spatial curvature

A drop of ink spreads in a glass of water: its edges move faster than its center, and the drop's shape changes. Likewise, a clump of dark matter collapsing under its own gravity expands unevenly, with different shells flying apart at different speeds. Previously, astrophysicists could accurately describe only the simplest case, a uniform sphere with a sharp boundary, which has a single expansion rate.

Think of a merry-go-round: the farther you sit from the center, the faster you're carried around. For a long time, astronomers assumed galaxies work the same way — stars at the edges should orbit more slowly than those near the center. But back in the 1970s, it turned out that in many spiral galaxies, the speed of stars barely drops with distance from the center.

When two heavy balls merge into one, ripples spread across the water's surface for a long time. A black hole behaves similarly: after a merger, it 'rings' for a while, emitting special gravitational oscillations — quasinormal modes. Usually, this ring fades quickly, like an echo dying out in an empty hall.

The night sky looks like a random scattering of stars. But zoom out to enormous distances, and the chaos disappears. Galaxies gather into long filaments and flat walls, with colossal voids gaping between them — cosmic voids. This structure is called the cosmic web.

The early universe resembled an overheated cauldron, seething with quantum fluctuations (random bursts of energy). In this chaos, like steam over boiling water, a special field, the scalar field, condensed. It became the 'engine' that made space expand at an incredible rate. This process is called inflation.

The early universe was less like a calm pond and more like a boiling cauldron. Matter flowed, collided, and swirled against the backdrop of rapid spatial expansion. To understand how stars and galaxies emerged from this hot soup, physicists build digital simulations. This new work is the third part in a series on lattice-based cosmological modeling. The first two focused on fields; this one deals with fluids.

Right after the Big Bang, space cooled unevenly. In some places, folds could have formed — threads of energy as thin as a hair but incredibly dense. Physicists call them cosmic strings. They oscillate, collide, and emit gravitational waves — ripples in the fabric of space itself.

Forget the flat sheet: embryonic tissue is a dynamic landscape of hills and folds. On convexities, cells stretch; in concavities, they compress, as if performing a dance governed by laws eerily similar to spacetime curvature.

In the first moments after the Big Bang, the universe expanded at a terrifying rate. This process is called inflation, and it smoothed out all the wrinkles, making the cosmos homogeneous. But what started inflation itself?

A quantum wave is like a long-exposure photograph: everything’s blurred, but the blur itself reveals motion. Usually these frozen waves are treated as convenient abstractions. Yet if at each point in the image you estimate, by brightness, the moment on the particle’s internal clock it landed there, flat space suddenly acquires curves.

In the ordinary world without dark energy, the mass of any object is always positive. That seems obvious: positive mass attracts, creating gravity. But the real universe has dark energy — a mysterious force making the cosmos expand faster and faster.

The boundary of a black hole is like the edge of a waterfall: cross it, and there's no way back. But unlike a waterfall, this boundary can be very fragile: a light nudge is enough to make it vanish. Physicists have found that the horizon's stability is set by an imaginary 'light flow' coming from the past. Invisible streams pierce spacetime.

A runner on the middle of a track suddenly switches to a walk — not speeding up or slowing down, but maintaining a constant pace. Something similar may have happened to the universe itself shortly after the Big Bang.

Dim the lights. The stage belongs to a shadow theater, with just r puppeteers, but the screen obeys the laws of hyperbolic geometry. Every wave of the hand births a pattern that mathematicians call a discrete group of isometries.

In the ocean, a whirlpool pulls everything into a closed loop, just as a gravitational wave in empty space twists time into a loop. Gravitational wave — a ripple in the fabric of spacetime, and its special shape can turn the usual flow of events into a closed cycle. In such a zone, an object can return to its own past without violating the laws of physics.

In mathematics there is a sieve that sifts not dust, but infinity itself. It’s called a Q-space: here any subset turns out to be a Gδ set — a countable intersection of open sets, as if sifted through an unimaginably fine mesh.

The cosmological principle – the notion that the Universe is homogeneous and isotropic on large scales – has guarded our understanding of the world since the time of Edwin Hubble and Georges Lemaître, whose ideas formed the basis of the Big Bang model.

The Universe is an orchestra playing the symphony of the Big Bang. For a long time, the conductor was thought to be dark energy — an unwavering metronome setting the pace of expansion.

