Abstract
The main intention of this thesis is to motivate and investigate the \(B\)–\(L\) phase transition as the possible origin for the thermal phase of the hot early universe. Before we are ready to do so, we have to acquaint ourselves with the observational evidence for this phase and understand which physical processes have or may have taken place in it. For this reason we shall provide a brief review of early universe cosmology in this chapter, thereby compiling the background material for the further discussion. We will first discuss the present composition of the universe (cf. Sect. 2.1) and then some of the main events in the thermal history of the universe in reverse chronological order (cf. Sect. 2.2). We would like to emphasize that in this introductory chapter we will crudely restrict ourselves to aspects which are relevant for our purposes. More balanced and comprehensive presentations of the topic are for instance provided in standard textbooks [1–3] or dedicated review articles.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note that in the recent cosmic past, shortly after the onset of star formation, the entropy contained in black holes has come to dominate over the entropy in radiation [18].
- 2.
In the following discussion we shall restrict ourselves to the relic abundance of primordial neutrinos. If neutrinos are Dirac fermions, the abundance of antineutrinos should at each time be approximately the same as the abundance of neutrinos.
- 3.
In order to ensure that the universe as a whole is electrically charge neutral, there has to be present one electron for each proton in the universe. As a single proton is, however, roughly \(1,\!800\) times heavier than an electron, the contribution from electrons to the total energy presently stored in matter is negligibly small, which is why we will not consider it any further.
- 4.
It is also large compared to the observed abundance of luminous matter. The density parameter of stars is smaller than \(\Omega _b^0\) by one order of magnitude, \(\Omega _{\text {stars}} \simeq 2.7 \times 10^{-3}\) [27]. Most baryons are thus optically dark, probably contained in some diffuse intergalactic medium [28].
- 5.
Antiparticles of cosmic origin such as antiprotons and positrons are seen in cosmic rays. Their fluxes are, however, consistent with the assumption that they are merely secondaries produced in energetic collisions of cosmic rays with the interstellar medium rather than primordial relics.
- 6.
For recent reviews on dark matter, cf. for instance Refs. [32–35]. Another ansatz to account for the various observed, but unexplained gravitational effects is to modify the theory of general relativity. While modifications of gravity (cf. in particular Refs. [36, 37]) are often able to explain isolated phenomena, they usually struggle to give a consistent description of all observed phenomena, which is why we will not consider them any further in this thesis.
- 7.
- 8.
The first astronomer to stumble upon the problem of the missing mass in galaxy clusters was Fritz Zwicky. In 1933, observations of the Coma Cluster led him to conclude that the galaxies in the cluster should actually fly apart, if there were not large amounts of invisible matter present in it, holding them together [41]. Zwicky is hence usually credited as the discoverer of dark matter.
- 9.
As light neutrinos turn nonrelativistic only at very late times in the cosmological evolution, they represent, in fact, a form of hot dark matter in the current universe.
- 10.
Later on we shall use a rounded version of the value in Eq. (2.15), namely \(\Omega _{\text {DM}}^{\text {obs}}h^2 = 0.11\).
- 11.
Certain scenarios of warm dark matter or mixed dark matter which is composed of a mixture of cold, warm and or hot components, are also admissible [43, 44]. Likewise, also small amounts of baryonic matter in the form of massive compact halo objects (MACHOs) [45, 46] and or cold molecular gas clouds [47] may well contribute to the dark matter in galaxy halos.
- 12.
- 13.
Naively one might expect the energy density of the vacuum to be related to the Planck scale, \(\rho _\Lambda \sim M_P^4\). Interpreting dark energy as the energy of the vacuum, one then has to explain why \(\rho _\Lambda \simeq 0.73 \rho _c^0 \sim 10^{-123} M_P^4\). For a classic discussion of this so far unsolved problem cf. Ref. [55].
- 14.
Given the allowed range of the total neutrino mass (cf. Eq. (2.7)), matching the two expressions for \(\rho _{\nu _i}\) in Eqs. (2.18) and (2.19) and solving for \(z\) shows that the heaviest neutrino, which eventually contributes most to \(\Omega _\nu ^0\), turns nonrelativistic at a redshift of \(\mathcal {O}(10..100)\).
- 15.
Curiously enough, the matter-dominated era lasts sufficiently long to allow for the formation of such complex structures as galaxies, solar systems and human beings, which, from the perspective of mankind, appears to be a fortunate cosmic coincidence. The question of why dark energy becomes relevant exactly at the present time, i.e. why presently \(\Omega _\Lambda \sim \Omega _m\) rather than \(\Omega _\Lambda \ll \Omega _m\) or \(\Omega _\Lambda \gg \Omega _m\), is one of the greatest puzzles of modern cosmology. Cf. e.g. Ref [56].
