Inflaton Field
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Inflaton Field
The inflaton field is a hypothetical scalar field which is conjectured to have driven cosmic inflation in the very early universe. The field, originally postulated by Alan Guth, provides a mechanism by which a period of rapid expansion from 10−35 to 10−34 seconds after the initial expansion can be generated, forming a universe consistent with observed spatial isotropy and homogeneity. Cosmological inflation The basic model of inflation proceeds in three phases: * Expanding vacuum state with high potential energy * Phase transition to true vacuum * Slow roll and reheating Expanding vacuum state with high potential energy In quantum field theory, a vacuum state or vacuum is a state of quantum fields which is at locally minimal potential energy. Quantum particles are excitations which deviate from this minimal potential energy state, therefore a vacuum state has no particles in it. Depending on the specifics of a quantum field theory, it can have more than one ...
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Scalar Field Theory
In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar. Since they do not involve polarization complications, scalar fields are often the easiest to appreciate second quantization through. For this reason, scalar field theories are often used for purposes of introduction of novel concepts and techniques. The signature of the metric employed below is . Classical scalar field theory A general reference for this section is Ramond, Pierre (2001-12-21). Field Theory: A Modern Primer (Second Edition). USA: Westview Press. , Ch 1. Linear (free) theory The most basic scalar field theo ...
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Gluon
A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind quarks together, forming hadrons such as protons and neutrons. Gluons are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics (QCD). Gluons themselves carry the color charge of the strong interaction. This is unlike the photon, which mediates the electromagnetic interaction but lacks an electric charge. Gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than quantum electrodynamics (QED). Properties The gluon is a vector boson, which means, like the photon, it has a spin of 1. While massive spin-1 particles have three polarization states, massless gauge bosons like the gluon have only two polarization states because gauge ...
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Cosmological Constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. He later removed it. Much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy. Einstein originally introduced the constant in 1917 to counterbalance the effect of gravity and achieve a static universe, a notion that was the accepted view at the time. Einstein's cosmological constant was abandoned after Edwin Hubble's confirmation that the universe was expanding. From the 1930s until the late 1990s, most physicists agreed with Einstein's choice of setting the cosmological constant to zero. That changed with the discovery in 1998 that the expansion of the universe is accelerating, im ...
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Hubble's Law
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum. Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is known as the Hubble flow. It is described by the equation , with ''H''0 the constant of proportionality—the Hubble constant—between the "proper distance" ''D'' to a galaxy, which can change over time, unlike the comoving distance, and its speed of separation ''v'', i.e. the derivative of proper distance with respect ...
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Einstein–Hilbert Action
The Einstein–Hilbert action (also referred to as Hilbert action) in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the metric signature, the gravitational part of the action is given as :S = \int R \sqrt \, \mathrm^4x, where g=\det(g_) is the determinant of the metric tensor matrix, R is the Ricci scalar, and \kappa = 8\pi Gc^ is the Einstein gravitational constant (G is the gravitational constant and c is the speed of light in vacuum). If it converges, the integral is taken over the whole spacetime. If it does not converge, S is no longer well-defined, but a modified definition where one integrates over arbitrarily large, relatively compact domains, still yields the Einstein equation as the Euler–Lagrange equation of the Einstein–Hilbert action. The action was first proposed by David Hilbert in 1915. Discussion Deriving equations of motion from an action has several advantages. First, it allows ...
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Action (physics)
In physics, action is a scalar quantity describing how a physical system has dynamics (physics), changed over time. Action is significant because the equations of motion of the system can be derived through the principle of stationary action. In the simple case of a single particle moving with a constant velocity (uniform linear motion), the action is the momentum of the particle times the distance it moves, integral (mathematics), added up along its path; equivalently, action is twice the particle's kinetic energy times the duration for which it has that amount of energy. For more complicated systems, all such quantities are combined. More formally, action is a functional (mathematics), mathematical functional which takes the trajectory (also called path or history) of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has dimensional analysis, dimensions of energy × time or momentu ...
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Xi (letter)
Xi is the 14th letter of the Greek alphabet (uppercase Ξ, lowercase ξ; el, ξι), representing the voiceless consonant cluster . It is pronounced in Modern Greek, and generally or in English. In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh . Xi is distinct from the letter chi, which gave its form to the Latin letter X. Greek Both in classical Ancient Greek and in Modern Greek, the letter Ξ represents the consonant cluster /ks/. In some archaic local variants of the Greek alphabet, this letter was missing. Instead, especially in the dialects of most of the Greek mainland and Euboea, the cluster /ks/ was represented by Χ (which in classical Greek is chi, used for ). Because this variant of the Greek alphabet was used in Magna Graecia (the Greek colonies in Sicily and the southern part of the Italian peninsula), the Latin alphabet borrowed Χ rather than Ξ as the Latin letter that represented the /ks/ cluster ...
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Coupling Constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, r^2, between the bodies; thus: G in F=G m_1 m_2/r^2 for Newtonian gravity and k_\text in F=k_\textq_1 q_2/r^2 for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers. A modern and more general definition uses the Lagrangian \mathcal (or equivalently the Hamiltonian \mathcal) of a system. Usually, \mathcal (or \mathcal) of a system describing an interaction can be separated into a ''kinetic part'' T and an ''interaction part'' V: \mathcal=T-V (or \mathcal=T+V). In field theory, V always contains 3 fields te ...
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Inflaton Field
The inflaton field is a hypothetical scalar field which is conjectured to have driven cosmic inflation in the very early universe. The field, originally postulated by Alan Guth, provides a mechanism by which a period of rapid expansion from 10−35 to 10−34 seconds after the initial expansion can be generated, forming a universe consistent with observed spatial isotropy and homogeneity. Cosmological inflation The basic model of inflation proceeds in three phases: * Expanding vacuum state with high potential energy * Phase transition to true vacuum * Slow roll and reheating Expanding vacuum state with high potential energy In quantum field theory, a vacuum state or vacuum is a state of quantum fields which is at locally minimal potential energy. Quantum particles are excitations which deviate from this minimal potential energy state, therefore a vacuum state has no particles in it. Depending on the specifics of a quantum field theory, it can have more than one ...
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Gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light. On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circ ...
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Cosmic Inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from  seconds after the conjectured Big Bang singularity to some time between and  seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago). Inflation theory was developed in the late 1970s and early 80s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Alexei Starobinsky, Alan Guth, and Andrei Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation." It was developed further in the earl ...
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Higgs Field
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positive) parity, no electric charge, and no colour charge, that couples to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately. The Higgs field is a scalar field, with two neutral and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry. Its " Mexican hat-shaped" potential leads it to take a nonzero value ''everywhere'' (including otherwise empty space), which breaks the weak isospin symmetry of the electroweak interaction, and via the Higgs mechanism gives mass to many particles. Both the field and the boson are named after physicist Peter Higgs, who in 1964, alo ...
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