Observational Tests of theTimescape Cosmology
David L. Wiltshire (University of Canterbury, NZ)
DLW: New J. Phys. 9 (2007) 377
Phys. Rev. Lett. 99 (2007) 251101
Phys. Rev. D78 (2008) 084032
Phys. Rev. D80 (2009) 123512
Class. Quantum Grav. 28 (2011) 164006
B.M. Leith, S.C.C. Ng & DLW:
ApJ 672 (2008) L91
P.R. Smale & DLW, MNRAS 413 (2011) 367
P.R. Smale, MNRAS (2011) in press
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Overview of timescape cosmology
Standard cosmology, with 22% non-baryonic darkmatter, 74% dark energy assumes universe expands assmooth fluid, ignoring structures on scales<∼
100h−1 Mpc
Actual observed universe contains vast structures ofvoids (most of volume), plus walls and filamentscontaining galaxies
Timescape scenario - first principles model reanalysingcoarse-graining of “dust” in general relativity
Hypothesis: must understand nonlinear evolution withbackreaction, AND gravitational energy gradients withinthe inhomogeneous geometry
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6df: voids & bubble walls (A. Fairall, UCT)
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Within a statistically average cell
Need to consider relative position of observers overscales of tens of Mpc over which δρ/ρ∼−1.
GR is a local theory: gradients in spatial curvature andgravitational energy can lead to calibration differencesbetween our rulers and clocks and volume averageones
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Relative deceleration scale
(i)
0.4
0.6
0.8
1.0
1.2
0 0.05 0.1 0.15 0.2 0.25
−1010 m/s 2
z
α
(ii)
0.02
0.04
0.06
0.08
0.10
0.12
0 2 4 6 8 10z
α /(Hc)
/(Hc)α
Instantaneous relative volume deceleration of walls relative to volume average background
α = H0cγw
˙γw/(q
γ2w − 1) computed for timescape model which best fits supernovae
luminosity distances: (i) as absolute scale nearby; (ii) divided by Hubble parameter to large z.
With α0∼ 7× 10−11m s−2 and typically α∼ 10−10m s−2 for
most of life of Universe, get 37% difference incalibration of volume average clocks relative to our own
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Apparent cosmic acceleration
Volume average observer sees no apparent cosmicacceleration
q =2 (1 − fv)
2
(2 + fv)2.
As t → ∞, fv → 1 and q → 0+.
A wall observer registers apparent cosmic acceleration
q =− (1 − fv) (8fv
3 + 39fv
2− 12fv − 8)
(
4 + fv + 4fv
2)2
,
Effective deceleration parameter starts at q∼ 12, for
small fv; changes sign when fv = 0.58670773 . . ., andapproaches q → 0− at late times.
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Cosmic coincidence problem solvedSpatial curvature gradients largely responsible forgravitational energy gradient giving clock rate variance.
Apparent acceleration starts when voids start to open.
