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 Observations: * Antigravity is stronger than gravity at horizon-size distances ~ 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  EINSTEIN’S VACUUM DARK ENERGY  EINSTEIN’S VACUUM REPRESENTED BY COSMOLOGICAL CONSTANT  REPRESENTED BY COSMOLOGICAL CONSTANT 

(Gliner 1965): EINSTEIN’S VACUUM AS MACROSCOPIC FLUID *   = (c 2 /8  G)  * 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 *   = (c 2 /8  G)  = (0.72 ± 0.03) g/cm 3 * DE antigravity dominates in the Universe as a whole at z 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 ds 2 = A(R) dt 2 – R 2 d Ω 2 –A -1 dR 2 A (R) = 1 – 2GM/R – (8  G/3) ρ Λ R 2 Newtonian limit: 1 + U ≈ A 1/2 ≈ 1 - GM/R - (4  G/3) ρ Λ R 2 F (R) = - grad U = - GM/R 2 + (8  G/3) ρ Λ R

M F E F E FNFNFNFN Newton’s Law Newton’s Law F N = - G M/R 2 Einstein’s Law F E = - GM eff /R 2 F E = + (8  /3) G ρ  R (per unit mass) ANTIGRAVITY IN NEWTONIAN MECHANICS M eff = (4  /3)  eff R 3 = (4  /3) (  + 3p) R 3 = - (8  /3) G ρ  R 3

M F E F E FNFNFNFN ZERO-GRAVITY RADIUS | F N | = | F E |: R  = [ 3 M/(8  ρ  ) ] 1/3 ≈ 1 [ M/10 12 M sun ] 1/3 Mpc (Chernin et al. 2000) Groups of galaxies: M = (1-10) M sun  R  = 1-2 Mpc Clusters of galaxies: M = (1-10) M sun  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  = Mpc IF M = (2-4) M sun,  x =   Karachentsev et al nanoverse 6 Mpc | |

ZERO-GRAVITY RADIUS IN PHASE SPACE Group: R < R  Gravity dominates Flow: R > R  Antigravity dominates HST data Karachentsev et al RR

GAP BETWEEN GROUP AND FLOW: NATURAL LOCATION FOR ZERO-GRAVITY SURFACE 1.2 < R  < 1.6 Mpc H med = 57 km/s/Mpc HST data Karachentsev et al RR

ESTIMATOR FOR LOCAL DENSITY OF DARK ENERGY  x = (3/8  ) M/R  3 IF M 12 = 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 CEN A R  = 2 ± 0.3 Mpc H med = 60 km/s/Mpc

M81 Karachentsev et al R  = 1.2 ± 0.3 Mpc H med = 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 RΛRΛ

RADIAL FLOW MOTION d 2 R/dt 2 = - GM/R 2 + G(8  /3)  x R First integral (1/2) V 2 = GM/R + G (4  /3)  x R 2 + E, (E =Const) When R >> R , V  H  R H  = [G (8  /3)  x ] 1/2 = 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  = 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: H med = km/s/Mpc Independent estimate of local density of dark energy:  x = 3/(8  G) H med 2 = (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 ~ Mpc LOCAL COSMOLOGY PROVIDES NEW STRONG INDEPENDENT EVIDENCE FOR EINSTEIN’S UNIVERSAL ANTIGRAVITY