- 16.
Prior to hydrogen recombination, at \(T \sim 0.5\,\text {eV}\), helium decouples in a similar way. As hydrogen is still fully ionized at this time, the universe remains opaque after helium recombination.
- 17.
- 18.
Perturbations in the photon-baryon fluid can only evolve causally as long as they extend over scales smaller than the sound horizon. This explains the position of the first acoustic peak in the CMB power spectrum. It is located at an angular scale of roughly \(1^\circ \) or equivalently at \(\ell \sim 200\), which corresponds to the angular diameter of the sound horizon at last scattering.
- 19.
Given a scale factor \(a \propto t^p\), \({\Omega _{\text {tot}} - 1}\) scales like \(\dot{a}^{-2} \propto t^{2(1-p)}\). During the phases of radiation and matter domination we respectively have \(p = 1/2\) and \(p = 2/3\).
- 20.
- 21.
Data on helium-3 solely derives from the solar system and high-metallicity regions of ionized hydrogen in our galaxy, which makes it difficult to infer its primordial abundance. On top of that, the theory of stellar helium-3 synthesis is in conflict with observations. For these two reasons, helium-3 is usually not used as a cosmological probe.
- 22.
Recall that BBN enables us to trace the evolution of the hot thermal phase up to temperatures as high as \(T_{\text {RH}}^{\text {min}} \simeq 4\,\text {MeV}\) or equivalently cosmic times as early as \(t \simeq 0.05\,\text {s}\) (cf. Sect. 2.2.2).
- 23.
The QCD scale \(\Lambda _{\text {QCD}}\) corresponds to the energy scale at which, according to its renormalization group running in perturbative QCD, the strong coupling constant \(g_s\) formally diverges.
- 24.
Likewise, when referring to some Higgs product operator \(s^\dagger s\) acquiring a VEV \(v\), we will also sometimes write \(v = \left\langle s\right\rangle \), although we actually mean \(v = \left\langle s^\dagger s\right\rangle ^{1/2}\).
- 25.
Gauge configurations belonging to different homotopy classes are transformed into each other via large gauge transformations.
References
E.W. Kolb, M.S. Turner, The early universe. Front. Phys. 69, 1–547 (1990)
S. Dodelson, Modern Cosmology (Academic University Press, Amsterdam, 2003)
V. Mukhanov, Physical foundations of cosmology (University Press, Cambridge, UK, 2005)
M. Trodden, S. M. Carroll, TASI lectures: Introduction to cosmology. [astro-ph/0401547].
V. Rubakov, Introduction to Cosmology, PoS(RTN2005)003 (2005).
K. Nakamura et al. (Particle Data Group), Review of particle physics, J. Phys.G G37, 075021 (2010).
E. Komatsu et al., (WMAP Collaboration), Seven-year WMAP observations: cosmological interpretation. Astrophys. J. Suppl. 192, 18 (2011)
W.J. Percival et al., (SDSS Collaboration), Baryon acoustic oscillations in the sloan digital sky survey data release 7 galaxy sample. Mon. Not. Roy. Astron. Soc. 401, 2148–2168 (2010)
A.G. Riess, L. Macri, S. Casertano, M. Sosey, H. Lampeitl et al., A redetermination of the hubble constant with the hubble space telescope from a differential distance ladder. Astrophys. J. 699, 539–563 (2009). [0905.0695].
M. Hicken, W. Wood-Vasey, S. Blondin, P. Challis, S. Jha et al., Improved dark energy constraints from 100 new CfA supernova type ia light curves. Astrophys. J. 700, 1097–1140 (2009). [0901.4804].
R. Kessler, A. Becker, D. Cinabro, J. Vanderplas, J. A. Frieman et al. First-year sloan digital sky survey-II (SDSS-II) supernova results: hubble diagram and cosmological parameters, Astrophys. J. Suppl. 185, 32–84 (2009). [0908.4274].
M. Kowalski et al., (Supernova Cosmology Project), Improved cosmological constraints from new, old and combined supernova datasets. Astrophys. J. 686, 749–778 (2008). [0804.4142].