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Best fit parameters
Hubble constant H0+ ∆H
0= 61.7+1.2
−1.1 km/s/Mpc
present void volume fraction fv0 = 0.76+0.12−0.09
bare density parameter ΩM0= 0.125+0.060
−0.069
dressed density parameter ΩM0= 0.33+0.11
−0.16
non–baryonic dark matter / baryonic matter mass ratio(ΩM0
− ΩB0)/ΩB0
= 3.1+2.5−2.4
bare Hubble constant H0 = 48.2+2.0−2.4 km/s/Mpc
mean phenomenological lapse function γ0
= 1.381+0.061−0.046
deceleration parameter q0
= −0.0428+0.0120−0.0002
wall age universe τ0
= 14.7+0.7−0.5 Gyr
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Key observational tests
Best–fit parameters: H0
= 61.7+1.2−1.1 km/s/Mpc, Ωm = 0.33+0.11
−0.16
(1σ errors for SneIa only) [Leith, Ng & Wiltshire, ApJ 672(2008) L91]
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Test 1: SneIa luminosity distances
0 0.5 1 1.5 230
32
34
36
38
40
42
44
46
48
z
µ
Type Ia supernovae of Riess 2007 Gold data set fit withχ2 per degree of freedom = 0.9
Type Ia supernovae of Hicken 2009 MLCS17 set fit withχ2 per degree of freedom = 1.08
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Dressed “comoving distance” D(z)
0
0.5
1
1.5
2
1 2 3 4 5 6z
0
1
1z
(i)
(iii)(ii)
H0D
0
0.5
1
1.5
2
2.5
3
3.5
200 400 600 800 1000z
(i)(ii)(iii)
H0D
Best-fit timescape model (red line) compared to 3 spatially
flat ΛCDM models: (i) best–fit to WMAP5 only (ΩΛ = 0.75);(ii) joint WMAP5 + BAO + SneIa fit (ΩΛ = 0.72);(iii) best flat fit to (Riess07) SneIa only (ΩΛ = 0.66).
Three different tests with hints of tension with ΛCDMagree well with TS model.
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Supernovae systematics
H0
Ωm
0
Gold (167 SneIa)
56 58 60 62 64 66 680
0.1
0.2
0.3
0.4
0.5
0.6
0.7
H0
Ωm
0
SDSS−II 1st year (272 SneIa)
56 58 60 62 64 66 680
0.1
0.2
0.3
0.4
0.5
0.6
0.7
H0
Ωm
0
MLCS17 (219 SneIa)
56 58 60 62 64 66 680
0.1
0.2
0.3
0.4
0.5
0.6
H0
Ωm
0
MLCS31 (219 SneIa)
56 58 60 62 64 66 680
0.1
0.2
0.3
0.4
0.5
0.6
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Recent Sne Ia results; PR Smale + DLWSALT/SALTII fits (Constitution,SALT2,Union2) favourΛCDM over TS: ln BTS:ΛCDM = −1.06,−1.55,−3.46
MLCS2k2 (fits MLCS17,MLCS31,SDSS-II) favour TSover ΛCDM: ln BTS:ΛCDM = 1.37, 1.55, 0.53
Different MLCS fitters give different best-fit parameters;e.g. with cut at statistical homogeneity scale, forMLCS31 (Hicken et al 2009) ΩM0
= 0.12+0.12−0.11;
MLCS17 (Hicken et al 2009) ΩM0= 0.19+0.14
−0.18;SDSS-II (Kessler et al 2009) ΩM0
= 0.42+0.10−0.10
Supernovae systematics (reddening/extinction, intrinsiccolour variations) must be understood
TS model most obviously consistent if dust in othergalaxies not significantly different from Milky Way
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Baryon acoustic oscillation measures
(i)1
1.1
1.2
1.3
1.4
0 0.2 0.4 0.6 0.8 1
fAP
(i)
(ii)
z
(iii)
(ii) 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.2 0.4 0.6 0.8 1
H0 DV (i) (ii)(iii)
z
Best-fit timescape model (red line) compared to 3 spatially flat ΛCDM models as earlier: (i)
Alcock–Paczynski test; (ii) DV
measure.
BAO signal detected in galaxy clustering statistics
Current DV measure averages over radial andtransverse directions; little leverage for z <
∼1
Alcock–Paczynski measure - needs separate radial andtransverse measures - a greater discriminator for z <
∼1
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Gaztañaga, Cabre and Hui MNRAS 2009
z = 0.15-0.47 z = 0.15-0.30 z = 0.40-0.47
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Gaztañaga, Cabre and Hui MNRAS 2009
redshift ΩM0h2 ΩB0
h2 ΩC0/ΩB0
range0.15-0.30 0.132 0.028 3.70.15-0.47 0.12 0.026 3.60.40-0.47 0.124 0.04 2.1
Tension with WMAP5 fit ΩB0' 0.045, ΩC0
/ΩB0' 6.1 for
LCDM model.
