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Electroweak epoch

The electroweak epoch was a pivotal stage in the early universe, occurring around 10^{-12} seconds after the Big Bang at a temperature of about 10^{15} K, during which the electromagnetic and weak nuclear forces remained unified as a single electroweak interaction mediated by massless gauge bosons.^[1]^[2]^[3]^[4] This epoch followed the grand unification era, where the strong nuclear force had already separated from the electroweak force, leaving the universe dominated by a plasma of quarks, leptons, antiquarks, antileptons, gluons, and the massless electroweak gauge bosons.^[1]^[2] At these extreme conditions, the electroweak symmetry preserved the unification, with all particles relativistic and interacting symmetrically.^[3] As expansion continued, the temperature dropped to the electroweak scale (around 100 GeV, corresponding to ~10^{15} K), triggering spontaneous symmetry breaking via the Higgs mechanism, which separated the electroweak force into the distinct electromagnetic force (mediated by the massless photon) and weak force (mediated by the massive W and Z bosons).^[1]^[2] This second major symmetry breaking in cosmic history established the four fundamental forces in their modern forms—gravity, strong nuclear, weak nuclear, and electromagnetic—and allowed for the emergence of massive particles, transitioning the universe toward the subsequent quark epoch.^[1]^[3] The electroweak epoch holds significant implications for particle physics and cosmology, as its dynamics mirror those tested in laboratories like CERN's Large Hadron Collider, where collisions recreate the high-energy conditions of symmetry breaking and confirm the Higgs boson's role.^[5] In extensions beyond the Standard Model, a strongly first-order phase transition during this period could have generated primordial gravitational waves potentially observable today and contributed to baryogenesis, accounting for the observed baryon asymmetry in the universe.^[6]

Introduction

Definition and Overview

The electroweak epoch represents a critical phase in Big Bang cosmology during which the electromagnetic and weak nuclear forces were unified into a single electroweak force, distinct from the strong nuclear force and gravity. This unification occurred under conditions of extreme temperature and density, where the symmetries of the fundamental interactions were preserved at high energies.^[7] In the broader cosmological timeline, the electroweak epoch followed the inflationary period, which rapidly expanded the universe, and preceded the quark epoch, marking a transition toward the formation of hadrons. At this stage, the universe consisted primarily of a hot plasma of elementary particles, including quarks, leptons, and gauge bosons, interacting via the unified electroweak force.^[2] A defining characteristic of the epoch was the high symmetry among the fundamental forces, enabled by energies exceeding approximately 100 GeV, corresponding to temperatures around $10^{15} K. This symmetry allowed the electromagnetic and weak interactions to manifest as a single entity, influencing particle behavior in ways not observed at lower energies today.^[1]^[8] The electroweak epoch spanned from shortly after the end of cosmic inflation, around $10^{-32} seconds, to approximately $10^{-12} seconds after the Big Bang, though precise boundaries can vary slightly depending on the specific cosmological model employed.^[7]^[4] As the universe expanded and cooled, this phase culminated in the separation of the electromagnetic and weak forces into distinct interactions.^[2]

