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Related Concept Videos

Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of motion,...
Second Uniqueness Theorem01:16

Second Uniqueness Theorem

Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
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Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

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Non-gaussianity consistency relation for multifield inflation.

Naonori Suma Sugiyama1, Eiichiro Komatsu, Toshifumi Futamase

  • 1Astronomical Institute, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan. sugiyama@astr.tohoku.ac.jp

Physical Review Letters
|July 21, 2011
PubMed
Summary
This summary is machine-generated.

Detecting primordial non-Gaussianity could rule out single-field inflation. However, multifield models must satisfy a specific inequality relating bispectrum (fNL) and trispectrum (τNL) amplitudes, challenging inflation if violated.

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Area of Science:

  • Cosmology
  • Theoretical Physics
  • Particle Physics

Background:

  • Single-field inflation models are challenged by detecting the
  • local form
  • bispectrum of primordial perturbations.
  • Multifield inflation models remain viable even if such bispectra are detected.

Purpose of the Study:

  • To investigate the constraints imposed by primordial non-Gaussianity on multifield inflation models.
  • To establish an inequality that, if violated, would challenge most multifield inflation scenarios.

Main Methods:

  • Utilizing the δN formalism to describe multifield models.
  • Deriving an inequality relating the bispectrum amplitude (fNL) and a local-form trispectrum amplitude (τNL).

Main Results:

  • Multifield models described by the δN formalism must obey the inequality τNL > 1/2(6/5fNL)^2, with potential logarithmic scale dependence.
  • Violation of this inequality would rule out the majority of multifield inflation models.

Conclusions:

  • The detection of a violation of the derived inequality would significantly challenge the viability of multifield inflation.
  • This finding questions the role of inflation as the primary mechanism for generating primordial perturbations in the universe.