Inflation why and how
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Inflation : why and how ?. Gert Jan Hoeve, December 2012. Problems with the Hot Big Bang. Flatness | Ω -1|<10 16 at nucleosythesis Unwanted relics Horizon problem Homogeneity over parts of space that are presumably not causally correlated . Baryogenesis

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Inflation : why and how ?

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Inflation why and how

Inflation: whyandhow?

Gert Jan Hoeve, December 2012


Problems with the hot big bang

Problemswith the Hot Big Bang

  • Flatness

    • |Ω-1|<1016 at nucleosythesis

  • Unwantedrelics

  • Horizon problem

    • Homogeneity over parts of spacethat are presumablynotcausallycorrelated.

  • Baryogenesis

    • Conventionaltheories of symmetrybreaking are insufficientfor the observedammount of baryons


  • The solution inflation

    The solution: inflation

    d2a/dt2 >> 0

    or equivalently,

    -(dH/dt)/H2 >> 1

    Between Planck time (10-43) andGUT decoupling (10-35)

    Alan Guth, 1981

    Picture: Wikipedia


    How does cosmic inflation solve the flatness problem

    How does cosmicinflationsolve the flatnessproblem?

    • Ω is pushedtowards 1 duringinflation

    • ‘Stretching’


    Unwanted relics magnetic monopoles

    Unwantedrelics: magneticmonopoles

    • Abundant at high temperature

    • Slow decay


    Why do we have a horizon problem

    Why do we have a horizon problem?

    • Cosmic Microwave Background radiationoriginated 500,000 yearsafter the BB.

    • No causalcorrelationpossible


    Inflation solves the horizon problem

    Inflationsolves the horizon problem:

    Picture: one minute astronomer


    How much inflation do we need

    How muchinflation do we need?

    Inflationends at t0 = 10-35 s, we are at t1 = 1017 s

    In radiationdominateduniverse |Ω-1|proportional to time

    |Ωnow-1| ≤ 10-2 |ΩGUT-1|≤ 10-54

    Recall|Ω-1|=|k|/(Ha)2

    Duringinflation H=constant, so|Ω-1|proportional to 1/a2

    Total expansion > ~ 1027


    Baryogenesis

    Baryogenesis

    • Three conditions (Sakharov’sconditions)

      • Baryon numberviolatinginteractions

        • obvious

      • C violationand CP violation

        • Becauseany B-violatinginteractionwouldbemirroredby a complementaryinteraction

      • Thermal non-equilibrium (or CPT violation)

        • Otherwise the backwardsreactionwouldbeequilly strong


    B violating interactions

    B-violatinginteractions

    • Standard model:

      sphalerons

    • Differenceleptonnumber

      andbaryonnumerconserved

    • Example:

      (u+u+d)+(c+c+s)+(t+t+b)  e++μ++τ+


    C and cp violation

    C and CP violation

    • B-violatingprocess must outratesymmetricprocess

    • Both symmetries

      must beviolated


    Thermal non equilibrium at baryogenesis

    Thermal non-equilibrium at baryogenesis

    • Phasetransitionbubbles

    • Thermal energy gradient at bubbleedge

    • Local breakdown of time symmetry


    How did inflation arise

    How didinflationarise?

    Scalar field V(φ) causesspontaneoussymmetrybreaking

    First or second order phasetransition?

    B. Clauwens , R. Jeanerot, D-term inflationafterspontaneoussymmetrybreaking

    H. Bohringer


    Original model guth 1981

    Original model (Guth, 1981)

    • False/real vacuum

    • First order phasetransition

    • Reheatingproblems


    Slow roll inflation linde 1982

    Slow-rollinflation (Linde, 1982)

    • d2φ/dt2 + 3H dφ/dt = -dV(φ)/dφ

    • Friedman H2 = (1/2 dφ/dt+V(φ))/3 –k/a2

    • Inflationdecays as slopeincreases

    • H=(da/dt)/a


    Quintessential scalar field

    Quintessentialscalar field

    • 5th fundamental force

    • Continueousdecayingscalar field

    • Couldexplaininflationanddark energy at the same time!

    • M. Trodden, Baryogenesisand the new cosmology, 2002


    Conclusion

    Conclusion

    Cosmologicalinflation is a viable hypothesis, but in desperate need of a more solid foundation (and experimental confirmation) from the realm of particle physics.


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