Historical Context

The concept of the electroweak epoch emerged from the development of electroweak theory in the 1960s, when physicists sought to unify the electromagnetic and weak nuclear forces. Sheldon Glashow proposed an SU(2) × U(1) gauge model in 1961, introducing a neutral vector boson to mediate weak interactions alongside the photon, though it initially lacked a mechanism for massive weak bosons. In 1967, Steven Weinberg advanced this framework in his seminal paper "A Model of Leptons," incorporating spontaneous symmetry breaking—later associated with the Higgs mechanism—to generate masses for the charged weak bosons (W±) and a neutral boson (Z), while preserving the photon's masslessness; this model also predicted weak neutral currents. Independently, Abdus Salam developed a parallel formulation in 1968, completing the core unification predictions that linked the two forces at high energies. The theory gained rigor in 1971 when Gerardus 't Hooft and Martinus Veltman demonstrated its renormalizability, enabling precise calculations and resolving infinities in quantum corrections. Experimental validation followed swiftly: weak neutral currents were discovered in 1973 by the Gargamelle bubble chamber experiment at CERN's Proton Synchrotron, confirming Weinberg's predictions. The definitive confirmation came in 1983 with the discovery of the W± and Z bosons by the UA1 and UA2 collaborations at CERN's Super Proton Synchrotron collider, whose masses aligned closely with electroweak predictions around 80 and 91 GeV, respectively; this breakthrough earned Glashow, Weinberg, and Salam the 1979 Nobel Prize in Physics, with Carlo Rubbia and Simon van der Meer receiving the 1984 Nobel for the experimental achievement. These milestones solidified electroweak unification as a cornerstone of the Standard Model.^[9]^[10]^[11] In the 1970s and 1980s, electroweak theory was incorporated into Big Bang cosmology through grand unified theories (GUTs), such as the SU(5) model proposed by Howard Georgi and Glashow in 1974, which embedded electroweak unification within a larger framework where all fundamental forces except gravity converge at energies around 10¹⁵ GeV, corresponding to the early universe's GUT epoch shortly before the electroweak phase. This integration framed the electroweak epoch—spanning from shortly after the end of cosmic inflation, around 10^{-32} seconds, to approximately 10^{-12} seconds after the Big Bang—as the period when the unified electroweak force separated into distinct electromagnetic and weak interactions amid cooling temperatures near 10¹⁵ K. Early models, influenced by GUTs, envisioned the electroweak symmetry breaking as a first-order phase transition to explain baryon asymmetry via mechanisms like bubble nucleation. However, lattice gauge theory simulations from the 1990s onward, refined in subsequent studies, established that the transition in the Standard Model is instead a smooth crossover, lacking the sharp discontinuities of a first-order process.^[12]^[13]^[4]

Physical Conditions

Timeline and Temperature Scale

The electroweak epoch commenced approximately $10^{-36} seconds after the Big Bang, immediately following the conclusion of the grand unification epoch during which the strong nuclear force decoupled from the electroweak interaction.^[4] This timing corresponds to the point where the universe's temperature had cooled sufficiently below the grand unification scale but remained high enough for electroweak unification to dominate fundamental interactions. The epoch ended around $10^{-12} seconds, at which juncture the electroweak symmetry breaking occurred, leading to the differentiation of the electromagnetic and weak forces and the onset of the quark epoch.^[14] At the onset of the electroweak epoch, the universe's temperature was approximately $10^{27} K, corresponding to energies around $10^{15} GeV. As the epoch progressed, the temperature decreased to the critical value for symmetry breaking of approximately 159.5 ± 1.5 GeV (~ $10^{15} K), marking the thermal boundary where the unified electroweak force began to separate. This equivalence between temperature and energy scales is fundamental in cosmology, as it allows thermal energies to be directly compared to particle masses and interaction strengths, with kT providing the characteristic energy per particle degree of freedom, where k is the Boltzmann constant (k = 8.617 \times 10^{-5} eV/K). During this phase, the universe was in a radiation-dominated era, where the Hubble parameter H, describing the expansion rate, was given by H \approx 1/(2t), with t being the cosmic time.^[14] This relation implies that the temperature scaled inversely with the scale factor a as T \propto 1/a, leading to a cooling rate dT/dt = -H T. Consequently, the rapid expansion driven by the high energy density of relativistic particles accelerated the drop in temperature, setting the temporal boundaries of the epoch through the interplay of thermodynamic evolution and gravitational dynamics.^[15]