J.C. Mather, E. Cheng, D. Cottingham, R. Eplee, D. Fixsen et al., Measurement of the cosmic microwave background spectrum by the cobe firas instrument. Astrophys. J. 420, 439–444 (1994)
J.C. Mather, D. Fixsen, R. Shafer, C. Mosier, D. Wilkinson, Calibrator design for the COBE far infrared absolute spectrophotometer (FIRAS). Astrophys. J. 512, 511–520 (1999). [astro-ph/9810373].
G.F. Smoot, C. Bennett, A. Kogut, E. Wright, J. Aymon et al., Structure in the COBE differential microwave radiometer first year maps. Astrophys. J. 396, L1–L5 (1992)
D. Fixsen, The temperature of the cosmic microwave background. Astrophys. J. 707, 916–920 (2009). [0911.1955].
M. Archidiacono, E. Calabrese, A. Melchiorri, The case for rark radiation. Phys. Rev. D84, 123008 (2011). [1109.2767].
C.A. Egan, C.H. Lineweaver, A larger estimate of the entropy of the universe. Astrophys. J. 710, 1825–1834 (2010). [0909.3983].
A. Ringwald, Prospects for the direct detection of the cosmic neutrino background. Nucl. Phys. A827, 501C–506C (2009). [0901.1529].
S. Hannestad, Primordial neutrinos. Ann. Rev. Nucl. Part. Sci. 56, 137–161 (2006). [hep-ph/0602058].
T.L. Smith, S. Das, O. Zahn, Constraints on neutrino and dark radiation interactions using cosmological observations. Phys. Rev. D85, 023001 (2012)
S. Fukuda et al., (Super-Kamiokande Collaboration), Tau neutrinos favored over sterile neutrinos in atmospheric muon-neutrino oscillations. Phys. Rev. Lett. 85, 3999–4003 (2000). [hep-ex/0009001].
Q. Ahmad et al., (SNO Collaboration), Measurement of the rate of \(\nu _e + d \rightarrow p + p + e^-\) interactions produced by \(^8\text{ B }\) solar neutrinos at the Sudbury Neutrino Observatory. Phys. Rev. Lett. 87, 071301 (2001). [nucl-ex/0106015].
W. Hu, D.J. Eisenstein, M. Tegmark, Weighing neutrinos with galaxy surveys. Phys. Rev. Lett. 80, 5255–5258 (1998). [astro-ph/9712057].
J. Lesgourgues, S. Pastor, Massive neutrinos and cosmology. Phys. Rept. 429, 307–379 (2006). [astro-ph/0603494].
S.A. Thomas, F.B. Abdalla, O. Lahav, Upper bound of \(0.28\,\text{ eV }\) on the neutrino masses from the largest photometric redshift survey. Phys. Rev. Lett. 105, 031301 (2010). [0911.5291].
M. Fukugita, P.E. Peebles, The cosmic energy inventory. Astrophys. J. 616, 643–668 (2004). [astro-ph/0406095].
R. Cen, J.P. Ostriker, Where are the baryons? Astrophys. J. 514, 1 (1999). [astro-ph/9806281].
W. Buchmuller, R. Peccei, T. Yanagida, Leptogenesis as the origin of matter. Ann. Rev. Nucl. Part. Sci. 55, 311–355 (2005). [hep-ph/0502169].
G. Steigman, When clusters collide: constraints on antimatter on the largest scales. J. Cosmol. Astropart. Phys. 0810, 001 (2008). [0808.1122].
A.G. Cohen, A. De Rujula, S. Glashow, A matter-antimatter universe? Astrophys. J. 495, 539–549 (1998). [astro-ph/9707087].
G. Bertone, D. Hooper, J. Silk, Particle dark matter: evidence, candidates and constraints. Phys. Rept. 405, 279–390 (2005). [hep-ph/0404175].
J. Einasto, Dark Matter. [0901.0632].
D. Hooper, TASI 2008 Lectures on Dark Matter. [0901.4090].
G. Bertone (ed.), Particle Dark Matter: Observations, Models and Searches (Cambridge University Press, Cambridge, 2010), p. 738.
M. Milgrom, A modification of the newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365–370 (1983)
J.D. Bekenstein, Relativistic gravitation theory for the MOND paradigm. Phys. Rev. D70, 083509 (2004). [astro-ph/0403694].
V.C. Rubin, J. Ford, W. Kent, Rotation of the andromeda nebula from a spectroscopic survey of emission regions. Astrophys. J. 159, 379–403 (1970)
S. Faber, R. Jackson, Velocity dispersions and mass to light ratios for elliptical galaxies. Astrophys. J. 204, 668 (1976)
R. Catena, P. Ullio, A novel determination of the local dark matter density. J. Cosmol. Astropart. Phys. 1008, 004 (2010). [0907.0018].
