main concepts scientists sections
Scientist

Alexander Friedmann

1888–1925 · Cosmology, Mathematics, Meteorology
Russian and Soviet mathematician and geophysicist who in 1922 first found non-stationary solutions to Einstein's equations, predicting the expansion of the Universe. His pioneering work preceded Hubble's observations and laid the foundation for modern cosmology. His untimely death prevented him from seeing the triumph of his ideas.

Biography

Graduated from Saint Petersburg University, worked at the Polytechnic Institute and the Main Geophysical Observatory. He also worked in meteorology and dynamic meteorology, and participated in balloon flights.

Key discoveries

💡 Friedman was not only a mathematician but also an experienced aeronaut: he took part in balloon flights for meteorological research.
"He asserted that the Universe is not static but evolves."
Concepts
Reionization
Laws
Friedmann equations
Scientists
Willem de SitterJames Gunn

Related articles

Dynamical Systems2014-11-182 minarXiv:1411.5069
Forecasting Without a Model: Nonparametric Prediction of Chaos and Climate
A translator learns not from a dictionary but from speech. They listen to native speakers and pick up rules that are written in no textbook. Similarly, a new method for forecasting complex systems such as climate or turbulence does not require knowing their equations. Instead, it looks at data and learns to predict their behavior.
Tyrus Berry·Dimitrios Giannakis·John Harlim
Henri PoincaréPeter ShorIsaac NewtonDiffusion Modelschaos theoryStochastic modelingstochastic processesdifferential equation
SimplePopularAdvanced
Cosmology2025-10-241 minarXiv:2510.21976express
Dark Energy Is Not Constant: A New Look at the Universe's Acceleration
The Universe is a grand highway where galaxies, like cars, are moving apart faster and faster. The gas pedal is controlled by mysterious dark energy.
Salvatore Capozziello·Himanshu Chaudhary·G. Mustafa·S. K. J. Pacif
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindedark energycosmological constantdark matterquintessenceexpansion of the universe
SimplePopularAdvanced
General Relativity2026-01-111 minarXiv:2601.07007express
The Universe Falls Silent Smoothly, Not with a Bang
Scientists proposed a model in which the mysterious force (dark energy) possesses something like inertia: it needs time to respond, like a heavy pendulum. Because of this, the expansion of the Universe doesn’t accelerate forever, but instead decays, like a pendulum in thick honey.
Swapnil Kumar Singh
Bekenstein boundBekenstein-Hawking entropyJacob BekensteinStephen HawkingLudwig Boltzmanndark energyquintessenceexpansion of the universedark mattercosmological constant
SimplePopularAdvanced
Cosmology2026-01-131 minarXiv:2601.08943express
Dark Energy as a Spring: A Model with No Tuning
In the late 1990s, Saul Perlmutter, Adam Riess, and Brian Schmidt observed supernovae and found: the universe is expanding faster and faster.
Axel de la Macorra·Jose Agustin Lozano Torres
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindedark energycosmological constantdark matterquintessenceexpansion of the universe
SimplePopularAdvanced
Cosmology2026-02-172 minarXiv:2602.15448express
Cosmos Without Averaging: How Inhomogeneity Changes the Universe
In one hospital ward it's +40°C, in another +10°C, and on average it's +25°C. If temperature affected something nonlinearly (say, the rate of bacterial growth) the average would give a wrong prediction. The same problem arises when cosmologists describe a universe where galaxies are packed into clusters and voids yawn between them.
S. R. Pinto·P. P. Avelino
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindegalaxy clustercosmological constantmodified gravityexpansion of the universeinflation
SimplePopularAdvanced
Cosmology2026-03-221 minarXiv:2603.21277express
A Couple of Formulas Describe the Universe's Acceleration
Standard cosmology relies on the Big Bang and dark energy, but there is an alternative — the Lemaître–Tolman–Bondi model, where the Universe's expansion is explained not by a mysterious force, but by natural unevenness in the distribution of matter — clusters of…
A. Carvalho·A. Krone-Martins·A. Da Silva·J. P. Mimoso·C. Bœhm
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universecosmological constant
SimplePopularAdvanced
Atmospheric and Oceanic Physics2026-03-281 minarXiv:2603.27288express
Weather Forecast: Sharp Focus
The atmosphere is a chaotic system, and a detailed global forecast requires monstrous computing power. StretchCast sidesteps this by working like the human eye: it creates 'sharp vision' over a selected region with an ultra-fine grid, while seeing the rest of the world blurry, but sharp enough to capture global connections.
Jin Feng
Peter ShorIsaac NewtonLeonhard EulerDiffusion ModelsStochastic modelingMarkov chainWater
SimplePopularAdvanced
Machine Learning2026-04-101 minarXiv:2604.09818express
Fungi Underground Are Visible from Space
Beneath your feet in the forest, a quiet life unfolds: fungi weave around tree roots and trade nutrients with them. But how do you count how many fungal species are in the soil without digging up the whole forest? It turns out the answer can be seen from space.
