Marc Lachize-Rey Grenoble 2008 Outline I Historical elements - - PowerPoint PPT Presentation
La constante cosmologique Marc Lachize-Rey (APC, Paris) Marc Lachize-Rey Grenoble 2008 Outline I Historical elements II Elements of cosmology III Observational evidences for accelerating universe IV Possible solutions Dark
Marc Lachièze-Rey – Grenoble 2008
La constante cosmologique
Marc Lachièze-Rey (APC, Paris)
Marc Lachièze-Rey – Grenoble 2008
I Historical elements II Elements of cosmology
III Observational evidences for accelerating universe IV Possible solutions Dark energy ? Modify gravity ? The genuine cosmological constant Not a « problem » but a possible solution The physics with lambda
Marc Lachièze-Rey – Grenoble 2008
General relativity :
later : Cosmic distance Recalibration : Λ useless ?
= 0
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Gravitation = geometry of space-time: metric g --> Riemann and Ricci tensors, Einstein tensor G The material content of the universe determines the geometry : Einstein Equation : G(g) = χ T T = energy-momentum tensor of material content = the source of gravitation
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Relativistic Cosmology (Einstein 1917)
GR is an ideal tool for cosmology : cosmic model = a space-time describing the whole universe, solution of Einstein equations function of the average material content (matter, radiation, etc.) Einstein wants a cosmic model:
No such solution to Einstein equation as written
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G(g) = χ T G(g) = χ T + Λ g
New term Λ = cosmological constant
Only at cosmological scales.
Static : attraction by matter balanced by repulsion by Λ space = a three-sphere : closed, no boundary !
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Lemaître (1931) : primordial atom (--> later : big bang)
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Lemaître (1931) : primordial atom (--> later : big bang)
Age problem : wrong calibrations --> Age of the Universe < age of the Earth ! possible solution : Λ
also, galaxy formation difficult without Λ :
Lemaître « saves » the big bang with Λ
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(Einstein will get out of the cosmological debate)
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Ωmatter = 1 But Age of the universe: One needs Λ Galaxy formation --> idem
(a classical cosmological test)
confirms the need of Λ : CDM-Λ
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Present Value = Hubble constant = H0 ≈ 70 km /sec /Mpc
< 0 acceleration > 0 deceleration
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(≈ 0.7)
RΛ=(Λ)-1/2 ∼ 3 Gpc
Marc Lachièze-Rey – Grenoble 2008
Material content = source of gravitation :
For any substance :
in cosmological units (density parameter)
cosmological influence depends on ρ +3p
Non relativistic matter ( = dust) p ≈ 0 : w = 0 Radiation p = ρ / 3 : w= 1 / 3 Nothing else known in physics
Marc Lachièze-Rey – Grenoble 2008
( Equation of State)
For a flat Universe:
– Matter-dominated Universe – Radiation-dominated Universe – Vacuum-dominated Universe
R3,R t 2 /3 R4,R t1/2
R0,R eHt
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Exotic substance as a source of gravitation ? Accelerating ⇔ ρ +3p < 0 ⇔ w < -1/3 w = -1 : same cosmological effect than Λ w ∼ -1 : similar effects: exotic (dark) energy some physical basis ? see later
Marc Lachièze-Rey – Grenoble 2008
Summary
.98 < Ωtotal < 1.08 Ωrad ~ 5 10-5 Ωbaryons ~ 0.04 Ωmatter ~ .3 ==> ΩΛ ~ .7 Even without SN’s observations
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III Observational evidences for accelerating Universe
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The strongest the more direct historically the first evidence for lambda
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tU = « time » duration since the univers was « very small ».
Finite by definition in big bang models.
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Galaxy formation If Λ =0, no sufficient time for the galaxies to form (Lemaître, 1930’s) 1980’s --> CDM Λ paradigm
Marc Lachièze-Rey – Grenoble 2008
Supernovas (SNIa) = luminosity distance measurements
Perlmutter 2003,Physics Today
CLASSICAL COSMOLOGICAL TEST : Hyp : SNIa are standardizable candles Dlum = L 4 f
Riess et al. 1998, AJ 116,,
1009 (High-Z SN Search) Perlmutter et al 1999, ApJ 517, 565 (SCP)
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Supernova cosmology project (Knop, Perlmuter)
Do we have good data, good interpretation of them ?
the photons and modify our perception of SN data?
