Thermal history of the Universe

Given the total density from Eq. (4.17), the temperature follows from the equation of state which depends in turn on what particles are present. For any one species i, with temperature T,. we have from the Fermi-Dirac or Bose-Einstein distribution, Eq. (2.41), 

At each stage, particles coupling to photons (7) = Ty) with m,c2 kTy are relativistic and present in comparable numbers to photons. When kTy drops to true1, they annihilate with their antiparticles and/or decay, or if the coupling is so weak that T Ty, they contribute little mass-energy and are suppressed . The temperature is then fixed as a function of density, and hence time, by the relation 

During most of the first 0.1 second after the Big Bang (ABB), the relativistic particles are photons, electrons, positrons and Nv species of neutrinos and antineutrinos Nv is expected to be 3, from ve, vfl and vr. There is a sprinkling of non-relativistic protons and neutrons which make a completely negligible contribution to the energy density. The temperature is then given by 

After 1 s or so, the neutrinos decouple from the cosmic plasma and expand isentropically for ever afterwards remaining as microwave neutrinos with 

The number rj, together with the known background temperature Tyf), measures the cosmological baryon density today  

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Fig. 4.1. Schematic thermal history of the Universe showing some of the major episodes envisaged in the standard model. GUTs is short for grand unification theories and MWB is short for (the last scattering of) the microwave background radiation. The Universe is dominated by radiation and relativistic particles up to a time a little before that of MWB and by matter (including non-baryonic matter) thereafter, with dark energy eventually taking over.

A pictorial representation of some of the important events in the thermal history of the universe is shown in Figure 12.5. The description of the evolution of the universe begins at 10-43 s after the Big Bang, the so-called Planck time. The universe at that time had a temperature of 1032K kBT 1019GeV) and a volume that was 10-31 of its current volume. [To convert temperature in K to... 

The equilibrium in the hot particle soup is maintained through frequent elementary particle reactions mediated by the quanta of the three fundamental interactions. The expansion of the Universe dilutes the densities and, consequently, the reaction rates get gradually lower. The adiabatic expansion lowers monotonically also the temperature (the average energy density). (Actually, there is a one-to-one mapping between time and temperature.) The following milestones can be listed in the thermal history of the Universe (Kolb and Turner 1990). 

In summary, the thermal history of the early Universe is very simple. It just assumes a global isotropic and uniform Universe. In its simplest version - no structure of any kind on scales larger than individual particles - the contents of the Universe are determined by "standard elmentary physics" i) ag lobal expansion governed by GR, ii) particles interactions governed by the "Standard Model" of Particle Physics, iii) distributions of particles governed by the laws of Statistical Physics. 

Gafifey M. J. (1990) Thermal history of the asteroid belt implications for accretion of the terrestrial planets. In Origin of the Earth (eds. H. E. Newsom and J. H. Jones). Oxford University Press, Oxford, pp. 17-28. 

Tajika, E. (1992) Evolution of the atmosphere and ocean of the Earth global geochemical cycles of C,H,0,N, and S, and degassing history coupled with thermal history. Doctoral Thesis, University Tokyo, 416 pp. 

Schmitz, M. D., Bowring, S. A. Robey, J. v. A. 1998. Constraining the thermal history of an Archean craton U-Pb thermochronology of lower crustal xenoliths from the Kaapvaal craton, southhem Africa. In 7th International Kimberlite Conference, Extended Abstracts. University of Cape Town, Cape Town, 766-768. 

The University of Utah pilot-scale combustion test furnace referred to as the "L1500" is a nominal 15 MMBtu/hr (4.4 MW) pilot-scale furnace designed to simulate commercial combustion conditions, particularly the thermal history of operating commercial coal-fired boilers. 

D. S. McWilliams, Study of the Effect of Thermal History on the Structural Relaxation and Thermoviscoelasticity of Amorphous Polymers, Ph.D. Dissertation, School of Chemical Engineering, Purdue University, Lafayette, Ind., 1996. 

In the present state of the universe, only a very small part of the energy is in the form of protons, neutrons and electrons that make up ordinary matter in all the galaxies. The rest consists of thermal radiation at a temperature of about 2.8 K and particles called neutrinos that interact very weakly with other particles. The small amount of matter which is in the form of stars and galaxies, however, is not in thermodynamic equilibrium. The affinities for the reactions that are currently occurring in the stars are not zero. The nuclear reactions in the stars produce all the known elements from hydrogen [2-4]. Hence the observed properties such as the abundance of elements in stars and planets cannot be described using the theory of chemical equilibrium. A knowledge of the rates of reaction and the history of the star or planet are necessary to understand the abundance of elements. 

Alden Hayes Emery, Jr. (1925-, Ph.D. 54 University of Illinois) has the distinction of being the faculty with the longest tenure in the history of the School, 35 years in 1989. Emery made significant contributions in the field of thermal diffusion and after 1960 in non-Newtonian fluid mechanics. After a 1971 sabbatical leave to Israel, he changed research directions. He started working on biochemical engineering, a research area that still occupies a major portion of his time. In the 1970 s and 1980 s he formed the powerful biochemical engineering research team with H.C. Lim and G.T. Tsao. 

Yoon PJ (2000). Effect of Thermal History on the Rheological Properties of Thermoplastic Polyurethanes, Doctoral Dissertation at the University of Akron, Akron, Ohio. 

Binder, C. R. "Electron Spin Resonance Its Application to the Study of Thermal and Natural Histories of Organic Sediments", Ph.D. Thesis, Pennsylvania State University, 1965,... 

Figure 17 Isothermal melting of Ziegler-Natta isotactic poly(propylene). (a) Spherulites with mixed birefringence at Tc = 148°C. The top middle figure displays the melting for the same thermal history, (b) Subsequent to crystallization, the temperature was raised to 171°C spherulites acquire negative birefringence, (c), (d) and (e) Isothermal melting at 171°C for 80, 200 and 300 min, respectively. Reproduced with permission from W.T. Huang, Dissertation, Florida State University, 2005. (See Color Plate Section at the end of this book.)...

Schubert G. (1986) Thermal histories, compositions, and internal structures of the moons of the solar system. In Satellites (eds. J. A. Burns and M. S. Matthews). University of Arizona Press, Tucson, pp. 224-292. 

Eventually, the answer was found by Albert Einstein and the Polish physicist Marian Smoluchowski (1872-1917), then a professor at the University of Lviv. The title of one of Einstein s papers on the theory of Brownian motion is rather telling On the motion of particles suspended in resting water which is required by the molecular-kinetic theory of heat . Einstein and Smoluchowski considered chaotic thermal motion of molecules and showed that it explains it all a Brownian particle is fidgeting because it is pushed by a crowd of molecules in random directions. In other words, you can say that Brownian particles are themselves engaged in chaotic thermal motion. Nowadays, science does not make much distinction between the phrases Brownian motion and thermal motion — the only difference lies back in history. The Einstein-Smoluchowski theory was confirmed by beautiful and subtle experiments by Jean Perrin (1870-1942). This was a long awaited, clear and straightforward proof that all substances are made of atoms and molecules. ... 

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