• Gene University, Finland.

• Dark energy (DE) first detected by studying recession and distances of galaxies billions of light years) away. (21,600km/s)/1,000 million ly =216 km/s increase in recession in 10 million ly.

• Represent DE as uniform constant density.

• v = 7.2 • 10-30 g/cm3 =

• A very tiny value but almost ¾ of the total density

• Distance R from center • Net acceleration=Gravity deceleration (1/R2) + DE “antigravity”(R)At zero gravity radius, Rv, balance.

Gravity and DE antigravity balance.

RRv

MW,M31

Study dark energy via its effects in our Local Group

Dynamical Regions of Local Group with Dark Energy

Central bound binary:

MW-M31 binary as bound system (in,out).Mos Most of mass

Expansion beyond Rv.

Dwarf galaxies moving out in a spherical static . potential.

.

At zero gravity, Rv gravity deceleration-dark energy “antigravity” balance. Rv = (3M/(8v ))1/3 .

Rv R

MW,M31

Potential plot: Binary gravitational PLUS dark energy potential.

HST data:Karachentsev et al. 2009

Use outflow region in V vs R plot to estimate Local Group gravitating mass and

dark energy• Small outer members flying out under LG gravity

deceleration and DE acceleration.• Time from the center must be ~age of universe . • Find the mass and dark energy which result in

observed outward velocities (Vs) at different distances (Rs).

Conclusions• Dark energy as well as gravitating mass

affects motions in groups of galaxies. • Dark energy has the same accelerating

effects and distance dependence at scales of millions as it does over billions of light years.

Path of discovery• Gravity: Apple to Moon to

Universe• Dark energy: Universe to Local Group