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Dwarf galaxies & Cosmology

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Jorge Peñarrubia & Matt Walker

Let’s start from the beginning …

The Universe is expanding!

Hubble 1929

Cosmology: The Equations

space-time vs mass/energy

mass/energy = density/pressure

IF the Universe is isotropicand homogeneous

Friedman-Lemaitre-

Robertson-Walker (FLRW)

metric

Combining the above formulae …

Friedman eqs : scale factor vs time

a(t)

equation of continuity

Hubble parameter

Cosmology: The Equations

Equation of state of the Universe

w=0 Matter

w=1/3 Relativistic particles

Matter

Relativistic particles

Accelerating Universe

Cosmology: The Issues

The Homogeneity Problem “The Universe becomes less homogeneous with time due to gravity. How can we explain a Universe so smooth in the past?”

The curvature Problem

The Horizon Problem

observations: Ω0 ≈1

theory:

“The curvature of the Universe was very small at t≈0 “

Co-moving Horizon (aH)-1 tends to zero as t≈0

“How can the CMB be so homogeneous if different regions were not casually-connected at t≈0 ?”

Solution: Inflation

Curvature

Horizon

aH=exp[Ht] H H as t 0

Curvature k is not arbitrarily low ab initio

{1 –exp[-H (ti-t) ]} H-1

Horizon is not arbitrarily small at t≈0