, 251303 (2017).
   5. APS Physics Viewpoint: Reining in Alternative Gravity, by F. Schmidt, Physics 10, 134; Dec. 18, 2017.

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   Last updated/modified: 2 December, 2018