Toward a Unified Description of Dark Energy and Dark Matter

In the past decade, cosmology has entered an era of high precision, and in the future it may become a unique laboratory to test theories of fundamental physics, from gravitation laws to microphysics. Amongst the many questions raised by this science in turmoil, one of the most important is indisputably the one of the energy content of the Universe. Knowing what the Universe is precisely made of, and in which proportions, allows not only to determine its age but also to reconstruct the history, to predict its past and future. In fact in the attempt to solve this question cosmologists have made two of the most promising discoveries in the history of modern physics : the existence of dark matter and dark energy. While dark matter is unavoidable to explain at the same time the angular fluctuations of the cosmic microwave background and the formation and the properties of galaxies, dark energy has been originally invoked to account for the observed recent acceleration of the cosmic expansion. The so-called concordance model of cosmology assumes that this dark energy is in fact the cosmological constant once introduced by Einstein himself as an attempt to incorporate Mach’s principle within general relativity. However, the usual interpretation of the cosmological constant in terms of quantum vacuum fluctuations is in disagreement with observed value by a few dozens orders of magnitude ! Furthermore, as the vacuum energy is assumed constant everywhere at all times, it is hard to explain how it became dominant only a few billion years ago. This would mean that we live in a very particular, and even privileged, epoch of cosmic history. Is this an extraordinary coincidence ? Yet this anthropic consideration is quite deceiving for scientists.

Figure 1 : Diagramme de Hubble des supernovae lointaines et prédictions théoriques pour le modèle de concordance (Ωm=0.3, ΩΛ=0.7 ; pointillés) et le modèle de matière noire anormalement pesante (trait plein). Les deux modèles rendent compte du diagramme de Hubble des supernovae lointaines avec une précision remarquable. (En bleu, les données de la collaboration SNLS et en rouge les données du HST ; cf. P. Astier et al., Astron. Astrophys. 447 (2006) et Riess A.G. et al., ApJ 607 (2004), 665-687). Cliquer sur l’image pour l’agrandir

Figure 1 : Hubble Diagram of far-away supernovae and theoretical predictions for the concordance model (Ωm=0.3, ΩΛ=0.7 ; dashed line) and the AWE dark matter model (solid line). Both models account fairly for observed data. (In blue, data from the SNLS collaboration and in red data from the HST gold sample ; cf. P. Astier et al., Astron. Astrophys. 447 (2006) and A.G. Riess et al., ApJ 607 (2004), 665-687). Click on the image to enlarge it To overcome these difficulties, the authors have proposed the AWE Hypothesis (« Abnormally Weighting Energy ») in which the dark sector of cosmic matter violates the equivalence principle on cosmological scales. This principle, as well introduced by Einstein, assumes that all kind of energies produce and undergo the same form of gravity. This principle is extremely well tested (to a part out of a thousand billion) in laboratories, i.e. at local scales in contrast what would happen if violation of the equivalence principle would be scale-dependant ? In other words, what would happen if the equivalence principle was rigorously verified at local scales, where dark matter and dark energy are present in tiny amount, but is violated on cosmological scales where dark matter and dark energy are dominant ? The authors have precisely shown that this could naturally happen if some particles, those of dark matter for instance, do not couple to gravitation in the same way as ordinary matter. These particles would therefore see gravitational fields with a gravitational strength different from ordinary matter. The authors have answered these questions by showing how at a given scale the gravitational strength becomes dependent on dark matter concentration.

Figure 2 : Vraisemblance de divers paramètres cosmologiques pour le modèle de matière noire anormalement pesante (à partir des données de SNLS). Le maximum de vraisemblance est obtenu pour un âge d’environ 16 milliards d’années (contre 13 milliards d’années pour le modèle de concordance), Ωm=0.05, ΩAWE=0.14 et ΩDE=0.76. Ce résultat permet d’identifier a posteriori, et avec l’analyse des supernovae seulement, la matière ordinaire aux baryons, la matière AWE à la matière noire froide et l’énergie noire aux termes dus à la variation du couplage gravitationnel. Cliquer sur l’image pour l’agrandir