F. Zwicky, Die rotverschiebung von extragalaktischen nebeln. Helv. Phys. Acta 6, 110–127 (1933)
D. Clowe, M. Bradac, A.H. Gonzalez, M. Markevitch, S.W. Randall et al., A direct empirical proof of the existence of dark matter. Astrophys. J. 648, L109–L113 (2006). [astro-ph/0608407].
M. Viel, J. Lesgourgues, M.G. Haehnelt, S. Matarrese, A. Riotto, Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-alpha forest. Phys. Rev. D71, 063534 (2005). [astro-ph/0501562].
K. Jedamzik, M. Lemoine, G. Moultaka, Gravitino, axino Kaluza-Klein graviton warm and mixed dark matter and reionisation. J. Cosmol. Astropart. Phys. 0607, 010 (2006). [astro-ph/0508141].
B. Paczynski, Gravitational microlensing by the galactic halo. Astrophys. J. 304, 1–5 (1986)
P. Tisserand et al., (EROS-2 Collaboration), Limits on the macho content of the galactic halo from the eros-2 survey of the magellanic clouds. Astron. Astrophys. 469, 387–404 (2007). [astro-ph/0607207].
F. De Paolis, G. Ingrosso, P. Jetzer, M. Roncadelli, A case for a baryonic dark halo. Phys. Rev. Lett. 74, 14–17 (1995). [astro-ph/9410016].
A.G. Riess et al., (Supernova Search Team), Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998). [astro-ph/9805201].
S. Perlmutter et al., (Supernova Cosmology Project), Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophys. J. 517, 565–586 (1999). [astro-ph/9812133], The Supernova Comology Project.
B. Ratra, P. Peebles, Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D37, 3406 (1988)
C. Wetterich, Cosmology and the fate of dilatation symmetry. Nucl. Phys. B302, 668 (1988)
C. Armendariz-Picon, V.F. Mukhanov, P.J. Steinhardt, Essentials of \(k\) essence. Phys. Rev. D63, 103510 (2001). [astro-ph/0006373].
B. Jain, P. Zhang, Observational tests of modified gravity. Phys. Rev. D78, 063503 (2008). [0709.2375].
T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rept. 513, 1–189 (2012)
S. Weinberg, The cosmological constant problem. Rev. Mod. Phys. 61, 1–23 (1989)
I. Zlatev, L.-M. Wang, P.J. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett. 82, 896–899 (1999). [astro-ph/9807002].
R. Dicke, P. Peebles, P. Roll, D. Wilkinson, Cosmic black-body radiation. Astrophys. J. 142, 414–419 (1965)
W. Hu, S. Dodelson, Cosmic microwave background anisotropies. Annu. Rev. Astron. Astrophys. 40, 171–216 (2002). [astro-ph/0110414].
D. Samtleben, S. Staggs, B. Winstein, The cosmic microwave background for pedestrians: a review for particle and nuclear physicists. Annu. Rev. Nucl. Part. Sci. 57, 245–283 (2007). [0803.0834].
R. Sachs, A. Wolfe, Perturbations of a cosmological model and angular variations of the microwave background. Astrophys. J. 147, 73–90 (1967)
E.F. Bunn, A.R. Liddle, M. White, Four year COBE normalization of inflationary cosmologies. Phys. Rev. D54, 5917–5921 (1996). [astro-ph/9607038].
K.A. Olive, G. Steigman, T.P. Walker, Primordial nucleosynthesis: theory and observations. Phys. Rep. 333, 389–407 (2000). [astro-ph/9905320].
F. Iocco, G. Mangano, G. Miele, O. Pisanti, P.D. Serpico, Primordial Nucleosynthesis: from precision cosmology to fundamental physics. Phys. Rep. 472, 1–76 (2009)
R.V. Wagoner, W.A. Fowler, F. Hoyle, On the synthesis of elements at very high temperatures. Astrophys. J. 148, 3–49 (1967)
R.H. Cyburt, B.D. Fields, K.A. Olive, The NACRE thermonuclear reaction compilation and big bang nucleosynthesis. New Astron. 6, 215–238 (2001). [astro-ph/0102179].
R.H. Cyburt, B.D. Fields, K.A. Olive, An Update on the big bang nucleosynthesis prediction for Li-7: The problem worsens. J. Cosmol. Astropart. Phys. 0811, 012 (2008). [0808.2818].
