Gravitacinis telkimasis ir tankio fluktuacijos

Gravitational concentration and density fluctuations

How tiny density contrasts grew under the influence of gravity, allowing stars, galaxies and clusters to form

Since the Big Bang, the Universe has evolved from a nearly uniform state into a cosmic mosaic of stars, galaxies, and giant, gravitationally bound clusters. But all of these large-scale structures grew out of tiny density fluctuations—at first very small irregularities in the density of matter, which were eventually amplified by gravitational instabilities. In this article, we will delve deeper into how these tiny inhomogeneities arose, how they have evolved, and why they are crucial to understanding the rich and diverse formation of large-scale structures in the Universe.

1. Origin of density fluctuations

1.1 Inflation and quantum seeds

One of the main theories of the early Universe is cosmic inflation – states that the Universe underwent an extremely rapid exponential expansion immediately after the Big Bang. During inflation, quantum fluctuations inflaton field (in the field that causes inflation) were stretched to cosmic scales. These tiny deviations in energy density were "frozen" in spacetime, becoming the primary seeds for all subsequent structure.

  • Scale invariance: Inflation predicts that these density fluctuations are almost scale-independent, meaning that the amplitude is approximately the same over a wide range of lengths.
  • Gaussianity: Observations show that the primary fluctuations were mostly abundant, indicating that there is no strong "clustering" or asymmetry in the distribution of these fluctuations.

After inflation ended, these quantum fluctuations effectively transformed into classical density perturbations, spreading throughout the Universe and becoming the basis for the formation of galaxies, clusters, and superclusters millions and billions of years later.

1.2 Evidence for the cosmic microwave background (CMB)

Cosmic microwave background gives us a picture of the Universe from about 380 thousand years after the Big Bang — when free electrons and protons came together (recombination), and photons were free to propagate. Detailed measurements by COBE, WMAP, and Planck showed temperature fluctuations as small as one part in 105These temperature fluctuations reflect the initial density contrasts in the initial plasma period.

Main conclusion: The amplitude and angular power spectrum of these fluctuations are in excellent agreement with predictions from inflationary models and a Universe dominated by dark matter and dark energy. [1,2,3].

2. Growth of density fluctuations

2.1 Linear perturbation theory

After inflation and recombination, the density fluctuations were sufficiently small (δρ/ρ « 1) so that they can be studied by the methods of linear perturbation theory in the expanding Universe. Two fundamental factors determined the evolution of these fluctuations:

  • Dominance of matter and radiation: During radiation-dominated epochs (in the early Universe), photon pressure resisted the accumulation of matter, limiting the growth of excess matter. After the transition to matter dominance (a few tens of thousands of years after the Big Bang), matter fluctuations could grow more rapidly.
  • Dark matter: Unlike photons or relativistic particles, cold Dark matter (DM) does not experience the same radiation pressure; it may begin to collapse earlier and more efficiently. In this way, dark matter creates a "framework" that baryonic (ordinary) matter later follows.

2.2 Transition to non-linear mode

As the fluctuations intensify, the denser regions become even denser, until they eventually exit the linear growth region and undergo nonlinear collapse.In the nonlinear regime, gravitational attraction becomes more important than the assumptions of linear theory:

  • Formation of halos: Small clumps of dark matter collapse into "halos" where baryons later cool and form stars.
  • Hierarchical connection: In many cosmological models (especially ΛCDM), structures form from the bottom up: smaller ones form first, and then merge to form larger ones — galaxies, groups, and clusters.

Nonlinear evolution is often achieved using N-body simulations (e.g. Millennium, Illustris, EAGLE), which track the gravitational interactions of millions or billions of dark matter "particles" [4]These simulations reveal filamentary structures called the cosmic web.

3. The roles of dark matter and baryonic matter

3.1 Dark matter – gravitational framework

A wealth of evidence (spin curves, gravitational lensing, cosmic velocity fields) suggests that most of the matter in the Universe is made up of dark matter, which does not act electromagnetically but has gravitational influence [5]. Since dark matter behaves as "collision-free" and was "cold" (non-relativistic) early on:

  • Effective concentration: Dark matter clumps together more efficiently than hot or warm matter, allowing structures to form on finer scales.
  • Hall frame: Dark matter clusters become gravitational wells into which baryonic matter (gas and dust) is subsequently attracted, where it cools and forms stars and galaxies.

3.2 Baryonic physics

When gas enters dark matter halos, other processes begin:

  • Radiative cooling: Gases lose energy by radiating (e.g., atomic emission), so they can continue to contract.
  • Star formation: As density increases, stars form in the densest regions, illuminating protogalaxies.
  • Feedback: Energy from supernovae, stellar winds, and active nuclei can heat and expel gas, regulating future phases of star formation.

4. Hierarchical formation of large structures

4.1 From small seeds to massive swarms

Widely applicable ΛCDM model (Lambda Cold Dark Matter) explains how structures form "bottom-up." Early small halos eventually coalesce to form more massive systems:

  • Dwarf galaxies: Some of the early star-forming objects that later merged into larger galaxies.
  • Milky Way-like galaxies: Formed when many smaller sub-halos merged.
  • Galaxy clusters: Clusters consisting of hundreds or thousands of galaxies, born from the merging of group-level haloes.

4.2 Monitoring confirmation

Astronomers, observing merging clusters (e.g., the Bullet Cluster, 1E 0657–558) and large-scale surveys (e.g., SDSS, DESI) that capture millions of galaxies, confirm the cosmic web predicted by the theories. Over cosmic time, galaxies and clusters have grown together with the expansion of the Universe, leaving their imprint on the distribution of matter seen today.