GCH bestfit: ΩB0= 0.079 ± 0.025, ΩC0
/ΩB0' 3.6.
TS prediction ΩB0= 0.080+0.021
−0.013, ΩC0/ΩB0
= 3.1+1.8−1.3 with
match to WMAP5 sound horizon within 4% and no 7Lianomaly.
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Redshift time drift (Sandage–Loeb test)
–3
–2.5
–2
–1.5
–1
–0.5
01 2 3 4 5 6
(iii)
(i)
(ii)
z
H−1
0
dz
dτfor the timescape model with fv0 = 0.762 (solid line) is compared to three
spatially flat ΛCDM models with the same values of (ΩM0
, ΩΛ0
) as in previous figures.
Measurement is extremely challenging. May be feasibleover a 10–20 year period by precision measurements ofthe Lyman-α forest over redshift 2 < z < 5 with nextgeneration of Extremely Large Telescopes
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Apparent Hubble flow variance
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Apparent Hubble flow variance
As voids occupy largest volume of space expect tomeasure higher average Hubble constant locally untilthe global average relative volumes of walls and voidsare sampled at scale of homogeneity; thus expectmaximum H
0value for isotropic average on scale of
dominant void diameter, 30h−1Mpc, then decreasing tillevelling out by 100h−1Mpc.
Consistent with a Hubble bubble feature (Jha, Riess,Kirshner ApJ 659, 122 (2007)); or “large scale flows”with certain characteristics (cf Watkins et al).
Expected maximum “bulk dipole velocity”
vpec = (32H0 − H
0)30
hMpc = 510+210
−260 km/s
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N. Li & D. Schwarz, arxiv:0710.5073v1–2
-0.05
0
0.05
0.1
0.15
0.2
40 60 80 100 120 140 160 180
(HD
-H0)
/H0
r (Mpc)NZIP Conference, Wellington, 18 October 2011 – p.20/??
PR Smale + DLW, in preparation
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The value of H0
Value of H0
= 74.2 ± 3.6 km/s/Mpc of SH0ES survey (Riess
et al., 2009) calibrated by NGC4258 maser distance at 7.5Mpc is a challenge for the timescape model. BUT
Expect variance in Hubble flow below scale ofhomogeneity with typical higher valueHvw0
= 72.3 km/s/Mpc at 30h−1 Mpc scale
H0
determinations independent of local distance ladder:
WiggleZ FLRW BAO value (Beutler et al,arXiv:1106.3366): H
0= 67 ± 3.2 km/s/Mpc
Quasar strong lensing time delays; e.g., (Courbin et al,1009.1473): H
0= 62+6
−4 km/s/Mpc
Megamaser distance of UGC3789 H0
= 66.6 ± 11.4
km/s/Mpc, (69 ± 11 km/s/Mpc with“flow modeling”).
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SummaryApparent cosmic acceleration can be understood purelywithin general relativity; by (i) treating geometry ofuniverse more realistically; (ii) understandingfundamental aspects of general relativity of statisticaldescription of general relativity which have not beenfully explored – quasi–local gravitational energy,of gradients in spatial curvature etc.
Extra ingredients – regional averages etc – go beyondconventional applications of general relativity
Description of spacetime as a causal relationalstructure – retains principles consistent with GR
Many details – averaging scheme etc – may change,but fundamental questions remain in any approach
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OutlookOther work
Several observational tests (Alcock-Paczynski test,Clarkson, Bassett and Lu test, redshift time drift etc)discussed in PRD 80 (2009) 123512
Work in progress
Adapting Korzynski’s “covariant coarse-graining”approach to more rigorously define regional averages(with James Duley)
Analysis of variance of Hubble flow in style of Li andSchwarz on large datasets (with Peter Smale)
Full analysis of CMB anisotropy spectrum in timescapemodel (with Ahsan Nazer)
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