Fitting the luminosity data from type Ia supernovae by means of the cosmic defect theory
description
Transcript of Fitting the luminosity data from type Ia supernovae by means of the cosmic defect theory
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Fitting the luminosity data from Fitting the luminosity data from type Ia supernovae by means type Ia supernovae by means of the cosmic defect theoryof the cosmic defect theory
Angelo TartagliaAngelo TartagliaDIFIS – Politecnico and INFN DIFIS – Politecnico and INFN
Torino, ItalyTorino, Italy
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Plan of the talkPlan of the talk Starting point and motivationStarting point and motivation Outline of the Cosmic Defect theoryOutline of the Cosmic Defect theory Fit of the observational dataFit of the observational data Defects and Vector Theories: general Defects and Vector Theories: general
LagrangiansLagrangians Open problemsOpen problems
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The accelerated expansion The accelerated expansion (luminosity data of SnIa’s)(luminosity data of SnIa’s)
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The power spectrum of CMBThe power spectrum of CMB
k=0
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Presently agreed expansionPresently agreed expansion
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Einstein equationsEinstein equations
Tc
GgRgR 4
821
Spacetime geometry “Matter”
Why is Λ on the left?
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Something missingSomething missing
•Inflation•Gravity in clusters and galaxies•Accelerated expansion
There is something missing
Modify GR Introduce the missing entities
Give up GR and look for another theory
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...8)(21
104 TTc
GgRgR
Accept a four- (N-) dimentional spacetime manifoldAdd “matter” components
Isotropy and homogeneityPerfect fluid
2cρwpEos
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ΛΛ Cold Dark Matter Cold Dark Matter
Simplest and most effective model for the universe; however:• “matter” must be 7 times what we “see” (~30% of the source);• Λ corresponds to 70% of the souce
but …
what is Λ?
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Trying a new approach: Trying a new approach: The Cosmic Defect theoryThe Cosmic Defect theory
Motivation, besides the simple fitting of the data:
• describing the large scale behaviour of the universe in terms of intrinsic properties of a four-dimensional continuum;• interpreting space-time as Einstein’s GR ether
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Strain in a continuumStrain in a continuumN-dimensional “sheet”N-dimensional “sheet”
Strain induced by boundary conditions
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A defectA defect
Internal “spontaneous” strain state
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Four-dimensional point defectFour-dimensional point defect
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aa
μμ dyφdx
aa
μμ dy
yxdx
Geometry, elasticity and defectsGeometry, elasticity and defects
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In a strained medium each point is in one to In a strained medium each point is in one to one correspondence with points in the one correspondence with points in the
unstrained stateunstrained state
yx
The new situation is diffeomorphic to the old one
ξ is a function of x
Intrinsic coordinates Extrinsic coord.
Displacement
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Induced metricInduced metric
2g
ν
β
μ
α
αβμν
νμ
μν xξ
xξη
xξ
xξ
ε21
Strain tensor
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““Radial” displacement field Radial” displacement field (space (space isotropy and homogeneity)isotropy and homogeneity)
000 ,,,tuξ
θsinurφξ;ur
θξ;
kr
ur
ξ;tu
tξ
21
22
22
2
2
22
00 sin2
;2
;12
;221 ruru
kru
tu
tu
rr
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The line elementThe line element
22222
2
2222
1φdθsinrθdr
krdrtdtds
22222
2
2222
12 φdθsinrθdr
krdruτττdds
utτdtdtduτd
1
22222
2
2222
22 sin
11 drdr
krdrutdt
dtduds
Unperturbed
Strained
0k
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A Robertson-Walker universeA Robertson-Walker universe
τuτττa 222
222222222 φdθsinrθdrdraτdds
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How can we choose a Lagrangian How can we choose a Lagrangian expressing the presence of the expressing the presence of the
defect?defect?