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(SN observations)
Riess et al. http://fr.arxiv.org/abs/astro-ph/0611572
In its first four years, 102 type Ia SNe, at z from 0.10 to 0.78.
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(Essence )
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concordance
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WMAP
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CMB alone measurements are degenerate in ΩM & ΩΛ (requires h)
+ something else something else
Different combinations of HST, SN, LSS, BAO, Shear, LTSW are consistent : Overconstrained Overconstrained model : model :
ΩΛ = 0.758 +- 0.06 HST Key Project measurement of the Hubble constant (Freedman et al. 2001, ApJ 553, 47): h100 = 0.72 +- 0.08
ΩΛ = 0.719 +- 0.03
~ 1 M ~ 0.7
Marc Lachièze-Rey – Grenoble 2008
Galaxy clusters
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Galaxy clusters
S.W. Allen et al. 2002 (arXiv:astro-ph/0205007v1) X-ray gas mass fraction (in a sample of luminous X clusters <-- Chandra Observatory) as a function of z --> cosmological constraints Ωm = 0.30+0.04, ΩΛ = 0.95 assuming
(<-- Hubble Key Project)
(independent mass confirmation from gravitational lensing studies.)
ρ =2500 ρcritical --> radius r2500 : approximately constant value
Marc Lachièze-Rey – Grenoble 2008
Marc Lachièze-Rey – Grenoble 2008
BAO = baryonic acoustic oscillations = Acoustic Peaks
seen in CMB also in galaxy distrib. as a peak in Correlation function = the acoustic signature (the same than seen in CMB, but at z <1)
Luminous Red Galaxy (LRG) sample from SDSS (46 748 galaxies with 0.16<z<0.47)
Eisenstein et al. 2005, ApJ 633, 560
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BA0’s : Cosmic ruler
∼150 Mpc
Cosmic ruler
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BA0’s
150 Mpc SDSS Aso 2DF Project : Ly alpha 150 Mpc
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BAOs
Assuming spatially flat Conley et al. arXiv:astro-ph/0602411v2
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Cosmic shear
Waerbeke et al. 2005, A&A 429, 75
Decarte survey VIRMOS
arXiv:astro-ph/0406468v1 normalisation of the mass power spectrum σ8 = (0.83 ± 0.07) ( M/0.3)−0 .49 combined with WMAP -->
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Integrated Sachs Wolfe Effect
Cabré et al., astro-ph/0603690
Correlation CMB -- galaxy distribution
cross-correlate WMAP3 data with galaxy samples extracted from the SDSS DR4 (SDSS4) as a function of angular scale well fitted by the integrated Sachs-Wolfe (ISW) effect ΩΛ = 0.80 − 0.85 (68% CL) 0.77 − 0.86 (95% CL).
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Integrated Sachs Wolfe Effect
Correlation functions
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IV - How to explain cosmic acceleration ?
Not compatible with Friedmann equations without lambda, and « ordinary » matter only assume all observations are not wrong or badly interpreted
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proposed explanations
Requires a lot of fine tunings
Categorizing Different Approaches to the Cosmological Constant Problem S.Nobbenhuis arXiv:gr-
qc/0411093
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Is the “good” Einstein equation with or without Λ ?
natural passage from Newton theory to GR deformation theory : deformation parameter
Without decisive argument : observations.
Theoretical Arguments
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Orders of magnitude
Density ρΛ ~ 2 ρmatter large number : « cc problem » This number is not large : « coincidence problem » 10-122 MP
4 == 10-54 MEW 4
Lenghts: Planck scale : constante cosmologique :
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(Kolb, Buchert, Célérié…) : Averaging effect of inhomogeneities
Only explanation with no new physics; involves a new view on cosmology Einstein equation : G(g) = χ T
but G(<g>) ≠ < G(g) > = χ < T >
« The cosmological effect of the neglected term in an inhomogeneous universe can account for SN’s observed properties » (and mimick cosmic acceleration in an homogeneous universe) Is that true ? Does it explain other cosmological data ?
Marc Lachièze-Rey – Grenoble 2008
Constrained by solar system expts (equivalence principle), binary pulsar…
scalar-tensor (Brans-Dicke…), tensor-tensor, vector-tensor …
(often equivalent to above) All modifications arbitrary and ad hoc (fine tuning)
(involve Weyl tensor)
− ♥ the simplest one : R --> R+ Constante
is precisely lambda ! ♥
Marc Lachièze-Rey – Grenoble 2008
3 • Strings and branes inspired explanations (More dimensions)
gravity explores more dimensions
gravity is trapped on a 4-dimensional brane world at short distances, but propagates into a higher dimensional space at large distances.