G. Steigman, D. Schramm, J. Gunn, Cosmological limits to the number of massive leptons. Phys. Lett. B66, 202–204 (1977)
G. Mangano, G. Miele, S. Pastor, T. Pinto, O. Pisanti et al., Relic neutrino decoupling including flavor oscillations. Nucl. Phys. B729, 221–234 (2005). [hep-ph/0506164].
J. Bernstein, L.S. Brown, G. Feinberg, Cosmological helium production simplified. Rev. Mod. Phys. 61, 25 (1989)
G. Mangano, P.D. Serpico, A robust upper limit on \(N_{\rm{eff}}\) from BBN, circa. Phys. Lett. B701, 296–299 (2011). [1103.1261].
M. Kawasaki, K. Kohri, N. Sugiyama, Cosmological constraints on late time entropy production. Phys. Rev. Lett. 82, 4168 (1999). [astro-ph/9811437].
S. Hannestad, What is the lowest possible reheating temperature? Phys. Rev. D70, 043506 (2004). [astro-ph/0403291].
R.H. Cyburt, J.R. Ellis, B.D. Fields, K.A. Olive, Updated nucleosynthesis constraints on unstable relic particles. Phys. Rev. D67, 103521 (2003). [astro-ph/0211258].
M. Kawasaki, K. Kohri, T. Moroi, Hadronic decay of late-decaying particles and Big-Bang nucleosynthesis. Phys. Lett. B625, 7–12 (2005). [astro-ph/0402490].
M. Pospelov, Particle physics catalysis of thermal big bang nucleosynthesis. Phys. Rev. Lett. 98, 231301 (2007). [hep-ph/0605215].
M. Kawasaki, K. Kohri, T. Moroi, Big bang nucleosynthesis and hadronic decay of long-lived massive particles. Phys. Rev. D71, 083502 (2005). [astro-ph/0408426].
K. Jedamzik, Big bang nucleosynthesis constraints on hadronically and electromagnetically decaying relic neutral particles. Phys. Rev. D74, 103509 (2006). [hep-ph/0604251].
M. Kawasaki, K. Kohri, T. Moroi, A. Yotsuyanagi, Big bang nucleosynthesis and gravitino. Phys. Rev. D78, 065011 (2008)
G. Aad et al., (ATLAS Collaboration), Combined search for the standard model higgs boson using up to \(4.9\,\text{ fb }^{-1}\) of pp collision data at \(\sqrt{s} = 7 \,\text{ TeV }\) with the ATLAS detector at the LHC. Phys. Lett. B710, 49–66 (2012). [hep-ph/9809381].
S. Chatrchyan et al., (CMS), Combined results of searches for the standard model higgs boson in pp collisions at \(\sqrt{s} = 7 \,\text{ TeV }\). Phys. Lett. B710, 26–48 (2012). [1202.1408].
G. ’t Hooft, Symmetry breaking through bell-jackiw anomalies. Phys. Rev. Lett. 37, 8–11 (1976).
G. ’t Hooft, Computation of the quantum effects due to a four-dimensional pseudoparticle. Phys. Rev. D14, 3432–3450 (1976).
N. Manton, Topology in the Weinberg-Salam Theory. Phys. Rev. D28, 2019 (1983)
F.R. Klinkhamer, N. Manton, A saddle Point solution in the Weinberg-Salam theory. Phys. Rev. D30, 2212 (1984)
V. Kuzmin, V. Rubakov, M. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe. Phys. Lett. B155, 36 (1985)
P.B. Arnold, L.D. McLerran, Sphalerons, small fluctuations and baryon number violation in electroweak theory. Phys. Rev. D36, 581 (1987)
H. Klapdor-Kleingrothaus, S. Kolb, V. Kuzmin, Light lepton number violating sneutrinos and the baryon number of the universe. Phys. Rev. D62, 035014 (2000). [hep-ph/9909546].
P.B. Arnold, L.G. Yaffe, Nonperturbative dynamics of hot non-abelian gauge fields: beyond leading log approximation. Phys. Rev. D62, 125013 (2000). [hep-ph/9912305].
S.Y. Khlebnikov, M. Shaposhnikov, The statistical theory of anomalous fermion number nonconservation. Nucl. Phys. B308, 885–912 (1988)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Schmitz, K. (2014). Early Universe Cosmology. In: The B−L Phase Transition. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-00963-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-00963-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00962-9
Online ISBN: 978-3-319-00963-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)