Robin Young·Michael E. Van Nuland·E. Toby Kiers·Tomáš Větrovský·Petr Kohout·Petr Baldrian·Srinivasan Keshav
Alexander Friedmannmicroorganismspectroscopy
SimplePopularAdvanced
Cosmology2026-04-151 minarXiv:2604.13423express
The Universe Grew Up Unevenly
When the first stars ignited, their ultraviolet light began stripping electrons from hydrogen atoms. The universe transformed from a neutral fog into transparent plasma. This process, cosmic reionization, proceeded unevenly: slowly at first, like a fire catching in damp wood, then faster as the flames spread through dry tinder.
Paulo Montero-Camacho·Yin Li·Marco Barquero-Hernández·Pablo Renard·Yang Wang·Xiao-Dong Li
Friedmann equationsAlan GuthAlexander FriedmannAndrei LindeReionizationReionizationneutron star mergermicrolensinggalactic evolution
SimplePopularAdvanced
General Relativity2026-04-181 minarXiv:2604.17017express
The Universe Was Speeding Up — Now It's Slowing Down
Imagine inflating a balloon. At first, it expands slowly; then someone gives a sharp blast of air, and it swells faster. But as the airflow weakens, the balloon's growth slows again. According to a new study, the Universe has behaved much the same way: after the Big Bang, it expanded, then suddenly accelerated, and now that acceleration is fading.
Khomesh R. Patle·G. P. Singh
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universedark energybig bangdark matterquintessence
SimplePopularAdvanced
General Relativity2026-04-201 minarXiv:2604.18861express
How the Universe's Expansion Rate Picks the Best Scenario
The universe in its first moments is like an inflating balloon. Cosmologists are trying to figure out what makes it puff up, and there's no shortage of ideas. One idea is to tweak Einstein's gravity slightly — adding an 'extra ingredient' that only kicks in at mind-boggling energies.
S. D. Odintsov·V. K. Oikonomou·Pyotr Tsyba·Olga Razina·Dauren Rakhatov
Friedmann equationsequivalence principleAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universequintessencemodified gravitybig bang
SimplePopularAdvanced
Cosmology2026-04-301 minarXiv:2604.27771express
The Universe's Size and Expansion Are Uncertain
The Universe is like an inflating balloon. Quantum mechanics forbids measuring exactly how big it is and how fast it's inflating at the same time. This principle permeates the cosmos: a new equation states that the Universe's expansion and its size are linked by a fundamental uncertainty.
Savvas M. Koushiappas
Friedmann equationsHeisenberg uncertainty principleAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universequintessencecosmological constantdark energyuncertainty principle
SimplePopularAdvanced
General Relativity2026-05-112 minarXiv:2605.11292express
The Universe as a Pendulum: From Inflation to Ordinary Expansion
A pendulum chooses how to swing on its own. If you give it a strong push, it quickly returns to a smooth rhythm. If you hold it at its extreme position, it will stay there, but as soon as you let go, it resumes its usual motion.
Seturumane Tema·S. Shajidul Haque·Saurya Das·Peter Dunsby
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universebig banginflationReionizationchaos theory
SimplePopularAdvanced
General Relativity2026-05-162 minarXiv:2605.16751express
The Breathing Universe
A hot coffee on the table cools down: heat spreads from the hot center to the edges. The authors suggest that the universe behaves in a similar way, just on scales of billions of light-years. Their model describes not the usual dark energy, but a smooth redistribution of energy within the cosmos, akin to the slow flow of heat from denser regions to rarefied ones.
Gilberto Aguilar-Pérez·Miguel Cruz·Samuel Lepe
Friedmann equationsBekenstein boundAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universebig bangquintessencespacetime curvaturedark energy
SimplePopularAdvanced
General Relativity2026-05-191 minarXiv:2605.20076express
How the Universe Became Smooth: Unraveling the First Moments
The birth of the universe resembles not an explosion, but a traffic jam. At first, a tiny fraction of a second after the Big Bang, space expanded sluggishly, like cars stuck in gridlock. Then came a sharp surge — accelerated expansion, which cosmologists call inflation.
M. Montes·José Edgar Madriz Aguilar·A. Bernal·Diego Allan Reyna
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindeinflationbig bangexpansion of the universegalactic evolutionReionization
SimplePopularAdvanced
Cosmology2026-05-252 minarXiv:2605.26050express
Dark Matter Decays, the Universe Smooths Out
On the kitchen counter, there's a flour scale and a measuring cup for water. Individually, they're precise, but when you bake bread, the recipe calls for the perfect ratio. Astronomers have a similar dispute about the universe's expansion rate.
Rahul Dhyani·Purba Mukherjee·Arindam Chatterjee·Anjan A Sen
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindedark matterdark energyexpansion of the universequintessencebig bang
SimplePopularAdvanced
Cosmology2026-05-273 minarXiv:2605.28797express
Cosmic Friction: How Disorder Fixes the Universe
