DARK ENERGY
1.1 Cosmological models and their hypotheses
1.1.1 Introduction
The progress of physical cosmology during the past ten years has led to a “standard” cosmological model in agreement with all available data. Its parameters are measured with increasing precision but it requires the introduction of a dark sector, including both dark matter and dark energy, attracting the attention of both observers and theoreticians. Among all the observational conclusions, the existence of a recent acceleration phase of the cosmic expansion has become more and more robust. The quest for theunderstandingofitsphysicaloriginishoweverjuststarting(PeeblesandRatra, 2003;PeterandUzan,2005;Copelandetal.,2006;Uzan,2007).Modelsandspeculations are flourishing and we may wonder to what extent the observations of our localuniversemayrevealthephysicalnatureofthedarkenergy.Inparticular,there exist limitations to this quest intrinsic to cosmology, related to the fact that most observations are located on our past light-cone (Ellis, 1975), and to finite volume effects (Bernardeau and Uzan, 2004) that can make many physically acceptable possibilities indistinguishable in practice.
This text discusses the relations between the cosmic acceleration and the theory of gravitation and more generally with the hypotheses underlying the construction of our cosmological model, such as the validity of general relativity on astrophysical scales and the Copernican principle. We hope to illustrate that cosmological data now have the potential to test these hypotheses, which go beyond the measurements of the parameters.
Dark Energy: Observational and Theoretical Approaches, ed. Pilar Ruiz-Lapuente. Published by Cambridge University Press. c Cambridge University Press 2010.
Dark energy, gravitation and the Copernican principle
1.1.2 Cosmology, physics and astronomy Cosmology sits at the crossroads between theoretical physics and astronomy.
Theoretical physics, based on physical laws, tries to describe the fundamental components of nature and their interactions. These laws can be probed locally by experiments.Theselawsneedtobeextrapolatedtoconstructcosmologicalmodels. Hence, any new idea or discovery concerning these laws can naturally call for an extension of our cosmological model (e.g. introducing massive neutrinos in cosmology is now mandatory). Astronomyconfrontsuswithphenomenathatwehavetounderstandandexplain consistently.Thisoftenrequirestheintroductionofhypothesesbeyondthose of the physicaltheories(Section1.1.3)inorderto“savethephenomena”(Duhem,1908), as is actually the case with the dark sector of our cosmological model. Needless to say, even if a cosmological model is in agreement with all observations, whatever their accuracy, it does not prove that it is the “correct” model of the universe, in the sense that it is the correct cosmological extrapolation and solution of the local physical laws. Dark energy confronts us with a compatibility problem since, in order to “save the phenomena” of the observations, we have to include new ingredients (cosmological constant, matter fields or interactions) beyond those of our established physical theories. However, the required value for the simplest dark energy model, i.e. the cosmological constant, is more than 60 orders of magnitude smaller than what is expected from theoretical grounds (Section 1.1.6). This tension between what is required by astronomy and what is expected from physics reminds us of the twenty-centuries long debate between Aristotelians and Ptolemaeans (Duhem, 1913), that was resolved not only by the Copernican model but more importantly by a better understanding of the physics, since Newton’s gravity was compatible only with one of these three models that, at the time, could not be distinguished observationally.
1.1.3 Hypotheses of our cosmological model The construction of any cosmological model relies on four main hypotheses:
(H1) a theory of gravity,
(H2) a description of the matter contained in the universe and its non-gravitational interactions,
(H3) symmetry hypotheses, and
(H4) a hypothesis on the global structure, i.e. the topology, of the universe.
These hypotheses are not on the same footing, since H1 and H2 refer to the physical theories. These two hypotheses are, however, not sufficient to solve the field
1.1 Cosmological models and their hypotheses
equations and we must make an assumption on the symmetries (H3) of the solutions describing our universe on large scales, while H4 is an assumption on some global properties of these cosmological solutions, with the same local geometry. Our reference cosmological model is the CDM model. It assumes that gravity is described by general relativity (H1), that the universe contains the fields of the standard model of particle physics plus some dark matter and a cosmological constant, the last two having no physical explanation at the moment. Note that in the cosmological context this involves an extra assumption, since what will be required by the Einstein equations is the effective stress–energy tensor averaged on large scales. It thus implicitly refers to a, usually not explicit, averaging procedure (Ellis and Buchert, 2005). It also deeply involves the Copernican principle as a symmetry hypothesis (H3), without which the Einstein equations usually cannot besolved,andusuallyassumesthatthespatialsectionsaresimplyconnected(H4). H2 and H3 imply that the description of standard matter reduces to a mixture of a pressureless fluid and a radiation perfect fluid.
