## [0711.4264] Dark energy as a mirage

 Authors: Teppo Mattsson Abstract: We show that the observed inhomogeneities in the universe have a quintessential effect on the observable distance-redshift relations. The effect is modeled quantitatively by an extended Dyer-Roeder method that allows for two crucial physical properties of the universe: inhomogeneities in the expansion rate and the growth of nonlinear structures. On large scales, the universe is homogeneous, but due to the forming nonlinear structures, the regions the detectable light traverses get emptier and emptier compared to the average. As space expands the faster the lower the local matter density, the expansion can then accelerate along our line of sight. This phenomenon provides both a natural physical interpretation and a quantitative match for the observations from the cosmic microwave background anisotropy, the position of the baryon oscillation peak, the magnitude-redshift relations of type Ia supernovae, the local Hubble flow and the nucleosynthesis, resulting in a new concordance model with 90% dark matter, 10% baryons, no dark energy and 14.8 Gyr as the age of the universe. The model is based only on the observed inhomogeneities so, unlike a large local void, it respects the cosmological principle, further explaining the late onset of the perceived acceleration as a consequence of the forming nonlinear structures. Altogether, the results seem to imply that dark energy is a mirage. [PDF]  [PS]  [BibTex]  [Bookmark]

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Hans Kristian Eriksen
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### [0711.4264] Dark energy as a mirage

Alessandro Melchiorri
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### [0711.4264]

Uhm...interesting but I still think that nature can't be so perverse to mimic
a model with dark energy throught perturbations at small redshifts and
throught bumps in the primordial spectrum and 1eV neutrinos at higher redshifts.

give me a single observational datapoint in favour of this model respect to LCDM
and of course I would change idea !
0710.5073 the effect of backreactions should be small (10%), otherways you would see a larger variance in the luminosity data.

David Wiltshire
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### [0711.4264]

As someone who first used solutions to an inhomogeneous averaging scheme without $\Lambda$, to come up with the same age of the universe that Mattsson claims, as well as other alternative "concordance parameters", back in gr-qc/0702082 - published in October in the New Journal of Physics, Focus on Dark Energy - http://www.iop.org/EJ/abstract/1367-2630/9/10/377/ - I feel obliged to make some comments.

As I have discussed in detail in the paper above, as well as in other papers, 0709.0732 and 0709.2535, which have completed peer-review and are due to appear this month in Physical Review Letters and Astrophysical Journal Letters respectively, I believe that the quantitative solution to the question of dark energy involves both the back-reaction of inhomogeneities and an understanding of a fundamental question concerning energy in general relativity, which we have naively overlooked. In particular, we can expect gradients in gravitational energy associated with spatial curvature gradients of Ricci type between bound systems - where galactic observers are located - and the volume-average position in freely expanding space: the location of the ideal "fundamental observer" in the averaging scheme of Thomas Buchert, which replaces the FLRW comoving observer.

Mattsson, like many others who have looked at averaging, does not consider the foundational question that in inhomogeneous cosmologies the calibration of rods and clocks can also vary, and one has to be careful to state operationally how any particular time parameter is related to our clocks, especially in deducing "acceleration" which involves two time derivatives. I agree with those who have argued that back-reaction is "too small" to infer cosmic acceleration insofar as an ideal volume-average comoving observer in freely expanding space is concerned. I calculate that such an observer will not infer cosmic acceleration. However, observers in bound systems - which includes us and every galaxy we exchange photons with - will infer cosmic acceleration if we naively assume that spatial curvature is the same everywhere and gravitational energy has no appreciable gradient. Without violating the Copernican principle, ideal observers in galaxies or in freely expanding space in a void can each measure an isotropic CMB while measuring different mean CMB temperatures and different angular scales in the CMB anisotropies... It all boils down to how you normalize gravitational energy (the zero of the Newtonian potential for those who think that way); which I set out to do by proposing a definition of the important concept of finite infinity, which George Ellis discussed qualitatively in 1984, but never took further. For those who want less technical summaries than the papers above, the slides - http://www2.phys.canterbury.ac.nz/~dlw2 ... oquium.pdf - I have presented at GRG18 (July 07), Dark2007 (Sept 07) and various other places, are in the process of being converted into a conference proceeding article which will appear on astro-ph shortly.

To return to Mattsson's work, I believe that his extension of the Dyer-Roeder scheme is extremely interesting, and might be just the sort of calculational scheme I would need to deal with the integrated Sachs-Wolfe (ISW) effect in my approach to averaging. I suspect that the fact that Mattsson's age of the universe is the same as mine, and that he has two Hubble scales numerically very close to my bare Hubble parameter and dressed Hubble parameters, is due to an underlying commonality of some aspects of our formalism: we are both considering a variance in the apparent Hubble flow and taking spherically symmetric averages on a past light cone, while maintaining an effective Copernican principle. Beyond this we appear to differ considerably.