Particle Content and Interactions

During the electroweak epoch, the universe consisted of a high-temperature plasma dominated by the fundamental particles of the Standard Model, including quarks across all six flavors, three generations of charged leptons and neutrinos, the eight gluons, the photon, the W± and Z⁰ gauge bosons, and the Higgs boson.^[16] These particles existed as relativistic excitations, with quarks and gluons forming the primary constituents due to the extreme conditions.^[17] At temperatures above 100 GeV, the plasma was in a deconfined state, preventing the formation of hadrons. The state of matter was a quark-gluon plasma (QGP), characterized by free-streaming quarks, antiquarks, and gluons interacting weakly via asymptotic freedom at short distances.^[17] Chiral symmetry was restored at these energies, rendering all fermions massless and eliminating the chiral condensate that breaks this symmetry in the low-temperature QCD vacuum.^[16] The effective number of relativistic degrees of freedom in the Standard Model reached g_* ≈ 106.75, accounting for the contributions from bosons (with factor 1) and fermions (with factor 7/8), which determined the thermodynamic properties like energy and entropy densities.^[16] Interactions among these particles were governed by the unified electroweak force, alongside strong interactions via gluons. Rapid scattering processes, such as quark-gluon scatterings and electroweak gauge boson exchanges, along with pair annihilations and creations, maintained the plasma in thermal equilibrium, as interaction rates far exceeded the Hubble expansion rate.^[17] Neutrinos, fully coupled through weak interactions during this epoch, played a key role in equilibrating the plasma but decoupled later, around 1 second after the Big Bang at temperatures below 1 MeV, after which their distribution froze out and contributed to the relic lepton asymmetry observed today.^[18]

Theoretical Framework

Electroweak Unification

The electroweak unification describes how the electromagnetic and weak nuclear forces, which appear distinct at low energies, emerge as two aspects of a single fundamental interaction at high energies above approximately 100 GeV. This framework integrates the U(1) gauge symmetry of electromagnetism with the SU(2) structure of the weak force into a cohesive electroweak theory, enabling consistent descriptions of particle interactions through shared gauge bosons. Developed primarily through the contributions of Sheldon Glashow, Steven Weinberg, and Abdus Salam, the theory predicts that at sufficiently high temperatures, such as those prevailing in the early universe during the electroweak epoch, these forces behave as a unified entity.^[19] A key prediction of electroweak unification is the existence of neutral weak currents, mediated by a neutral gauge boson, alongside the charged currents already observed in weak interactions, as well as the inherent parity violation in weak processes due to the chiral nature of the weak force. These features distinguish the unified theory from earlier models of the weak interaction, providing testable signatures for experimental verification. The theory also forecasts specific relationships between the masses and coupling strengths of the electroweak bosons, ensuring the unification scale aligns with observable particle physics phenomena.^[20] Experimental confirmation of electroweak unification came first with the 1973 discovery of neutral currents in neutrino scattering experiments at CERN's Gargamelle detector, which matched the theory's predictions for their strength and parity-violating behavior. Further validation occurred in 1983 with the detection of the charged W bosons and neutral Z boson at the CERN Super Proton Synchrotron, where their measured masses—approximately 80 GeV for W and 91 GeV for Z—and decay couplings precisely aligned with electroweak predictions, solidifying the unification. These discoveries not only confirmed the model's core tenets but also demonstrated its predictive power across diverse experimental regimes.^[21]^[22] In contrast to grand unified theories (GUTs), where the strong force governed by SU(3) color symmetry separates from the electroweak sector at much higher energies around 10^{16} GeV during the earlier GUT epoch, electroweak unification operates at a distinctly lower scale without incorporating the strong interaction. This separation highlights the hierarchical nature of force unifications in the standard model, with electroweak symmetry persisting until lower temperatures in cosmic evolution. Additionally, the electroweak theory's formulation as a renormalizable quantum field theory, proven by Gerardus 't Hooft and Martinus Veltman through systematic handling of infinities in perturbative calculations, ensures its mathematical consistency and applicability for precise predictions.^[2]^[23]

