GravitationgovernscosmologicalevolutionfromtheBigBangtothepresentandthedistantfuture..
Attractive gravity on galactic scales
(c)2017 van Putten
VattrVrep
≅ 10−14
1
Repulsive gravity on cosmological scales
Weak Gravity
(c)2017 van Putten
Λ = ?https://www.aip.org/history/exhibits/einstein/ae65.htm
Who inflates the ball? What makes the universe expand or swell? That’s [by]
Lambda, there is no alternative
2
(c)2017 van Putten 3
Planck Collaboration (2013)
(c)2017 van Putten 4
Cosmological parameters for LambdaCDM
(c)2016 van Putten 15
q = 12ΩM −ΩΛ < 0 three-flat FRW universe( )
(c)2015 van Putten
ΩΛ = 0.692 ± 0.010H0 = 67.80 ± 0.77
Weak gravity on cosmological scales is repulsive
Planck 2014
Cosmological event horizons in FRW…
Dark energy:
Accelerated expansion (de Sitter when q=-1)
LambdaCDM cosmology
(Assumes GR and classical vacuum with no hidden low energy scales)
(c)2017 van Putten 5
(c)2017 van Putten 6
Is dark energy dynamic?
(c)2017 van Putten
Λ→ Λ
Λ⎡⎣ ⎤⎦ =energyarea
= 1cm
Geometrical units
(G = c = 1)
(van Putten, ApJ, 2016)
Holographic:
Λ[ ]= energyvolume
= 1cm2
Classical:
7
(c)2017 van Putten
ΩΛ =23
L0 =c5
G→ L0 = 1
Fundamental scale
ρΛ =Λ8π
= − pΛ
pΛ = −L0A
= − 14πRH
3
ρc =3
8πRH2
8
Lorentz invariance
(geometrical units)
Dimensional reduction by holography
…What makes the universe expand or swell? That’s THE COSMOLOGICAL HORIZON…
Λ[ ]→ Λ⎡⎣ ⎤⎦ =1cm
9(c)2017 van Putten
(Bekenstein ’81, ’t Hooft ’93, Susskind ’95)
van Putten, 2016, ApJ, 824, 43
Dynamical dark energy from holography
Λ = 1− q( )H 2
(c)2017 van Putten
l
r = RH
ω 0 = 1− qH0
ω = k2 + Λ
Fundamental frequency of geodesic deviation:
Dispersion relation in 3+1:
van Putten 2015 MNRAS 450 L48 van Putten 2017 ApJ 837 22
N.B. No thermodynamics involved
10
Cosmological evolution with dynamical dark energy
Gab = 8πTab − (1− q)H2gab
(c)2017 van Putten
ΩΛ =131− q( ), ΩM =
132 + q( )
ΩΛ =23, ΩM =
13
van Putten 2015 MNRAS 450 L48
de Sitter limit q=-1:
11
(c)2017 van Putten 12
-0.5 0 0.5 1
z
0
1
2
3
4
Q
-0.5 0 0.5 1
z
0.5
1
1.5
2
H(z
)/H0
-0.5 0 0.5 1
z
-2
-1.5
-1
-0.5
0
0.5
qq = -1.06q = -0.87q(ΛCDM) = -0.70q(ΛCDM) = -0.52
Cosmological evolution with dynamical dark energy
Can be tested against modern data…
GravitationgovernscosmologicalevolutionfromtheBigBangtothepresentandthedistantfuture..
Repulsive gravity on cosmological scales
Attractive gravity on galactic scales
(c)2017 van Putten
VattrVrep
≅ 10−14
13
Cosmological horizon
surface gravity
adS = cH0 = few Å s-2
SC-SC accelerationsClusters of 1e4 galaxies Distances of 20 Mpc 2.4e-12 m s-2
Gravitational attraction > cH: 0.000000000001% of the Universe
14
(c)2017 van Putten 15
Recently: DM in our solar neighborhood
Famae & McGaugh (2012)
Galaxy rotation curves Gravitational lensing
Weak gravitational attraction about cH or less
a≫ adS
a >> aH
a≪ adSa ∼ adS
Galaxy rotation curves
(c)2017 van Putten 16
(c)2017 van Putten 17
Rotation in spiral galaxies
Recently: DM in our solar neighborhood
M?
m?F?
aN =GMbr2
α = Vrot2
r
Expected acceleration by Newtonian gravitational attraction based on content in baryonic matter
Observed acceleration inferred from circular velocities
(c)2017 van Putten 18
Expected and observed behavior
Mb
m0FN
Observed:
M?
m?F?
Expected:
(c)2017 van Putten 19
Scaled rotation curvesFamae & McGaugh (2012)
Recently: DM in our solar neighborhood
aN < adS
Vrot ,observedVrot ,baryonic
⎛
⎝⎜
⎞
⎠⎟
2
= αaN
adS = cH ~ Angstrom s−2
(c)2017 van Putten 20
http://astroweb.case.edu/SPARC/RARmovie.mp4
(c)2017 van Putten 21
Gravitational potentials
u = 1r
Most of the Universe, and mostly repulsive by dark energy
strong gravity around black
holes
Newtonian gravity=>
(c)2017 van Putten
H = m012j2u '2+UN (u)
⎛⎝⎜
⎞⎠⎟
UN =12u − u0( )2 +U0
UE =UN − Rgu3
H = m012j2u '2+UE (u)
⎛⎝⎜
⎞⎠⎟
Gravitational Potentials and inertia
Einstein’s MOND
Newtonian inertia perturbed in weak gravity?
22
Gravitational potentials and inertia
(c)2017 van Putten 23
Vrot ,observedVrot ,baryonic
⎛
⎝⎜
⎞
⎠⎟
2
= m0m
Newton’s theory of gravitation with reduced inertia: F = ma with m < m0 :
aN =FNm0, α = FN
m:
Newton’s theory of gravitation and inertia hold true: F = ma with m = m0. In this event, we need dark matter:
Scenarios
(c)2017 van Putten 24
aN = adSSharp onset to weak gravity at:
(c)2017 van Putten 25
Recently: DM in our solar neighborhood
Observed:
Detailed analysis:
∝ 1r
Asymptotic behavior in weak gravity
a0 =cH2π
1− q (van Putten 2016, 2017)
(c)2017 van Putten 26
Summary
By volume, most of the evolution of the Universe evolves by weak gravity
Weak gravity is paramount to key cosmological parameters: the Hubble parameter, dark matter and dark energy.
The volume of galactic sub-regions satisfying Newton’s law based on observed baryonic matter is tiny, within a few kpc of galaxy centers.
By dimensional analysis, a characteristic scale for weak gravity is:
adS = cH0 ( ~ 1 Angstrom / s2)
(c)2017 van Putten 27
Challenges
In galaxy rotation curves, what characterizes the onset to weak gravity associated with adS?
Recently: DM in our solar neighborhoodWeak gravity co-evolves with cosmology? If so, how and can this be measured?
Galaxy rotation curves pose (i) the need for dark matter or (ii) a confrontation of the (strong) equivalence principle (gravitational mass and inertia are the same) with a0.
rt ~ RgRH = ξ kpcM111/2
van Putten 2015 MNRAS 450 L48; van Putten 2016 ApJ 824 43; van Putten ApJ 837 22
HW Question:
4πr2 Λ ≅ MExpect transition radius in galaxy dynamics:*
Derive the scale in :
28(c)2017 van Putten
ξ
Rg :RH :
gravitational radius of the galaxy (measured in baryonic mass)
Hubble radius
*Hint: use geometrical units and assume a de Sitter universe
" cosmology = galaxy dynamics"
Top Related