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Gravitation governs cosmological evolution from the Big Bang to the present and the distant future.. Attractive gravity on galactic scales (c)2017 van Putten V attr V rep 10 14 1 Repulsive gravity on cosmological scales Weak Gravity
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### Transcript of Gravitation governs cosmological evolution attr 10 · 2017-03-09 · Gravitation governs...

• 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 >> aH

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

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)