A blacksmith forges a sword. With each hammer blow, the red-hot metal flattens, but the hammer, the anvil, and the surrounding air all warm up slightly. Part of the impact energy is irreversibly lost as heat — a trade-off familiar to anyone who has ever driven a nail, and it turns out to be the key to the biggest mysteries of the cosmos.
Biswajit Pandey
second law of thermodynamicsFriedmann equationsLudwig BoltzmannRudolf ClausiusAlan Guthexpansion of the universecosmological constantinflationdark energyentropy
SimplePopularAdvanced
Cosmology2026-05-271 minarXiv:2605.28903express
A Universe Without Dark Energy? A Simple Model Bypasses the Standard One
The Universe follows strict rules, like players at a table. One of them: gravity always attracts, and energy cannot be negative.
Namit Chandak·Fulvio Melia·Junjie Wei
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindedark energyexpansion of the universecosmological constantdark mattermodified gravity
SimplePopularAdvanced
Cosmology2026-06-051 minarXiv:2606.07854express
The Universe as a Distant Forest: Testing Homogeneity
The Universe resembles a dense forest: up close, individual galaxy-trees are visible, gathered into groves, but from a distance everything merges into a solid green canopy. The boundary beyond which the cosmos becomes homogeneous is called the angular scale of homogeneity: it's the size of a patch of sky from which galaxies are distributed evenly.
Mariana Lopes-Dias·Carlos A. P. Bengaly·Xiaoyun Shao·Rodrigo Gonçalves·Paula S. Ferreira·Gabriela Coutinho de Carvalho·Jailson Alcaniz
Friedmann equationsgravitational lensingAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universegalaxy clustergalaxylarge-scale structure of the universelarge-scale structure
SimplePopularAdvanced
Cosmology2026-06-182 minarXiv:2606.20036express
Dark Energy from the Depths of the Atomic Nucleus
The universe is expanding at an accelerating rate, like dough that keeps rising faster even though the yeast ran out long ago. For twenty years, astronomers have been searching for the cause and call it dark energy. But what it is remains a mystery. New work proposes an unexpected source: the vacuum inside the atomic nucleus.
Dong Ha Lee·Carsten van de Bruck·Eleonora Di Valentino·Ludovic Van Waerbeke·Ariel Zhitnitsky
Friedmann equationslaw of conservation of energyAlan GuthAlexander FriedmannAndrei Lindedark energydark matterquintessencecosmological constantnuclear fusion
SimplePopularAdvanced
Cosmology2026-06-291 minarXiv:2606.30903express
A Cosmic Compromise: One Number Settles Three Disputes
Cosmology is like an orchestra where different sections suddenly start playing out of sync. Measurements of the universe's expansion rate (the Hubble constant) from the early and late universe give different numbers.
James M. Sullivan·Roger de Belsunce·Mikhail M. Ivanov
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindecosmological constantdark energyneutron star mergerexpansion of the universe
SimplePopularAdvanced
General Relativity2026-06-302 minarXiv:2606.31472
Dark Energy: Inevitability Born of Symmetry
The explosion of a distant supernova told us something hard to believe: the universe is expanding faster and faster. The engine of this acceleration is dark energy — nearly 70% of everything that exists.
Chiara Cecchini·Massimiliano Rinaldi
Friedmann equationsWitten's positive energy theoremAlan GuthAlexander FriedmannAndrei Lindedark energycosmological constantquintessencedark matterlarge-scale structure of the universe
SimplePopularAdvanced
HEP Phenomenology2026-07-302 minarXiv:2607.28321express
Where Did Matter Come From? A Fresh Look at the Boltzmann Equation
A fraction of a second after the big bang, the universe was a searing hot soup of particles and antiparticles. By all rights, they should have annihilated each other completely, leaving only emptiness. But for some unknown reason, one "extra" matter particle survived for every billion pairs. It was from these surviving scraps that galaxies, stars, and people eventually formed.
Motoi Endo·Yushi Mura·Tenta Tsuji
Boltzmann equationWheeler-DeWitt equationLudwig BoltzmannBryce DeWittCarlo RovelliQuantum Fieldquantum gravitybig bangperturbation theoryStandard Model
SimplePopularAdvanced
Cosmology2026-07-302 minarXiv:2607.28326express
Three Faces of the Cosmos: Geometry, Growth, and the Beginning
The standard cosmological model ΛCDM (which includes dark energy and cold dark matter) is the score of a cosmic symphony. It describes how space expanded after the big bang. How dark matter clumped together. How galaxies ignited. For a long time, everything played flawlessly.
Felicitas Keil·Isaac Tutusaus·Alain Blanchard
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindecosmological constantinflationsymplectic geometryStandard Model
SimplePopularAdvanced
General Relativity2026-08-072 minarXiv:2608.06852express
The Universe Couldn't Have Been Expanding Forever
A spotlight beam fades into the darkness, but if you trace it backward, you hit the lamp. The history of the universe might be the same: tracing its expansion backward, we run into a beginning. Physicists took the simplest model — a universe that stretches equally in all directions, like a cube with all sides growing.
Sebastian Garcia-Saenz·Junjie Hua·Abbas M. Sherif
Friedmann equationsAlan GuthAlexander FriedmannAndrei Lindeexpansion of the universebig banginflation
SimplePopularAdvanced