5. Characterization of density fluctuations

5.1 Power spectrum

One of the main tools of cosmology is matter power spectrum P(k), which describes how fluctuations vary depending on spatial scale (scale factor k):

  • On a large scale: Fluctuations remain linear for most of the history of the Universe, reflecting near-initial conditions.
  • On a smaller scale: Nonlinear interactions, which form in a hierarchical manner in earlier structures, begin to dominate.

Power spectrum measurements from KMF anisotropies, galaxy surveys, and Lyman-alpha forest data are in excellent agreement with the ΛCDM model [6,7].

5.2 Baryonic Acoustic Oscillations (BAO)

In the early Universe, photon-baryon oscillations left an imprint detectable as a characteristic scale (BAO scale) in the distribution of galaxies. Observing BAO "peaks" in galaxy clusters:

  • The details of the growth process of fluctuations in spacetime are being refined.
  • The rate of the Universe's expansion history (i.e. dark energy) is determined.
  • This scale becomes the standard "ruler" for measuring cosmic distances.

6. From primordial fluctuations to cosmic architecture

6.1 Space Network

As simulations show, the matter in the Universe is arranged in the form of a network, consisting of filaments and layers, interspersed with large voids:

  • Threads (filaments): Dark matter and chains of galaxies connecting clusters.
  • Layers (pancakes): Two-dimensional structures on a slightly larger scale.
  • Voids: Regions of lower density, remaining almost empty compared to denser filament intersections.

This space network is a direct result of the gravitational amplification of fluctuations dictated by dark matter dynamics [8].

6.2 Interaction between feedback and galaxy evolution

Once star formation begins, the picture is significantly complicated by feedbacks (stellar winds, supernovae, etc.). Stars enrich the intergalactic medium with heavier elements (metals), changing the chemistry of future stars. Powerful ejections can suppress or even completely stop star formation in massive galaxies. Thus, baryonic physics takes on an increasingly important role, determining the evolution of galaxies and surpassing the initial mechanics of halo structure formation.

7. Current research and future directions

7.1 High-resolution simulations

A new generation of supercomputer simulations (e.g., IllustrisTNG, Simba, EAGLE) increasingly integrate hydrodynamics, star formation, and feedback. By comparing these simulations with detailed observations (e.g., Hubble Space Telescope, JWST, advanced ground-based surveys), astronomers are refining models of early structure formation. This is testing whether dark matter must be purely "cold" or whether warmer or mutually interacting (SIDM) variants of dark matter are possible.

7.2 21 cm cosmology

Observing 21 cm line from neutral hydrogen at high redshift opens up a new opportunity to trace the epoch when the first stars and galaxies formed, perhaps even the earliest stages of gravitational collapse. Projects such as HERA, LOFAR and the future SKA aims to create maps of gas distribution in cosmic time, covering the epoch before and during reionization.

7.3 Searching for deviations from ΛCDM

Some astrophysical inconsistencies (e.g., the "Hubble voltage," fine-structure puzzles) have prompted the exploration of alternative models, such as warm dark matter or modified gravity. By observing how density fluctuations have evolved on both large and small scales, cosmologists have attempted to confirm or refute the standard ΛCDM model.

8. Conclusion

Gravitational accretion and the growth of density fluctuations are a key process in the formation of structures in the Universe.Microscopic quantum waves, stretched during inflation, later grew into a huge one as matter began to dominate and dark matter accumulated. space networkThis fundamentally important phenomenon allowed everything from the first stars in dwarf halos to the giant galaxy clusters that hold superclusters to form.

Today’s telescopes and supercomputers are increasingly revealing those layers of time, allowing us to compare theoretical models with the “grand design” etched into the Universe. As new observations and simulations proliferate, we continue to unravel the story of how tiny seeds of fluctuations grew into the grand cosmic architecture we see around us—a story that encompasses quantum physics, gravity, and the dynamic interactions of matter and energy.

References and further reading

  1. Guth, A. H. (1981). "Inflationary universe: A possible solution to the horizon and flatness problems." Physical Review D, 23, 347–356.
  2. Planck Collaboration. (2018). "Planck 2018 results. VI. Cosmological parameters." Astronomy & Astrophysics, 641, A6.
  3. Smoot, G. F., et al. (1992). "Structure in the COBE DMR First-Year Maps." The Astrophysical Journal Letters, 396, L1–L5.
  4. Springell, V. (2005). "The cosmological simulation code GADGET-2." Monthly Notices of the Royal Astronomical Society, 364, 1105–1134.
  5. Zwicky, F. (1933). "Die Rotverschiebung von extragalacticen Nebeln." Helvetica Physica Acta, 6, 110–127.
  6. Tegmark, M., et al. (2004). "Cosmological parameters from SDSS and WMAP." Physical Review D, 69, 103501.
  7. Cole, S., et al. (2005). "The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final data set and cosmological implications." Monthly Notices of the Royal Astronomical Society, 362, 505–534.
  8. Bond, JR, Kofman, L., & Pogosyan, D. (1996). "How filaments are woven into the cosmic web." Nature, 380, 603–606.

Additional sources:

  • Peebles, P.J.E. (1993). Principles of Physical Cosmology. Princeton University Press.
  • Kolb, EW, & Turner, MS (1990). The Early Universe. Addison-Wesley.
  • Mo, H., van den Bosch, FC, & White, S. (2010). Galaxy Formation and Evolution. Cambridge University Press.

Looking back at these sources, it becomes clear that the growth of small density perturbations is the foundation of cosmic history—it not only explains why galaxies exist at all, but also how their large-scale structures reflect the signatures of the earliest times of the Universe.

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