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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing...
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Updated: Apr 24, 2026

Bringing the Visible Universe into Focus with Robo-AO
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Everyone wants something better than ΛCDM.

Michael S Turner1,2

  • 1Departments of Astronomy and Astrophysics and of Physics, Kavli Institute for Cosmological Physics, The University of Chicago, Chicago, IL 60637-1433.

Proceedings of the National Academy of Sciences of the United States of America
|February 13, 2026
PubMed
Summary
This summary is machine-generated.

The Lambda Cold Dark Matter (ΛCDM) model describes the Universe's history but faces criticism. This review examines ΛCDM's status and explores how the Hubble tension could lead to a superior cosmological theory.

Keywords:
astrophysicscosmologyparticle physics

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Area of Science:

  • Cosmology
  • Particle Physics
  • Astrophysics

Background:

  • The Lambda Cold Dark Matter (ΛCDM) model is the standard paradigm in cosmology.
  • ΛCDM successfully explains the Universe's history and connects to particle physics.
  • Despite its success, ΛCDM faces significant criticism and challenges.

Purpose of the Study:

  • To review the current status of the ΛCDM model.
  • To discuss potential improvements and future directions in cosmology.
  • To analyze the role of the "Hubble tension" in advancing beyond ΛCDM.

Main Methods:

  • Literature review of the ΛCDM model and its critiques.
  • Analysis of observational data and theoretical challenges.
  • Discussion of the implications of the Hubble tension for cosmology.

Main Results:

  • ΛCDM, while successful, is not considered the final cosmological theory.
  • The "Hubble tension" presents a significant challenge to the ΛCDM model.
  • There is a consensus on the need for a new, improved cosmological model.

Conclusions:

  • The ΛCDM model requires re-evaluation in light of current tensions.
  • The "Hubble tension" may be a key driver for developing a new cosmological paradigm.
  • Future cosmological theories will likely incorporate new physics to resolve existing discrepancies.