Wednesday, 17 July 2013

Particle Creation- The Ultimate Free Lunch

You can't get something from nothing, there is no simply no such thing as a free lunch. But considering the beginning of the universe, where did all the particles come from? Common sense tells us that some breach of natural law such as energy conservation (the total heat energy added to a system equals the increase in internal energy minus any work) was necessary for the universe to begin in maximum entropy and zero energy. Such intuition fails at the level of quantum mechanics and relativity where that matter may be 'created and destroyed' via E = mc2 and the Uncertainty principle permits 'accidental' violations of energy conservation to occur spontaneously. But such a state of nothing may not be compared with 'absolute nothingness' because the laws of physics are presupposed to exist beforehand. We live in a zero energy universe, where the negative contribution of the energy of the gravitational field cancels out the matter and energy to give a null value; so really it's just a case of nothing-for-nothing. The issue of particle creation is an example of that free lunch, revisiting some ideas from inflation and cosmology. The false vacuum that ignited inflation was very different from any typical expanding gas (that has positive pressure performing work on the external environment and reducing its internal energy if no heat is added); we can think of the false vacuum as a curved but empty space-time with a constant negative pressure performing work on itself and increasing its total internal energy via an adiabatic process as it inflates. This provides a starting point for the creation of elementary particles, the original inflationary model included an inflaton embedded in a stable field potential and quantum tunnelling as a mechanism for ceasing the exponential expansion. Since tunnelling ends inflation by bubble nucleation, bubbles emerged but sufficient collisions couldn't occur to distribute energy in a homogeneous fashion (the so called 'graceful exit problem'). This poses a big complication for particle creation due to the fact that energy (which is trapped in the bubble walls) can only be freed by the collision of many such bubbles; the graceful exit problem means that the bubbles remain in inhomogeneous clusters. However, this difficulty in early inflationary models was resolved by the concept of a 'slow-roll', whereby inflation is unstable and goes through a phase transition where fluctuations begin at the plateau of a field potential and roll gradually (universe inflates during this time) until it eventually becomes a true vacuum and inflation ends. But the universe becomes too cold after this exponential expansion for any particles or radiation to form so a theory of reheating is required; during this epoch the inflaton field slowly decayed and transferred energy to create particles. Firstly, coherent oscillations of a scalar field occurs and may last for some time if no rapid decays happen, thus the particle decay duration may be a lot longer than the Hubble time. Next, when the Hubble time (here the age of universe) reaches the decay time, the slow-case allows only fermionic decays to occur but when bosonic particles are produced, this allows parametric resonance (like a child swinging on a swing and momentarily standing and squatting to increase the magnitude of the oscillation) to take over. Such parametric resonance promotes a fairly rapid decay termed preheating differentiate it from the initial stage. Occupation numbers (quantities that determine degree to which a quantum state may be filled with particles) produced via parametric resonance are large so that bosons are formed far from maximum entropy (equilibrium); they also give a reason why preheating does not occur is the only decay pathway is fermionic in accordance with the Pauli exclusion principle. Finally, following the formation of high occupation numbers by parametric resonance, the reheating can continue normally according to normal conditions and bosons should interact and decay as well as achieve a state of maximum entropy (equilibrium).

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