Studying Dark Energy with Nearby Dwarf Galaxies

Arthur D. Chernin Sternberg Astronomical Institute Moscow University

In collaboration with

I.D. Karachentsev, P. Teerikorpi, M.J. Valtonen, D.I. Makarov, G.G. Byrd, V.P. Dolgachev, L.M. Domozhilova

Definition:

Dark energy is non-clustering cosmic substance which produces antigravity

Discovery: Riess et al. 1998, Perlmutter et al. 1999

Observations:

* Antigravity is stronger than gravity at horizon-size distances ~ 1 000 Mpc

* Antigravity makes the Universe expand with acceleration

Fundamental theory:

Physical nature and microscopic structure of dark energy are completely unknown (beyond current particle “standard model”)

The simplest (and most likely) description

adopted in currently standard CDM cosmology:

DARK ENERGY DARK ENERGY EINSTEIN’S VACUUM EINSTEIN’S VACUUM

REPRESENTED BY COSMOLOGICAL CONSTANTREPRESENTED BY COSMOLOGICAL CONSTANT

•

•

(Gliner 1965):

EINSTEIN’S VACUUM AS MACROSCOPIC FLUID

* = (c2/8G)

* Equation of state p = - (c = 1)

* Density is perfectly uniform

* Density is the same constant in any reference frame

WMAP (2007): p/ = -1 ±0.1

WHY ANTIGRAVITY?

Effective gravitating density in GR eff = + 3 p

DE: eff = -2 < 0 antigravity

Recent observational data (WMAP-2007, etc.):

* DE contributes 70-75% to the present total mass/energy * = (c2/8G) = (0.72 ± 0.03) • 10-29 g/cm3

* DE antigravity dominates in the Universe as a whole at

z < zΛ ≈ 0.7; t > t Λ ≈ 7 Gyr

LOCAL EFFECTS OF DARK ENERGY

It has long been taken for granted that

Λ is significant only for the Universe as a whole

Chernin et al. (2000):

Antigravity is stronger than gravity at distances ~ 1 Mpc from us

LOCAL GRAVITY-ANTIGRAVITY POTENTIAL

Schwarzschild-de Sitter static spacetime:

point-like mass on DE background

ds2 = A(R) dt2 – R2 d Ω2 –A-1 dR2

A (R) = 1 – 2GM/R – (8G/3) ρΛ R2

Newtonian limit:

1 + U ≈ A1/2 ≈ 1 - GM/R - (4G/3) ρΛ R2

F (R) = - grad U = - GM/R2 + (8G/3) ρΛ R

MM FFEE

FFNN

Newton’s LawNewton’s Law FN = - G M/R2

Einstein’s Law FE = - GMeff/R2

FE = + (8/3) G ρ R (per unit mass)

ANTIGRAVITY IN NEWTONIAN MECHANICS

Meff = (4/3) eff R3 = (4/3) ( + 3p) R3 = - (8/3) G ρ R3

MM FFEE

FFNN

ZERO-GRAVITY RADIUS

| F N | = | F E|:

R = [ 3 M/(8 ρ) ]1/3

≈ 1 [ M/1012 Msun]1/3 Mpc (Chernin et al. 2000)

Groups of galaxies: M = (1-10) 1012 Msun R = 1-2 Mpc Clusters of galaxies: M = (1-10) 1014 Msun R = 5-10 Mpc

R is local counterpart of global redshift z ≈ 0.7

LOCAL GROUP & LOCAL EXPANSION FLOW

NATURAL TOOL TO DETECT AND MEASURE LOCAL DARK ENERGY

Zero-gravity radius R = 1.2-1.5 Mpc

IF M = (2-4) 1012 Msun,

x =

Karachentsev et al. 2006

nanoverse

6 Mpc|---------------------------------------------------|

ZERO-GRAVITY RADIUS IN PHASE SPACE

Group:

R < R

Gravity dominates

Flow:

R > R

Antigravitydominates

HST data

Karachentsev et al. 2009

R

GAP BETWEEN GROUP AND FLOW:NATURAL LOCATION FOR ZERO-GRAVITY SURFACE

1.2 < R < 1.6 Mpc

Hmed = 57 km/s/Mpc

HST data

Karachentsev et al. 2009

R

ESTIMATOR FOR LOCAL DENSITY OF DARK ENERGY

x = (3/8) M/R3

IF M12 = 2-4, R = 1.2 – 1.6 Mpc,

x = (0.5 – 2.6)

DE local density is nearly (if not exactly) equal to DE global density

Karachentsev et al. 2007

CEN A

R = 2 ± 0.3 Mpc Hmed = 60 km/s/Mpc

M81

Karachentsev et al. 2007

R = 1.2 ± 0.3 Mpc

Hmed = 62 km/s/Mpc

LOCAL DENSITY OF DARK ENERGY FROM

LG + Cen A + M81

x = (0.3 – 9)

LOCAL DE DENSITY IS NEAR GLOBAL DE DENSITY ON THE ORDER OR MAGNITUDE

LOWER LIMIT IS MOST IMPORTANT

LOCAL FLOW: DYNAMICAL MODEL

Group:

MW-M31 binary as bound two-body system

Expansion flow: dwarf galaxies as test particles moving in a spherical gravity-antigravity static potential

Local gravity-antigravity potential

RΛ

RADIAL FLOW MOTION

d2R/dt2 = - GM/R2 + G(8/3)x R

First integral

(1/2) V2 = GM/R + G (4/3) x R2 + E, (E =Const)

When R >> R,

V HR

H = [G (8/3) x ]1/2 = 62- 64 km/s/Mpc,

if x =

CDM: H H when antigravity getting stronger

LG FLOW: H H when antigravity getting stronger

Chernin et al. 2000, Karachentsev et al. 2003, Sandage et al. 2006:

Since antigravity dominates both global and local flows, global and local Hubble factors must be close to each other and to H = 62-64 km/s/Mpc

Observed values and the theory value are indeed equal within 10-15% accuracy

Local Hubble factor H measured in local flows around LG, Cen A, M81:

Hmed = 57-62 km/s/Mpc

Independent estimate of local density of dark energy:

x = 3/(8 G) Hmed2 = (0.9 – 1)

LOCAL DE DENSITY IS EQUAL TO GLOBAL DE DENSITY

CONCLUSIONS

* Dark energy exists on local scale ~ 1 Mpc * DE antigravity is strong on local scale

* Hubble constant is nearly the same everywhere due to dark energy with its perfectly uniform density * Local DE density at R ~ 1 Mpc is close or exactly equal to global DE density at R ~ 1 000 Mpc

LOCAL COSMOLOGY PROVIDES NEW STRONG INDEPENDENT EVIDENCE FOR EINSTEIN’S UNIVERSAL ANTIGRAVITY