Dynamics in a multi-dimensional world build your own Lany new degrees of freedom added to GR, arbitrarily , fine tuned to fit the data [lambda explains everything only one (constant) parameter ! ! ]
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Anthropic view (string « landscape »)
Many « worlds » « exist » ; each with a value of Λ meaning of « many worlds » ? meaning of « exist » ? ensemble approach possible (?) ; meaning of proba distribution (?) anthropic explanation : if P(Λ) and the Proba P(life) coincide (we are very far from to be able to say such things)
= number of observers in that universe (how to calculate that ?)
Anthropic « explains » everything !
Marc Lachièze-Rey – Grenoble 2008
4 • Quantum gravity arXiv:astro-ph/0702064v2 Effects related to spacetime foam in astrophysics A.A. Kirillov the large scale observational effects of the [quantum-geometric] foamed structure appear as the Dark Matter and Dark Energy phenomena.
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The « joker of cosmology » ?
= « substance » to mimic Λ (assumed to be zero)
(violates at least strong energy condition)
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Dark energy : No such thing in present physics! --> Invent it for the purpose. Two approaches
Arbitrary functions to represent kinetic term and potential Calculate EOS --> express with w(z) --> like the previous cases
myriads of solutions (more than 100 published), completely fine tuned two (or more !) arbitrary functions are required to fit ~ 2 numbers (from cosmology) the simplest = quintessence (genuine Λ fits everything with one constant only !)
Marc Lachièze-Rey – Grenoble 2008
Dictionnary (first approach )
(ex. Λ = a-m )
deduce ρ and w from momentum - energy conservation
entirely phenomenological
= dark energy with a time-dependent equ of state
Tracker fields, Holographic dark energy : ρΛ / ρmatter = r = Ct
quintom = quintessence + phantom
(may arise from quantum effects, like particle creation)
review and comparison in Silva e Costa and Makler (arXiv:astro-ph/0702418v1)
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Dictionnary (Lagrangian approach)
Non standard kinetic term in Lagrangian (kinetic K- essence : only kinetic term)
Klein Gordon
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All these approaches require fine adjustement
to reproduce the data
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Generic term for dark energy fluid with a time dependent equ of state, written w = w(z) = p(z)/ρ(z) acceleration ==> w < -1/3
Marc Lachièze-Rey – Grenoble 2008
[ Kinessence : exemples of parametrizations ]
SN Ia + SDSS + WMAP ==> w0 = -1.1, ΩM=0.25 Idem ==> w0 = -0.97, ΩM=0.28
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W = w0+wa (1-a)
Kinessence : parametrization
Constraints from SN’s
Marc Lachièze-Rey – Grenoble 2008
Quiessence
Dynamical age of the universe as a constraint on the parametrization of dark energy equation of state, V. B. Johri
time-independent equation of state : w = Ct Ex • Network of non-interacting cosmic strings (w = -1/3)
Observational constraints ==>
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Quintessence
Imagine a real Scalar field with standard Lagrangian (minimal coupling) Which gives the desired behaviour
w ≥ -1
(A priori w = w(z) --> a particular case of kinessence) a common choice (Ratra-Peebles) V ∝ Φ-α
Marc Lachièze-Rey – Grenoble 2008
Particular cases of quintessence : Scaling solutions
The energy density of the scalar field evolves by mimicking some the background fluid (ordinary matter or radiation)
For a set of initial conditions, acts as a dynamical attractor
P = -A / ρ
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Tracker fields (peculiar cases of quintessence)
Adjust potential so that the field density « adjusts » to that of matter
approaches an « attractor » solution
designed to solve the coincidence problem
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kinetic-energy-driven quintessence = K - essence
Non trivial kinetic term in Lagrangian : Pressure = Lagrangian density L = v(φ) F[K (φ)] (K (φ) = usual kinetic energy term) For some class of functions, admits solutions that track the equation of state of the dominant type of matter (radiation in the early universe) until pressure-less matter becomes dominant. Then the k-essence begins to evolve toward cosmological constant behavior (w= -1). (An exemple : tachyonic field) (Solutions giving w= Ct ≠ -1 are unstable)
Kinetic k-essence and Quintessence, Roland de Putter & Eric V. Linder (arXiv:0705.0400v1)
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General warning : data and models are often confronted with some a priori (e.g. flat space hypothesis)
Dynamical Dark Energy or Simply Cosmic Curvature? Clarkson, Cortes and Bassett (arXiv:astro-ph/0702670v1)
Marc Lachièze-Rey – Grenoble 2008
Dark energy : general facts :
acceleration : “cosmological constant problem” not explained (worse : in many case: unnatural)
(one may construct the functions in such an adhoc way to account for it : tracker models)
why w near -1, precisely the value corresponding to lambda ?