DARK ENERGY
3.1 Introduction
The late-time accelerated expansion of our universe (Perlmutter et al., 1997, 1998, 1999; Riess et al., 1998; Astier et al., 2006) is certainly a major challenge for cosmologists. It will durably affect the way we look at our universe and its future. It is interesting to recall the scientific context in which this accelerated expansion was discovered and promoted to a pillar of the present paradigm. Big Bang cosmology was spectacularly confirmed by the discovery of a remarkably homogeneous cosmic microwave background (CMB) possessing a perfect blackbody spectrum. Nucleosynthesis of the light elements is another of its successes. Important shortcomings of Big Bang cosmology were cured by the introduction of an inflationary stage in the early universe. Inflationary models are constrained by the primordial perturbations they produce, which leave their imprint on the CMB and eventually lead to the formation of cosmic structures through gravitational instability. The inflationary scenario found spectacular support in the detection of the tiny CMB angular anisotropies. These are in agreement with the simplest (single-field slow-roll) inflationary models. In particular, these anisotropies are in agreement with a spatially flat universe, a generic key prediction of inflationary models. Intererestingly,earlierobservations,suchasthemeasurementofcosmicpeculiar velocity fields made at the end of the eighties, pointed to a rather low content of dustlike matter, whether dark or baryonic, with m,0≤0.3. At that time, this observation was often interpreted as putting the inflationary scenario, despite its beauty and simplicity, in a delicate situation. Indeed, if there is nothing else in our universe, putting aside a negligible amount of relativistic species today, then our universe is (very) open, at odds with inflation. The discovery of the present
Dark Energy: Observational and Theoretical Approaches, ed. Pilar Ruiz-Lapuente. Published by Cambridge University Press. c Cambridge University Press 2010.
3.2 Dark energy
Accelerated expansion of the universe, together with the later confirmation of the spatial flatness of our universe (see the latest exquisite constraints on the spatial curvature released recently by WMAP (Wilkinson Microwave Anisotropy Probe) under certain assumptions like a constant dark energy equation of state: Komatsu et al., 2008) was a welcome surprise: while it opened the door to dark energy, it also reconciled the inflationary scenario with the present low content of dustlike matter. So the paradigm that has formed in the last decade is that the universe underwent two phases of accelerated expansion: the inflationary stage in the very early universe, and a late-time acceleration in which our universe entered only recently. Models trying to explain this late-time acceleration are dubbed dark energy (DE) models(SahniandStarobinsky,2000,2006;Padmanabhan,2003;Copeland,Sami and Tsujikawa, 2006; Ruiz-Lapuente, 2007; Durrer and Maartens, 2008). It is not the aim of this chapter to give an exhaustive review of all DE models. Rather, we would like to emphasize all the concepts that have emerged during the quest for the ‘true’ DE model.
ANAΔΗΜΟΣΙΕΥΣΗ ΑΠΟ ΤΟ ΒΙΒΛΙΟ :
DARKENERGY
Observational and Theoretical Approaches
Edited by
PILAR RUIZ-LAPUENTE University of Barcelona
21/4/2016
1.1 Cosmological models and their hypotheses
1.1.1 Introduction
The progress of physical cosmology during the past ten years has led to a “standard” cosmological model in agreement with all available data. Its parameters are measured with increasing precision but it requires the introduction of a dark sector, including both dark matter and dark energy, attracting the attention of both observers and theoreticians. Among all the observational conclusions, the existence of a recent acceleration phase of the cosmic expansion has become more and more robust. The quest for theunderstandingofitsphysicaloriginishoweverjuststarting(PeeblesandRatra, 2003;PeterandUzan,2005;Copelandetal.,2006;Uzan,2007).Modelsandspeculations are flourishing and we may wonder to what extent the observations of our localuniversemayrevealthephysicalnatureofthedarkenergy.Inparticular,there exist limitations to this quest intrinsic to cosmology, related to the fact that most observations are located on our past light-cone (Ellis, 1975), and to finite volume effects (Bernardeau and Uzan, 2004) that can make many physically acceptable possibilities indistinguishable in practice.
This text discusses the relations between the cosmic acceleration and the theory of gravitation and more generally with the hypotheses underlying the construction of our cosmological model, such as the validity of general relativity on astrophysical scales and the Copernican principle. We hope to illustrate that cosmological data now have the potential to test these hypotheses, which go beyond the measurements of the parameters.
Dark Energy: Observational and Theoretical Approaches, ed. Pilar Ruiz-Lapuente. Published by Cambridge University Press. c Cambridge University Press 2010.
Dark energy, gravitation and the Copernican principle
1.1.2 Cosmology, physics and astronomy Cosmology sits at the crossroads between theoretical physics and astronomy.
Theoretical physics, based on physical laws, tries to describe the fundamental components of nature and their interactions. These laws can be probed locally by experiments.Theselawsneedtobeextrapolatedtoconstructcosmologicalmodels. Hence, any new idea or discovery concerning these laws can naturally call for an extension of our cosmological model (e.g. introducing massive neutrinos in cosmology is now mandatory). Astronomyconfrontsuswithphenomenathatwehavetounderstandandexplain consistently.Thisoftenrequirestheintroductionofhypothesesbeyondthose of the physicaltheories(Section1.1.3)inorderto“savethephenomena”(Duhem,1908), as is actually the case with the dark sector of our cosmological model. Needless to say, even if a cosmological model is in agreement with all observations, whatever their accuracy, it does not prove that it is the “correct” model of the universe, in the sense that it is the correct cosmological extrapolation and solution of the local physical laws. Dark energy confronts us with a compatibility problem since, in order to “save the phenomena” of the observations, we have to include new ingredients (cosmological constant, matter fields or interactions) beyond those of our established physical theories. However, the required value for the simplest dark energy model, i.e. the cosmological constant, is more than 60 orders of magnitude smaller than what is expected from theoretical grounds (Section 1.1.6). This tension between what is required by astronomy and what is expected from physics reminds us of the twenty-centuries long debate between Aristotelians and Ptolemaeans (Duhem, 1913), that was resolved not only by the Copernican model but more importantly by a better understanding of the physics, since Newton’s gravity was compatible only with one of these three models that, at the time, could not be distinguished observationally.