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.

The universe hasn't always been expanding. In some models, it first contracted, nearly empty and flat, and then, upon reaching a limit, bounced back and started growing, like the world we know. This scenario is called bouncing cosmology.

From childhood, we're used to thinking of space as infinite and isotropic. But Einstein and Lemaître were already asking: could the Universe be closed in on itself, like a Möbius strip or a 3-torus?

The Universe behaves like a soap bubble swelling in a multidimensional foam. The dark bubble model explains why it's expanding ever faster: the spacetime bubble grows, and its membrane gains a tiny thickness — about a micron, like a bacterium. At such distances, gravity 'blurs' across this thickness and weakens.

A star contracts under its own gravity, and at some point its fate hangs on a razor-thin balance. Classical physics paints a grim picture: if the mass and the force of compression are tuned with terrifying precision, what emerges is not a black hole but a 'naked' singularity.

A translator hears not just words, but intonation, pauses, the tremor in a voice. Ordinary entropy analysis of cosmic perturbations is like meeting minutes: it records facts but loses the nuances. Pseudoentropy entropy is a new tool that captures the hidden "music" of the early universe.

Space is like a sheet of paper: gravity bends it, making lines converge toward the center. But if you bend too hard, the paper tears, just as space, under monstrous curvature, doesn't collapse into a point but forms a torn edge. That edge is the quantum boundary.

Time is a fickle thing. Inside a massive star, it flows calmly, like sand in an old clock on a mantelpiece. Outside, on the scale of the entire universe, it stretches along with space, as if the same clock were in an elevator that speeds up and slows down. For a long time, physicists puzzled over whether these two worlds could be glued together without visible seams.

You can zoom into a high-resolution photo for a long time — until suddenly a smooth face dissolves into individual pixels. Something similar, according to a new study, happens to spacetime itself. The authors propose that tiny intervals of length are not pre-existing 'parts' of the universe but results of measurements.

A balloon doesn't deflate all at once: first, dents appear on its surface, which run, merge, and finally the balloon shrivels into a point. Domain walls behave in much the same way — thin partitions that divided space in the first moments after the Big Bang.

A heavy ball rests on a trampoline, and the fabric sags beneath it. Any rolling ball nearby inevitably rolls toward the center. This is roughly how gravity works on the scale of the entire Universe. But what if the fabric were arched upward, like a dome? Then the ball would tend to roll outward.

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.

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.

When two dead stars collide in a distant galaxy, two messengers bring us the news: a shiver in space, a gravitational wave, and a flash of light. Both messengers race toward us across the entire Universe, but their paths can differ slightly. Light sometimes gets delayed by cosmic dust, while gravitational waves pass through everything almost without noticing obstacles.

A mathematical doughnut, a torus, sits on the boundary of a three-dimensional world where gravity acts. You can crumple and stretch it, and physicists decided to see how it behaves. Inside this world, space can be flat like a table, expanding like a soap bubble, or curved like a saddle. The doughnut boundary refused to stay smooth.

The quantum birth of the Universe is like a game of dice, where the chance of rolling a six is catastrophically small. The formalism of Hawking and Hartle, an elegant recipe for a world born from timelessness, has spent decades predicting that a universe like ours is fantastically improbable.

In one model, spacetime is a smooth lake, and quantum particles are fish swimming in it. Their motion inevitably creates ripples. The math insists that the water trembles — otherwise the theory collapses. This trembling is strictly ordered and comes in two types.

The universe abhors monotony. A century ago, Edwin Hubble and Georges Lemaître gave us an elegant picture: an expanding cosmos, smooth as the surface of an inflated balloon.

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.

A rubber band stretched in different directions behaves differently from a whole sheet of paper. If you pull on an edge, the deformation does not spread evenly but seems to linger in certain spots.

Usually, the story of the universe goes like this: there was nothing, then a bang, and ever since everything has been flying apart. But what if there was no 'nothing'? A group of physicists has shown that the universe could have existed forever: it just sometimes contracts and then expands again, like a spring.

You are pacing a huge hall in complete darkness. You walk from wall to wall, counting your steps, and suddenly realize that the distances don't add up as they should. It seems as if the floor is not flat but bulging like a hump or hollowed like a bowl. That's roughly what astronomers found when studying distant galaxies and sound waves frozen in the early Universe.