Marc Lachièze-Rey – Grenoble 2008
Conclusions :
worse : often unnatural [see below]) worse : one additional coincidence : w = -1
adjusting the function(s) (Padnamabanh)
Cannot exist classically
no such thing exists ! (see below)
Marc Lachièze-Rey – Grenoble 2008
Quantum dark energy ? : Energy of a quantum state ?
1 - There is no QFT in curved space-time (e.g. unitarity and covariance incompatible) 2 - [gravitational] energy is not a defined concept in quantum physics : All calculations give ∞
not of [vacuum] energy !!!
_________________ Mass (or potential) scales very unnatural : a lot of fine tuning required
_______
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Finite energy for a quantum state ? Only two ideas
exactly compensate --> zero energy density --> zero acceleration supersymmetry breaking ? How ? When ? Bad scale ?
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in fact “ dark energy problem ”
Lcut-off to explain Dark energy “unnatural” in high energy physics
try to explain a low energy problem with high energy physics ! (maybe acceleration has nothing to do with particle physics ) (despite the appellation, not a problem for the true Cosmological constant )
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The cut-off required to explain cosmic acceleration is incompatible with Casimir effect arXiv:astro-ph/0604265v1 : Casimir Effect confronts Cosmological Constant Gaurang Mahajan,∗ Sudipta Sarkar,† and T. Padmanabhan arXiv:0802.1531v1 [astro-ph] Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
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Why ΩΛ of the same order than Ωmatter today ? Why ΩΛ / Ωmatter not large ? No explanation (tracker type models are constructed in ad hoc fashion to answer this problem)
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The coïncidence problem
= « second cosmological constant problem ”. Why ΩΛ ≈ 2 Ωmatter Or why RΛ ≈ c H-1. Why now ?
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Is there any need for dark energy ? Only if some measurement gives w ≠ -1
Marc Lachièze-Rey – Grenoble 2008
Marc Lachièze-Rey – Grenoble 2008
6 • A true cosmological constant ?
GR is a theory with two constant : G and Λ Both have the same status : no natural value : given by observations Interpretation of Λ = the curvature of the fundamental state (=vacuum) of GR [ Einstein wish : vacuum of GR = nothing (no space-time) ; Not true in present GR ] No Λ : vacuum = Minkowski space-time with no curvature, no expansion With Λ : vacuum = de Sitter constant curvature (Λ) space-time, expanding
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Historical “arguments”
Newton --> Special Relativity : 1/c Newton --> quantum mechanics : h Newton (or SR) --> Λ (G already present)
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Deformation theory
deformation --> Poincaré algebra (= special relativity) deformation parameter = 1/c
deformation --> Operator algebra (= quantum mechanics) deformation parameter = h One could have found these theories with pure mathematical arguments Further deformations ? Poincaré algebra --> dS algebra (= GR with lambda) deformation parameter = Λ dS algebra is stable : cannot be deformed
Marc Lachièze-Rey – Grenoble 2008
Two scales for the world ?
RΛ = Λ-2
= curvature radius of the fundamental state of GR : vacuum (de sitter) space-time
et RΛ ≈ 1028 cm
(rem : Minkowski : RΛ = ∞)
Marc Lachièze-Rey – Grenoble 2008
Conclusions : Cosmology requires an accelerating factor
The true Λ explains all cosmological data. No new physics needed. The best candidate to solve the “problems” : value not unnatural The less ad hoc assumptions needed some theoretical motivations A convincing explanation requires a new theory If observational evidence gives w ≠ -1 (not the case today), dark energy required. (White, Padnamaban, Chongchitnan + Efstathiou)
danger to orient exclusively the research towards this question And neglect other [more ?] interesting questions
Two scientific cultures (G Smoot)