I do not buy into the necessity of adding 1eV hot dark matter, and I am not sure how important this is for Mattsson to be able to obtain the fit he does. [I am not ruling it out either; just for the Fractal Bubble (FB) model this is not likely to play a huge role in calibration.] Mattsson comments that the small angle features in the CMB anisotropy spectrum will be unchanged between the linear and nonlinear CHDM models. However, it is at large angles where $\Lambda$CDM and linear CHDM differ markedly in their CMB predictions, and as Mattsson says it is at those angles that his model and the linear CHDM models may also potentially differ on account of the ISW effect. If this is the case, will the nonlinear CHDM model remain a better fit to WMAP? Personally, if this was my paper I would have been concerned about displaying the Figure 1 fit to Doppler peaks which has been derived purely within the FLRW paradigm by Hunt and Sarkar, without reconsidering the whole problem from first principles. It is for these reasons that our own cosmological parameter fits in 0709.2535 are determined from supernovae, and from examining the fit to the baryon acoustic oscillation scale, and the angular scale of the sound horizon only. We do have the full CMB anisotropy spectrum in our sights, of course. However, since we are in the process of recalibrating all cosmological parameters, we will carefully reconsider every step in Wayne Hu's thesis before rewriting the codes and publishing a detailed fit to WMAP.

To be fair, Mattsson is really only considering the same set of simple tests as we do in 0709.2535, when it comes down to it. However, there is one important difference. As he states in section 3.6, at the bottom of p 26, his approach could be improved by using the nonlinear CHDM model as the baseline for data calibrations rather than the $\Lambda$CDM model. We have also used the flat $\Lambda$CDM model as the baseline for data calibrations, at the epoch of last scattering only, for the very good reason that $\Omega_\Lambda$ is effectively zero at that epoch for $\Lambda$CDM, and therefore its matter content, perturbation spectrum etc (within the ranges to be determined from a fit to WMAP data) is the same for the FB model at that epoch - modulo the fact that we best-fit primordial lithium and helium abundances with somewhat more baryons to non-baryons etc. Beyond this our parameters, such as the dressed $\Omega_M$ are derived from applying the FB model self-consistently as the baseline. What I would like to know is what is Mattsson's estimate for the equivalent of the $\Omega_M$ parameter that is inferred in FLRW models, and how does it relate to observational estimates which are independent of WMAP or galaxy clustering statistics? Surely it cannot be the same as the sum of Mattsson's barred $\Omega_{CDM}$ and $\Omega_B$? The FLRW $\Omega_M$ is inferred in many independent ways from different measurements.

Alessandro Melchiorri asks for a single observational data-point to distinguish from $\Lambda$CDM. I cannot provide them for Mattsson's model, which has different matter content, but I can for my own. See 0709.2535 ... in addition to a fit to Riess06 gold data which by Bayesian model comparison is statistically indistinguishable from $\Lambda$CDM, plus a match to BAO and sound horizon scales the FB model offers:

* a potential resolution of the primordial lithium abundance anomaly;

* a potential resolution of the CMB ellipticity anomaly;

* a potential resolution of the tension between the WMAP3 FLRW normalization of $\Omega_M$ and that obtained from other direct mass estimates such as x-rays from rich clusters of galaxies etc. (Our dressed $\Omega_M$ which is the one that most closely resembles the FLRW $\Omega_M$ best-fits at 0.33 - it does not add to anything to make 1. This concurs with many other mass estimates.)

* a potentially very detailed explanation for the Hubble bubble feature and the data points in fig 1 of 0710.5073 which are not randomly scattered between the two blue curves, as one might otherwise expect;

* insight into why Sandage et al, astro-ph/0603647, squabble with others about the value of the Hubble constant; the scale of averaging is important, and many local steps are determined on scales (50 Mpc) on which I estimate the Hubble "constant" is higher than its present epoch global average. Note: WMAP does not offer a direct "measurement" of the Hubble constant but has been fit to the FLRW paradigm only thus far. For the "fractal bubble model" the angular scale of the sound horizon matches the same angular scale as the flat $\Lambda$CDM model, for Sandage's value of $H_0$, and not for values greater than 70 km/s/Mpc.

* various insights about expansion age, which is increased. This should ultimately give predictions which may well differ from Mattsson's also by virtue of the fact that the age of the universe is position dependent, and will be much greater within voids than the 14.7 (+0.7/-0.5) Gyr we measure in galaxies. It is 18.6 Gyr at the volume average. That may be of relevance for structure formation, and obtaining the observed emptiness of voids.

Note also, the coincidence problem is solved without fine-tuning in the "fractal bubble model", since cosmic acceleration is an apparent effect due to clock-rate variance associated with the gravitational energy cost of spatial curvature gradients of Ricci type, and there is a tracker solution found in 0709.0732... Quantitatively apparent acceleration begins when the void volume fraction reaches 59% at a redshift of z=0.9. There are effectively two free parameters, which may be taken as the dressed Hubble parameter and the void volume fraction. The transition redshift z=0.9 (and other parameters) are then derived... The present epoch void-volume fraction of 76% is effectively the thing we mistake for "dark energy".

Of course, while I agree with Mattsson that inhomogeneities are the source of our confusion about dark energy, and that the cosmological constant is presently zero, I cannot agree with him that dark energy is simply a "mirage". Rather dark energy is a misidentification of those aspects of gravitational energy, which exist by virtue of the dynamical nature of spacetime in general relativity; i.e. gradients in those aspects of gravitational energy, which by virtue of the strong equivalence principle cannot be localized. I know this is hard for many of my colleagues to accept, as it means doing away with Newtonian intuition and going right back to first principles and thinking about measurement and observation with Einstein's theory, something a number of physicists are really not comfortable with. However, expanding space is an intrinsically dynamical situation, and before resorting to changing our best theory of gravity or adding exotic fluids, we have to face up to the fact that there are parts of general relativity which actually have not yet been fully explored, and that is where the actual paradigm shift may lie.