1.1.3 Hypotheses of our cosmological model The construction of any cosmological model relies on four main hypotheses:
(H1) a theory of gravity,
(H2) a description of the matter contained in the universe and its non-gravitational interactions,
(H3) symmetry hypotheses, and
(H4) a hypothesis on the global structure, i.e. the topology, of the universe.
These hypotheses are not on the same footing, since H1 and H2 refer to the physical theories. These two hypotheses are, however, not sufficient to solve the field
1.1 Cosmological models and their hypotheses
equations and we must make an assumption on the symmetries (H3) of the solutions describing our universe on large scales, while H4 is an assumption on some global properties of these cosmological solutions, with the same local geometry. Our reference cosmological model is the CDM model. It assumes that gravity is described by general relativity (H1), that the universe contains the fields of the standard model of particle physics plus some dark matter and a cosmological constant, the last two having no physical explanation at the moment. Note that in the cosmological context this involves an extra assumption, since what will be required by the Einstein equations is the effective stress–energy tensor averaged on large scales. It thus implicitly refers to a, usually not explicit, averaging procedure (Ellis and Buchert, 2005). It also deeply involves the Copernican principle as a symmetry hypothesis (H3), without which the Einstein equations usually cannot besolved,andusuallyassumesthatthespatialsectionsaresimplyconnected(H4). H2 and H3 imply that the description of standard matter reduces to a mixture of a pressureless fluid and a radiation perfect fluid.
DARK ENERGY
3.1 Introduction
The late-time accelerated expansion of our universe (Perlmutter et al., 1997, 1998, 1999; Riess et al., 1998; Astier et al., 2006) is certainly a major challenge for cosmologists. It will durably affect the way we look at our universe and its future. It is interesting to recall the scientific context in which this accelerated expansion was discovered and promoted to a pillar of the present paradigm. Big Bang cosmology was spectacularly confirmed by the discovery of a remarkably homogeneous cosmic microwave background (CMB) possessing a perfect blackbody spectrum. Nucleosynthesis of the light elements is another of its successes. Important shortcomings of Big Bang cosmology were cured by the introduction of an inflationary stage in the early universe. Inflationary models are constrained by the primordial perturbations they produce, which leave their imprint on the CMB and eventually lead to the formation of cosmic structures through gravitational instability. The inflationary scenario found spectacular support in the detection of the tiny CMB angular anisotropies. These are in agreement with the simplest (single-field slow-roll) inflationary models. In particular, these anisotropies are in agreement with a spatially flat universe, a generic key prediction of inflationary models. Intererestingly,earlierobservations,suchasthemeasurementofcosmicpeculiar velocity fields made at the end of the eighties, pointed to a rather low content of dustlike matter, whether dark or baryonic, with m,0≤0.3. At that time, this observation was often interpreted as putting the inflationary scenario, despite its beauty and simplicity, in a delicate situation. Indeed, if there is nothing else in our universe, putting aside a negligible amount of relativistic species today, then our universe is (very) open, at odds with inflation. The discovery of the present
Dark Energy: Observational and Theoretical Approaches, ed. Pilar Ruiz-Lapuente. Published by Cambridge University Press. c Cambridge University Press 2010.
3.2 Dark energy
Accelerated expansion of the universe, together with the later confirmation of the spatial flatness of our universe (see the latest exquisite constraints on the spatial curvature released recently by WMAP (Wilkinson Microwave Anisotropy Probe) under certain assumptions like a constant dark energy equation of state: Komatsu et al., 2008) was a welcome surprise: while it opened the door to dark energy, it also reconciled the inflationary scenario with the present low content of dustlike matter. So the paradigm that has formed in the last decade is that the universe underwent two phases of accelerated expansion: the inflationary stage in the very early universe, and a late-time acceleration in which our universe entered only recently. Models trying to explain this late-time acceleration are dubbed dark energy (DE) models(SahniandStarobinsky,2000,2006;Padmanabhan,2003;Copeland,Sami and Tsujikawa, 2006; Ruiz-Lapuente, 2007; Durrer and Maartens, 2008). It is not the aim of this chapter to give an exhaustive review of all DE models. Rather, we would like to emphasize all the concepts that have emerged during the quest for the ‘true’ DE model.
ANAΔΗΜΟΣΙΕΥΣΗ ΑΠΟ ΤΟ ΒΙΒΛΙΟ :
DARKENERGY
Observational and Theoretical Approaches
Edited by
PILAR RUIZ-LAPUENTE University of Barcelona
21/4/2016
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