Experimentum crucis Accelerating evolution of the Universe Summary
Discovery of acceleration of the Universe as an experimentum crucis
Marek Szyd lowski Pawe l Tambor Adam Krawiec
Department of Theoretical Physics, Catholic University of Lublin M. Kac Complex Systems Research Center Institute of Economics and Management, Jagiellonian University
6th ECAP, 2008 Krak´ow, 22 August 2008 Experimentum crucis Accelerating evolution of the Universe Summary
Outline
1 Experimentum crucis
2 Accelerating evolution of the Universe
3 Summary Experimentum crucis Accelerating evolution of the Universe Summary
Experimentum crusis
Isaac Newton first used the term experimentum crucis in his Opticks (1704).
In sciences, an experimentum crucis, or critical experiment, is an experiment capable of decisively determining whether or not a particular hypothesis or theory is correct. In particular, such an experiment must typically be able to produce a predictable result that no established hypothesis or theory is capable of producing. Experimentum crucis Accelerating evolution of the Universe Summary
Experimentum crucis
Important remark of John Stuart Mill: Experimentum crucis consists of not only one but at least three. In the cosmological context the different astronomical observations are used together: SNIa, CMB, baryon oscillation peak, gravitational lensing.
Lakatos distinguished in his concept of research programmes the ‘minor crucial experiments’ and ‘major crucial experiments’. The former is applied within the research programme (series of theories with the common hard core) while the latter is applied to competing research programmes. Experimentum crucis Accelerating evolution of the Universe Summary
Experimentum crucis (Such, 1975)
There are two practical approaches to conduct the experimentum crucis: In the framework of given theory we try to explain the occurring anomaly where new hypothesis explains it. acceleration and the nonzero cosmological constant The two or more competing theories: there is a phenomenon predicted by one theory but not others; measurements should precise enough to give a reliable answer. Einstein gravity theory and the modified gravity theories Experimentum crucis Accelerating evolution of the Universe Summary
Examples of experimentum crucis
1919 solar eclipse — the new theory has specific prediction and effect, not met in an existing theory; Arthur Eddington’ observations confirmed predictions of gravitational lensing made by Albert Einstein in general theory of relativity; 1900 black-body spectrum — anomalous experimental results, which no other existing theory can furnish an explanation (classical Rayleigh-Jeans law), can be explained by a new hypothesis (Max Planck quantum hypothesis) Experimentum crucis Accelerating evolution of the Universe Summary
Microwave Background Radiation
The measurements of cosmic microwave background radiation gives us: relic radiation has black-body spectrum at T = 2.7; it remnant of hot phase during the Universe evolution and support the Big-Bang theory. discovery of anisotropy of CMB at the level ∆T /T ∝ 10−5; following the Sachs-Wolf effect ∆T /T ∝ ∆ρ/ρ it is a smoking gun of the structure formation in the early Universe. Experimentum crucis Accelerating evolution of the Universe Summary
Philosophical issues
The problem of experimentum crucis the problem of existence of the experiment which is unquestionable in methodological sense rather than in the technical one. The experimentum crucis should concerns the phenomenon which is predicted by theory but absent in the competitive theory.
We propose the following scheme: Two theories: the CDM model with the cosmological constant (ΛCDM model) against the CDM model (without the cosmological constant), where the acceleration of the current Universe is phenomenon which is present in the former and not present in the latter. Experimentum crucis Accelerating evolution of the Universe Summary
Supernovae type Ia
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-1 0.01 0.1 1 z Experimentum crucis Accelerating evolution of the Universe Summary
Acceleration of the Universe
There are principally two hypothesis offering explanations of acceleration of current Universe. First, if we assume that the current evolution of current Universe is governed by the Friedmann-Robertson-Walker equation with a source of gravity in the form of perfect fluid than the Einstein equation reduced to the form acceleration equation 1 ¨a/a = − (ρ + 3p) 6 where a(t) is a scale factor, ρ and p is energy density and pressure respectively. Note that we have acceleration if the condition ρ + 3p > 0 is violated. We do not know such a fluid in the laboratory but the cosmologist recall in this context about the cosmological constant. Experimentum crucis Accelerating evolution of the Universe Summary
Historical remark
The cosmological constant appeared in the Newtonian explanation of anomalies in the motion of celestial bodies. But the cosmological constant is best known since the Einstein’s modification of gravitational field equation to obtain the static Universe.
The discovery of CMB and the accepting of evolutional Universe with a Big-Bang beginning made the cosmological constant obsolete.
The discovery of the current acceleration of the Universe reincarnated the cosmological constant term. Experimentum crucis Accelerating evolution of the Universe Summary
The cosmological constant
The cosmological constant term can be interpreted as a special kind of special fluid for which the pressure and energy density are constant p = −Λ and ρ = Λ. From the acceleration equation after substitution of above condition we obtain ¨a Λ = a 3 and if we have positive cosmological constant the Universe is accelerating. Corollary The positive cosmological constant can be treated as a source of acceleration (anti-gravitation). Experimentum crucis Accelerating evolution of the Universe Summary
How to interpret the cosmological constant
1. Λ is energy density of vacuum, however if we compare such interpretation with Λ obtained from SNIa data then we obtain that energy density of vacuum is 10120 larger than Λ obtained from observations. It is a coincidence problem. Other explanations of the acceleration in terms of substantial fluid violating the strong energy condition is called dark energy. 2. It is assumed that the gravity equations should be modified; eg. the nonlinear Lagrangian for gravity L = f (R), where R is the Ricci scalar; additional dimensions motivated by brane (Dvali-Gabadadze-Porrati model). Experimentum crucis Accelerating evolution of the Universe Summary
How to interpret the cosmological constant
3. Ellis and Buchert claim that the standard paradigm of cosmology (FRW model) should be changed: the universe shows small anisotropies and inhomogeneities which after averaging procedure over volume give rise to the explanation of the acceleration. Averaged inhomogeneous cosmologies describe observations of the large scale properties of the Universe. Experimentum crucis Accelerating evolution of the Universe Summary
Conclusions
The Bayesian statistical analysis of model selection favours as the best model the CDM model with the cosmological constant. The ΛCDM model is effective theory of the Universe which is the simplest in terms of information criteria (AIC, BIC). The observations of SNIa support the cosmological constant (as the additional parameter) but not explain the nature of it. Experimentum crucis Accelerating evolution of the Universe Summary
Summary
The acceleration of the current Universe in the framework of Einstein theory could be explained by positive cosmological constant. It is an experimentum crucis. The cosmological model without Λ can be rejected at more than 16σ level. The acceleration of the Universe could be explained also by the modified gravity theories. Here SNIa observations fails. While the ΛCDM model is still statistically favoured. Real scientific practise shows that experiments cannot confirm/falsify theory definitively but only make the theory more/less probable. The increasing role of statistics makes that it is an important problem.
Outlook Planning/constructing of the experimentum crucis.