Figure 2 : Likelihood of various cosmological parameters for the AWE dark matter model (from SNLS data). The maximum likelihood is obtained for an age of about 16 billion years (against 13 billions for the concordance model), and corresponds to a model with Ωm=0.05, ΩAWE=0.14 et ΩDE=0.76. This result allows identifying from supernovae alone, and a posteriori, ordinary matter to baryons, AWE to cold dark matter and dark energy to terms resulting from the variation of the gravitational strength. Click on the image to enlarge it If the amount of dark matter at sub-galactic scales is negligible, so is the amplitude of this effect. This is not the case on cosmological scales where dark matter dominates the energy content of the Universe. Our team has shown that over such cosmic distances, ordinary matter has experienced a stronger cosmic expansion, as its own gravitational coupling strength has been adapting to the dark matter domination. This change in the matter gravitational coupling results in an accelerating cosmic expansion until equilibrium is reached such that the gravitational coupling on cosmological scales stabilizes at a value which differs from the one measured in our Solar system. The resulting dark energy mechanism exhibits key features which appear very promising. (i) First, it does not require the existence of negative pressures such as in the case of the cosmological constant or other proposed models like quintessence. (ii) It allows explaining naturally the cosmic coincidence as result of the stabilization mechanism of the gravitational constant during the matter-dominated era. (iii) It fairly accounts for the Hubble diagram of type Ia supernovae (Figure 1) by predicting independently the amount of ordinary matter and dark matter as obtained by the detailed analysis of cosmic microwave background anisotropies. This suggests an explanation to the remarkable adequacy of the concordance model while predicting an age of the Universe which is compatible with existing observations (Figure 2). Finally, (iv) in the future this mechanism leads to a decelerated cosmic expansion described by the well-known Einstein-de Sitter cosmological model (Figure 3). Most important is the AWE hypothesis allows reducing dark energy as a new property of gravitation : the anomalous gravity of dark matter.

Figure 3 : Evolution passée et future de l’expansion cosmique dans les deux modèles de la figure 1. Alors que la constante cosmologique conduit à une expansion exponentielle jamais décélérée dans l’avenir, le modèle AWE conduit à un Univers purement matériel en expansion décélérée après un rééquilibrage de la constante de gravitation aux échelles cosmologiques. Ce rééquilibrage est visible dans le facteur d’expansion par les oscillations dans la courbe en trait plein. La pesanteur anormale de la matière noire allonge d’environ 2 milliards d’années l’âge de l’Univers par rapport à une constante cosmologique. Cliquer sur l’image pour l’agrandir

Figure 3 : Past and future evolution of cosmic expansion for the models plotted in figure 1. While the cosmological constant leads to an eternal exponential expansion in the future, the AWE Dark Matter ends up with a matter-decelerated expansion when its balancing action on the large-scale gravitational coupling becomes negligible. This balancing action can be seen as the future oscillations in the scale factor (solid line). The age of the Universe is about 3 billion years older for the AWE hypothesis than for the concordance model. Click on the image to enlarge it Further information : The authors : Jean-Michel Alimi is Research director at CNRS and head of the Laboratory Universe and Theories (LUTh) at the Observatory of Paris. André Füzfa is F.N.R.S. post-doctoral Research Fellow at GAMASCO (University of Namur, Belgium) and associated researcher at the Observatory of Paris.

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References : A. Füzfa, J.-M. Alimi, ’Dark Energy as a Born-Infeld Gauge Interaction Violating the Equivalence Principle’, Phys. Rev. Lett. 97, 061301 (2006) A. Füzfa, J.-M. Alimi, ’Non-Abelian Einstein-Born-Infeld-Dilaton Cosmology’, Phys.Rev. D73 (2006) 023520 J.-M. Alimi, A. Füzfa, ’Is Dark Energy Abnormally Weighting ?’, Proceedings of the International Workshop "From Quantum to Cosmos : Fundamental Physics Research in Space", held in Washington, DC, USA, May 2006 A. Füzfa, J.-M. Alimi, ’Is Dark Energy Abnormally Weighting ?’, Proceedings of the SF2A 2006 Conference, held in Paris, France, June 2006, astro-ph/0609099 A. Füzfa, J.-M. Alimi, ’An Awesome Hypothesis for Dark Energy : The Abnormally Weighting Energy’, Proceedings of the 11th Marcel Grossmann Conference, held in Berlin, Germany, July 2006, gr-qc/0702085

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Reference Toward a Unified Description of Dark Energy and Dark Matter from the AWE Hypothesis André Füzfa (FNRS, Belgique), Jean-Michel Alimi (LUTh, Obs-Paris) Phys Rev D

Contact Jean-Michel Alimi (Observatoire de Paris, LUTh et CNRS )

Dernière modification le 4 mars 2013