Symmetry and Gauge Group

The electroweak theory is based on the non-Abelian gauge group SU(2)_L \times U(1)_Y, where SU(2)_L acts on left-handed fermion fields and U(1)_Y assigns hypercharge Y to all fields.^[24] This structure unifies the weak and electromagnetic interactions through a spontaneously broken symmetry, with the left-handed quarks and leptons transforming as doublets under SU(2)_L, such as the lepton doublet (\nu_e, e)_L with Y = -1, while right-handed fields are singlets, like e_R with Y = -2. Similarly, quark doublets like (u, d)_L carry Y = 1/3, and right-handed quarks u_R, d_R have Y = 4/3, -2/3, respectively. The Higgs field is introduced as a complex scalar doublet \phi with Y = 1, which acquires a vacuum expectation value to break the symmetry. The mixing between the SU(2)_L and U(1)_Y gauge interactions is parameterized by the Weinberg angle \theta_W, defined such that \sin^2 \theta_W = g'^2 / (g^2 + g'^2), where g and g' are the respective coupling constants. This angle determines the relative strengths of the weak and electromagnetic forces, with the photon field emerging as a massless combination A_\mu = B_\mu \sin \theta_W + W^3_\mu \cos \theta_W and the Z boson as the orthogonal massive combination. Experimental measurements at the Z-pole yield \sin^2 \theta_W \approx 0.231.^[25] Spontaneous symmetry breaking occurs when the Higgs doublet develops a vacuum expectation value \langle \phi \rangle = (0, v/\sqrt{2})^T, with v \approx 246 GeV, reducing the gauge group to the unbroken U(1)_{EM} of electromagnetism. The interactions of matter fields with the gauge bosons are encoded in the covariant derivative

D_\mu = \partial_\mu - i g \frac{\tau^a}{2} W^a_\mu - i \frac{g'}{2} Y B_\mu,

where \tau^a are the Pauli matrices for the SU(2)_L generators. This formulation ensures gauge invariance and leads to the observed charged weak currents mediated by W^\pm bosons and neutral currents via the [Z](/page/Z).^[24]

Key Processes

Electroweak Symmetry Breaking

The electroweak symmetry breaking represents the spontaneous violation of the SU(2)_L × U(1)_Y gauge symmetry in the early universe, triggered as the temperature falls below the critical value T_c \approx 159.5 GeV. At high temperatures above T_c, thermal effects restore the symmetry, keeping the Higgs field in a symmetric vacuum state with zero expectation value. As the universe expands and cools through this threshold, the Higgs field undergoes a phase transition, settling into a state with a non-zero vacuum expectation value (VEV) of approximately 246 GeV at zero temperature, which breaks the electroweak symmetry while preserving the subgroup corresponding to electromagnetism. This process is described within the Standard Model framework, where the symmetry restoration at high temperatures arises from thermal corrections to the Higgs potential. According to the Goldstone theorem, the spontaneous breaking of a global symmetry would produce massless Goldstone bosons equal in number to the broken generators; however, in the gauged electroweak theory, three of these would-be Goldstone modes are absorbed by the W^\pm and Z gauge bosons via the Higgs mechanism, rendering them massive (with masses around 80 GeV and 91 GeV, respectively). The orthogonal combination of the neutral gauge fields remains unbroken, corresponding to the U(1)_{EM} electromagnetic symmetry, which leaves the photon massless and mediates the long-range electromagnetic force. This selective breaking ensures that only the electromagnetic interaction survives as a long-range force, while the weak interaction, now carried by massive bosons, becomes short-range, confined to distances on the order of $10^{-18} m.^[26] In the Standard Model, the electroweak transition is characterized as a smooth crossover rather than a sharp first- or second-order phase transition, primarily due to the Higgs boson mass exceeding 114 GeV, as established by LEP experiments. For Higgs masses below approximately 70 GeV, the transition could be first-order, but the observed Higgs mass of about 125 GeV ensures a continuous, second-order-like evolution without latent heat release or distinct phases. This crossover nature implies a gradual symmetry breaking over a narrow temperature range around T_c, with no significant barriers in the effective potential that would produce bubbles of broken symmetry phase.^[27]

