1. Dwarf galaxies & Cosmology Let’s start from the beginning … Jorge Peñarrubia & Matt Walker

2. The Universe is expanding! Hubble 1929

3. Cosmology: The Equations space-time vs mass/energy mass/energy = density/pressure IF the Universe is isotropic and homogeneous Friedman-Lemaitre- Robertson-Walker (FLRW) metric Combining the above formulae … Friedman eqs : scale factor vs time a(t) equation of continuity Hubble parameter

4. Cosmology: The Equations Equation of state of the Universe w=0 Matter w=1/3 Relativistic particles Matter Relativistic particles Accelerating Universe

5. Cosmology: The Issues 1.The Homogeneity Problem “The Universe becomes less homogeneous with time due to gravity. How can we explain a Universe so smooth in the past?” 2.The curvature Problem 1.The Horizon Problem observations: Ω 0 ≈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 ?”

6. Solution: Inflation 1.Curvature 2.Horizon aH=exp[Ht] H  H as t  0 Curvature k is not arbitrarily low ab initio {1 –exp[-H (t i -t) ]} H -1 Horizon is not arbitrarily small at t≈0