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Newtonian Cosmology: Understanding the Laws of Motion and Gravity in the Universe

Explore Newton's laws of motion and gravity in the context of cosmology. Discover how these fundamental principles shape the dynamics and expansion of the universe.

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Newtonian Cosmology: Understanding the Laws of Motion and Gravity in the Universe

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  1. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 Fundamental Cosmology: 3.Newtonian Cosmology “ If I have seen further than others, it is by standing upon the shoulders of giants.” Sir Isaac Newton (1642-1727) b. Woolsthorpe, England

  2. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 = The property that defines how strongly it is attracted by gravity The property that defines how strongly something resists any force 3.1: Newtonian Cosmology • Newton Laws of Motion • Bodies move with constant velocity unless acted on by outside force i.e. move in straight lines • The rate of change of momentum of a body is proportional to its’ acceleration • For every action there is an equal and opposite reaction Equivalence Principle Galileo: acceleration independent of mass

  3. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 Strong Nuclear Electromagnetic GUT ELECTROWEAK t=10-35s T=1027K E=1015Gev STRENGTH TOE t=10-12s T=1015K E=102Gev Weak Nuclear t=10-43s T=1031K E=1019Gev Gravity Gravity is weak but 3.1: Newtonian Cosmology • Gravity Dominates • mediator is massless • infinite range • only one charge On large scales - Gravity dominates

  4. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 The Cosmological Principle At any single epoch, the Universe appears Homogeneous and Isotropic to all Fundamental Observers The Hubble Parameter v(r) v(r’) r’ r and R(t) is the SCALE FACTOR a Where; Ro = R(to) such that r=ro at t=to O’ O -v(a) v(a) 3.1: Newtonian Cosmology • Can we derive the cosmological equations from purely Newtonian dynamics ?? All distances scaled by factor R(t) with increasing time with simple isotropic expansion

  5. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 Like a Faraday Cage ACCELERATION EQUATION 3.2: Newtonian (Dynamic) Derivation of Friedmann Equations • Newton: For a given observer at position , r, within a sphere. • Only mass interior to sphere affects the observer. • The mass exterior to sphere does not exert a force on the interior. • Simple derivation from dynamical arguments • c.f.GR BIRKHOFF’s THEOREM: • The gravitational field within a spherical cavity embedded within an infinite medium is zero. Consider a particle P, on the edge of an isotropically expanding sphere

  6. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 FRIEDMANN EQUATION ACCELERATION EQUATION 3.2: Newtonian (Dynamic) Derivation of Friedmann Equations ACCELERATION EQUATION • The Friedmann Equations Let 2cf=kc2

  7. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 Conservation of Energy Kinetic Energy Potential Energy 3.3: Newtonian (Energetic) Derivation of Friedmann Equations Analogous assumption: Ignore matter outside sphere of radius r(t) in expanding homogeneous universe • Derivation from Energetic arguments : Friedmann Equation Friedmann Equation

  8. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 U~ -kc2 Evolution of universes R U>0 U=0 U<0 • U<0: RHS will become negative at some value of • U=0: RHS >0 for all time t 3.3: Newtonian (Energetic) Derivation of Friedmann Equations • Dynamics in the Newtonian Universe • U>0: RHS >0 for all time

  9. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 First Law of Thermodynamics Homogeneity  no bulk heat flow (adiabatic)  dQ=dS=0  THE FLUID EQUATION 3.3: Newtonian (Energetic) Derivation of Friedmann Equations • The Fluid Equation

  10. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 Acceleration Equation 3.3: Newtonian (Energetic) Derivation of Friedmann Equations • The Acceleration Equation Friedmann Equation Fluid Equation • For any positive Energy Density the Universe is deccelerating • Pressure is always positive for baryons, photons, neutrinos, even WIMPS • but if P<-e/3 ???

  11. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 Friedmann Equation Fluid Equation Acceleration Equation 3.4: Summary • Newtonian Cosmology • Can derive cosmological equations from a purely Newtonian Perspective • However it’s a bit 怪しい, e.g., • Finite sphere embedded in Universe - violates HOMOGENEITY - special place ! • Preferred direction towards centre of sphere - violates ISOTROPY • Euclidean flat Universe is assumed

  12. Chris Pearson : Fundamental Cosmology 3: Newtonian Cosmology ISAS -2003 3.4: Summary 終 Fundamental Cosmology 3. Newtonian Cosmology Fundamental Cosmology 4. General Relativistic Cosmology 次：

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