Start from the phase space of a Robertson-Walker universe and look around for similar phase
spaces
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Phase space analogyPhase space analogy
FRW universeInertial expansion
Accelerated expansion
Decelerated expansion
Point particle
Free motion
Driving forceBraking force
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A simple classical problemA simple classical problem
Motion of a point massive particle in a viscous medium
2
21 xmeL
LdtS
xt
b
a
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Invariant formulation of the Invariant formulation of the same problemsame problem
x
s
s
x
edtxd
cmL
dsemS
2
2
11
2
1
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SpacetimeSpacetime“Dissipative” action integral“Dissipative” action integral
RdeS g
• Same structure as in the classical simple case
• The “viscous” properties of space-time are contained in the vector field
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Robertson Walker symmetryRobertson Walker symmetry
Isotropy and homogeneity in 3 dimensionsRW line element
1,0 sin1
22222
2222
kddr
krdradds
The symmetry is induced by the presence of a “defect”
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Impose the 4-isotropy around the Impose the 4-isotropy around the origin and use cosmic time as the origin and use cosmic time as the
“radial” coordinate“radial” coordinate
dkaaaaeS )(6 22kV
)0,0,0,(
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Symmetry and application of the minimal action principle do
not commute
Defect means
Symmetry first
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Non-trivial ifNon-trivial if
constantχ
)( 22
kaaaae L
Lagrangian
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Divergence free Divergence free vectorvector
3
3
3
,
0
0
aQ
a
g
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The expansion rateThe expansion rate((a and time in units of Qa and time in units of Q))
62
1
2/16
2/5
6ae
aaa
Choose the + sign
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Expansion rateExpansion rate
Accelerated expansion
Asymptotic stop
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Expansion versus cosmic timeExpansion versus cosmic time
Inflation
Acceleration
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Fitting the data from Fitting the data from SnIaSnIa
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z
Sm ζHζdlogzclogMmλ
051525
The distance modulusThe distance modulus
aaH
z
aa
1
0
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The energy function for the CD The energy function for the CD theorytheory
WLLH
34
02
5
662
acρκaaa
eκad
da χ
a
aκe
acρ-aa/
51
342
666
W
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Multicomponent cosmic fluidMulticomponent cosmic fluid2cρwp iii
i
i
w
w
ii aaρρ
13
130
0
aa
κe
aaρ-c
aa/
w
w
ii i
i
51
3
130
04
2
666
W
Equation of state
Conservation law
Expansion rate
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Fitting the data (192 SnIa)Fitting the data (192 SnIa)
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ΛCDM 2 = 1.029
CD 2 = 1.092
Reduced Reduced 22 of the fits of the fits
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The Hubble parameterThe Hubble parameter
H0 = (62.8 ± 1.7) km/sMpc
Most models ~64 km/sMpc
Observation ~75 km/sMpc
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Weaknesses and open problemsWeaknesses and open problems
Fitting the SnIa luminosity data with Fitting the SnIa luminosity data with a logarithmic function and two a logarithmic function and two parameters is “too easy”parameters is “too easy”
The inflation is too strong and long The inflation is too strong and long lasting (troubles with nucleosynthesis lasting (troubles with nucleosynthesis and formation of structures)and formation of structures)
The exponential in the action integral The exponential in the action integral is a poweful multiplier, but it should is a poweful multiplier, but it should be weakenedbe weakened
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The null divergence condition should be The null divergence condition should be a consequence of the singularity in a consequence of the singularity in correspondence of the defect, rather correspondence of the defect, rather than a formal constraint imposed on than a formal constraint imposed on the vector.the vector.
Once it has been induced, the Once it has been induced, the γγ vector vector has its own dynamics and energy has its own dynamics and energy content which must be taken into content which must be taken into accountaccount
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General Lagrangian treatment General Lagrangian treatment (non-exponential coupling)(non-exponential coupling)
...RγγRRe αββα
αβγγδ βααβ
RγγγνγμγγλRg
βαβ
αα
αα
ββ
α 122L
σασσααβ
β γRγ
Non-minimalcoupling
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The equations for The equations for aa and and
03633 222 χaABaaBaχaCaχCa
WaχχCaaχχBaaχA 322222 623
νμλCμB
μνλA
2
23
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Special or trivial solutionsSpecial or trivial solutions
320 /τaχ
00 constantχχ
032 χ,ABa any constant
AB
χ,Wτa23
20 0 any
Matter dominated FRW
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CorrespondencesCorrespondences Bimetric theories: “pre-shaped Bimetric theories: “pre-shaped
container”container” Vector-tensor theoriesVector-tensor theories Curvature fluidCurvature fluid
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Final remarksFinal remarksThe CD theory provides a consistent The CD theory provides a consistent
physical interpretation of space-physical interpretation of space-time giving a heuristic tool to time giving a heuristic tool to move across the Lagrangian move across the Lagrangian “engineering” mostly driven by the “engineering” mostly driven by the formal search for the desired formal search for the desired result. result.
This conceptual framework looks This conceptual framework looks promisingpromising
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A. Tartaglia, M. Capone, Int. Jour. Mod. Phys. D, 17, 275-299 (2008)
A. Tartaglia, N. Radicella, Phys. Rev. D, 76, 083501 (2007)
A. Tartaglia, M. Capone, V. Cardone, N. Radicella, arXiv:0801.1921, to appear on Int. Jour. Mod. Phys. D
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Thank you
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Why SnIa?Why SnIa?
Accreting white dwarf
Supernova explosion
Tycho Brahé 1572 (Chandra’s image)
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SnIa is a good candleSnIa is a good candle
Stable light curve
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…. according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.
Albert Einstein, Leiden, 1920
Ether againEther again