Higgs Mechanism

The Higgs mechanism provides the framework for mass generation in the Standard Model of particle physics, particularly within the electroweak sector, by introducing a scalar Higgs field that interacts with fermions and gauge bosons through the electroweak Higgs doublet \phi = \begin{pmatrix} \phi^+ \\ \phi^0 \end{pmatrix}.^[28]^[29]^[30] This doublet acquires a nonzero vacuum expectation value (VEV) due to spontaneous symmetry breaking, leading to Yukawa couplings that generate fermion masses and gauge interactions that endow the W and Z bosons with mass while leaving the photon massless.^[25] The mechanism was first proposed in the context of gauge theories by Englert and Brout, and independently by Higgs, with its integration into the full electroweak unification achieved by Weinberg.^[28]^[29]^[30] The Higgs potential driving this process is given by

V(\phi) = -\mu^2 |\phi|^2 + \lambda |\phi|^4,

where \mu^2 > 0 and \lambda > 0 ensure a stable minimum at |\phi| = v/\sqrt{2}, with the VEV v \approx 246 GeV determined from the Fermi constant via v = ( \sqrt{2} G_F )^{-1/2}.^[25] This VEV breaks the SU(2)_L \times U(1)_Y symmetry spontaneously, resulting in three Goldstone modes that are absorbed by the W^\pm and Z bosons to provide their longitudinal polarizations, while the remaining radial excitation manifests as the Higgs boson with mass M_H = \sqrt{2\lambda} v.^[29]^[25] For the electroweak gauge bosons, masses arise from the covariant kinetic term |D_\mu \phi|^2 in the Lagrangian, where D_\mu includes the SU(2)_L coupling g and U(1)_Y coupling g'. After symmetry breaking, the W^\pm bosons acquire mass M_W = \frac{g v}{2}, and the Z boson mass is M_Z = \frac{v}{2} \sqrt{g^2 + g'^2}, with the ratio M_Z / M_W = 1 / \cos \theta_W where \theta_W is the weak mixing angle.^[25] These expressions ensure consistency with low-energy weak interaction data, such as the muon decay rate parameterized by G_F.^[25] Fermion masses are generated through Yukawa interactions in the Lagrangian term \bar{\psi}_L y_f \phi \psi_R + \text{h.c.}, where y_f is the Yukawa coupling for fermion f. Upon acquiring the VEV, this yields m_f = y_f v / \sqrt{2}, with the Higgs-fermion coupling strength y_f = \sqrt{2} m_f / v dictating decay rates and mixing.^[25] This coupling hierarchy explains the observed fermion mass spectrum, from light neutrinos to the top quark.^[25] Beyond mass generation, the Higgs mechanism ensures perturbative unitarity in high-energy processes, particularly resolving divergences in longitudinal W_L W_L \to W_L W_L scattering amplitudes that would otherwise grow as s / v^2 (with center-of-mass energy squared s) and violate unitarity bounds above \sim 1 TeV in the absence of the Higgs. The exchange of virtual Higgs bosons in the s-, t-, and u-channels cancels these leading-order contributions, maintaining scattering cross-sections below the unitarity limit and stabilizing the theory up to the electroweak scale. This feature underscores the necessity of the Higgs for a consistent ultraviolet behavior of the electroweak sector.

Epoch Transition

Phase Transition Dynamics

In the Standard Model, the electroweak phase transition proceeds as a continuous crossover rather than a sharp discontinuity, as established by non-perturbative lattice simulations of the full electroweak sector. These computations demonstrate that the transition lacks latent heat, with the order parameter—the Higgs vacuum expectation value—evolving smoothly without abrupt changes in the free energy.^[27] Consequently, phenomena associated with first-order transitions, such as bubble nucleation and potential supercooling, do not occur; instead, the symmetry breaking unfolds gradually across a finite temperature range around 159.5 GeV.^[27] This crossover nature is triggered by the thermal mass of the Higgs field diminishing as the universe cools, allowing the field to settle into its broken-phase minimum.^[31] The dynamics of this crossover influence the universe's thermodynamic evolution, particularly through variations in the effective number of relativistic degrees of freedom, denoted g_*. Prior to the transition, g_* \approx 106.75, accounting for all Standard Model particles contributing to the radiation energy density as massless modes at high temperatures. As the symmetry breaks and the W and Z bosons, along with the Higgs, acquire masses and decouple from the relativistic plasma, g_* decreases to lower values (around 86.25 immediately after, further reducing as quarks and other particles decouple). This shift reduces the total entropy density and energy content in relativistic species, thereby altering the cosmic expansion rate, as the Hubble parameter H scales with \sqrt{g_*} T^2 / M_{\rm Pl}, where T is the temperature and M_{\rm Pl} is the Planck mass. During the electroweak epoch, the universe remains radiation-dominated, so the expansion is governed by the Friedmann equation:

