An Etymological Dictionary of Astronomy and Astrophysics
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The assumption whereby the density fluctuations in the very → early Universe would be produced by compressing or decompressing of all components of a homogeneous Universe. The adiabatic initial conditions lead to coherent oscillations in the form of peaks in the → temperature anisotropy spectrum. See also → acoustic peak, → baryon acoustic oscillation.

→ adiabatic; → initial; → condition.

A proposal regarding the initial state of the → Universe prior to the → Planck era. This → no boundary hypothesis assumes an imaginary time in that epoch. In other words, there was no real time before the → Big Bang, and the Universe did not have a beginning. Moreover, this model treats the Universe like a quantum particle, in an attempt to encompass → quantum mechanics and → general relativity; and attributes a → wave function to the Universe. The wave function has a large value for our own Universe, but small, non-zero values for an infinite number of other possible, parallel Universes.

Hartle, J., Hawking, S., 1983, "Wave function of the Universe," Physical Review D 28; → initial; → state.

Of, pertaining to, or occurring at the beginning.

Initial, from L. initialis, from initium "a beginning, an entrance," from p.p. stem of inire "to go into, begin," from → in- + ire "to go," → ion.

Âqâzin "pertaing to the beginning," from âqâz "beginning," from Proto-Iranian *āgāza-, from prefix ā- + *gāz- "to take, receive," cf. Sogdian āγāz "beginning, start," pcγz "reception, taking."

1) Conditions at an initial time t = t₀ from which a physical system or a given set of mathematical equations evolves.
2) Meteo.: A prescription of the state of a → dynamical system at a specified time; for all subsequent times, the → equation of motion and → boundary conditions determine the state of the system.

→ initial; → condition.

The mass of a star at its arrival on the → main sequence.

→ initial; → mass.

A mathematical expression describing the relative number of stars found in different ranges of mass for a cluster of stars at the time of its formation. It is defined as φ(log M) = dN / dlog M ∝ M ^-Γ, where M is the mass of a star and N is the number of stars in a logarithmic mass interval. The value of the slope found by Salpeter (1955) for → low-mass and → intermediate-mass stars in the → solar neighborhood is Γ = 1.35. The IMF can be expressed also in linear mass units: χ(M) = dN / DM ∝ M ^-α. Note that χ(M) = (1 / M lm 10) φ(log M), and α = Γ + 1. In this formalism the Salpeter slope is α = 2.35. There is a third way for representing the IMF, in which the exponent is x = -α. The IMF is not a single power law over all masses, from → brown dwarfs to → very massive stars (Kroupa, 2002, Science 295, 82). Different slopes have been found for different mass segments, as follows: α = 1.3 for 0.08 ≤ M_solar < 0.5; α = 2.3 for 0.5 ≤ M_solar < 1; α = 2.3 for 1 ≤ M_solar. The IMF at low masses can be fitted by a → lognormal distribution (See Bastian et al., 2010, ARAA 48, 339 and references therein). See also → canonical IMF.

→ initial; → mass; → function.

The value of the phase corresponding to the origin of time. Same as the → epoch angle.

→ initial; → phase; → angle.

An instant of infinite density, infinite pressure, and infinite temperature where the equations of general relativity break down, if the standard Big Bang theory is extrapolated all the way back to time zero. → singularity.

→ initial; → singularity.