H^2 = \frac{8\pi [G](/page/G)}{3} \rho,

where \rho is the total energy density, predominantly from relativistic particles (\rho \approx \frac{\pi^2}{30} g_* T^4).^[14] The crossover thus imprints a mild change in H, but without the violent reheating or entropy injections of a first-order scenario. The entire process unfolds over a brief timescale of rapid cooling, spanning approximately $10^{-11} to $10^{-10} seconds after the Big Bang, corresponding to temperatures from roughly 200 GeV to 100 GeV.^[14] At this juncture, the physical size of the particle horizon—the causal horizon for processes during the transition—is on the order of $10^{-10} light-seconds, limiting the spatial scales over which symmetry breaking can correlate.

Aftermath and Observational Links

Following the electroweak epoch, the symmetry breaking imparts masses to the W and Z bosons through the Higgs mechanism, with measured values of approximately 80.36 GeV (as of 2024) for the W bosons and 91.19 GeV for the Z boson.^[32]^[33] This mass generation confines the weak force to short ranges, on the order of $10^{-18} meters, determined by the inverse of the boson masses via the Compton wavelength \lambda \approx \hbar / (M c). As a result, weak interactions become short-range mediators of processes like beta decay, distinct from the long-range electromagnetic force that emerges concurrently as photons remain massless. The electroweak scale provides a potential site for baryogenesis, where the observed matter-antimatter asymmetry could arise during the phase transition. Sphaleron processes, non-perturbative transitions violating baryon number while preserving B - L, become active near the critical temperature and can convert lepton asymmetries into baryon asymmetries. However, the Standard Model's CP violation, primarily from the CKM matrix, is insufficient to generate the required asymmetry of \eta_B \approx 6 \times 10^{-10}, necessitating additional sources of CP violation in beyond-Standard-Model physics, such as extended Higgs sectors. In extensions of the Standard Model, a strongly first-order electroweak phase transition can produce a stochastic gravitational wave background through bubble nucleation and collisions.^[34] This signal, peaking in the millihertz frequency band, offers a promising target for detection by future space-based observatories like LISA, which could probe transition parameters such as the bubble wall velocity and latent heat release.^[34] Such observations would provide indirect evidence of new physics driving the transition, complementing collider searches. Direct relics from the electroweak epoch are absent due to the high temperatures erasing primordial signatures, but indirect imprints appear in precision cosmology. Constraints from cosmic microwave background (CMB) anisotropies, such as those from Planck, limit energy injections from potential heavy particle decays around this epoch, affecting recombination and reionization processes. Similarly, neutrino physics probes these links, as electroweak-scale decays into neutrinos could distort the CMB spectrum or influence big bang nucleosynthesis bounds via electromagnetic cascades. Beyond-Standard-Model scenarios, such as supersymmetry, can strengthen the electroweak phase transition to first order by introducing new scalar fields or multiplets that enhance the Higgs potential barrier.^[35] In minimal supersymmetric extensions, this alters the transition dynamics, enabling viable electroweak baryogenesis while providing stable neutralino candidates as thermal dark matter relics with masses around 200–500 GeV.^[35] These models predict compressed spectra of charginos and neutralinos, testable through direct detection experiments and improved measurements of the electron electric dipole moment.^[35]

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