Material distribution and small temperature differences leading to the formation of structures
Cosmic Variations in a Nearly Homogeneous Universe
Observations show that our Universe is very large on large scales. homogeneous, but not perfect. Small anisotropy (differences in direction) and heterogeneities (variations in the density of matter in space) in the early Universe are the essential seeds from which all cosmic structures grew. Without them, matter would remain evenly distributed and we would not have galaxies, clusters, or the cosmic web. We can study these tiny fluctuations:
- Through cosmic microwave background radiation (CMB) anisotropies: differences in temperature and polarization 1 out of 10-5 accuracy.
- Through large-scale structure: the arrangement of galaxies, filaments and voids resulting from gravitational growth from primordial seeds.
By analyzing these heterogeneities—both during the recombination period (through the CFS) and at later epochs (through galaxy cluster data)—cosmologists gain fundamental insights into dark matter, dark energy, and the inflationary origin of fluctuations. We will discuss below how these anisotropies arise, how we measure them, and how they drive structure formation.
2. Theoretical Framework: From Quantum Seeds to Cosmic Structures
2.1 Inflationary Origin of Fluctuations
Home primary heterogeneities the explanation is inflation: the exponential expansion of the early Universe. During inflation, quantum (inflationary field and metric) fluctuations extended to macroscopic scales and became "locked in" as classical density perturbations. These fluctuations are nearly scale invariant (spectral exponent ns ≈ 1) and mostly abundant, as observed in the CFS. After inflation ends, the Universe "overheats", and these perturbations remain imprinted on all matter (baryonic + dark) [1,2].
2.2 Development Over Time
As the Universe expanded, the perturbations of dark matter and the baryonic fluid began to grow under the influence of gravity if their magnitude exceeded the Jeans scale (after the recombination epoch). In the hot pre-recombination era, photons interacted closely with baryons, limiting early growth. After separation, the non-colliding dark matter could continue to accumulate more. The linear growth produces a characteristic power spectrum of density perturbations. Finally, after the transition to the nonlinear accretion regime, halos form in the excess regions, giving rise to galaxies and clusters, and voids form in the rarefied regions.
3. Anisotropies of the Cosmic Microwave Background Radiation
3.1 Temperature Fluctuations
KFS at z ∼ 1100 is extremely homogeneous (ΔT/T ∼ 10-5), but small deviations are expressed as anisotropy. They reflect acoustic oscillations in the photon–baryon plasma before recombination, as well as gravitational potential wells/overflows originating from early matter inhomogeneities. COBE first detected them in the 1990s; WMAP and Planck later greatly improved them, measuring several acoustic peaks in the angular power spectrum [3]. The positions and heights of the peaks allow for precise determination of the parameters (Ωb h², Ωm h², etc.) and confirms the almost scale-invariant nature of the primary fluctuations.
3.2 Angular Power Spectrum and Acoustic Peaks
When power is represented by Cℓ as a function of the multipole ℓ, "peaked" structures are observed. The first peak corresponds to the fundamental acoustic mode of photon–baryon recombination, while the other peaks represent higher harmonics. This pattern strongly supports an inflationary origin and a nearly flat geometry of the Universe.Small variations in temperature anisotropy and polarization of E-modes form the basis for modern cosmic parameter determination.
3.3 Polarization and B-modes
KFS polarization measurements further deepen our knowledge of heterogeneities. Scalar (density) perturbations create E-mode, while tensors (gravitational waves) could generate B-mode. The detection of primordial B-modes at large angular scales would confirm the existence of inflationary gravitational waves. Although only strict upper limits have been obtained so far, without a clear signal of primordial B-modes, the available temperature and E-mode data nevertheless indicate the scale-invariant, adiabatic nature of the early inhomogeneities.
4. Large-Scale Structure: The Distribution of Galaxies as a Reflection of Early Seeds
4.1 The Space Network and Power Spectrum
Space Network, consisting of thread, swarm and voids, born from gravitational growth from these primordial heterogeneities. Redshift surveys (e.g., SDSS, 2dF, DESI) record millions of galaxy positions, revealing 3D structures on scales from tens to hundreds of Mpc. Statistically, the power spectrum of galaxies P(k) on large scales agrees with a linear perturbation theory model under inflationary initial conditions, with additional evidence of baryonic acoustic oscillations (~100–150 Mpc).
4.2 Hierarchical Formation
As the heterogeneities collapse, smaller halos are formed first, which merge to form larger halos, thus forming galaxies, groups, and clusters. This hierarchical formation agrees well with ΛCDM model simulations, whose initial fluctuation fields are random manifolds with nearly scale-invariant power. Observations of cluster masses, void sizes, and galaxy correlations confirm that the Universe began with small density perturbations that expanded over cosmic time.
5. The Role of Dark Matter and Dark Energy
5.1 Dark Matter – The Engine of Structure Formation
Because dark matter does not interact electromagnetically and does not scatter with photons, it can gravitationally collapse earlier. This creates potential wells into which baryons later (after recombination) fall. The ratio of dark matter to baryons of about 5:1 means that dark matter has determined the framework of the cosmic web. Observations at the scale of the KFS and data on large-scale structure tie the dark matter fraction to ~26% of the total energy density.
5.2 Dark Energy in the Late Period
Although early heterogeneities and the growth of structures are largely controlled by matter, over the last few billion years dark energy (~70% of the Universe) began to dominate the expansion, slowing down the further growth of structures. Observations such as the redshift of cluster abundances or cosmic shear may confirm or refute the conventional notion of ΛCDM. So far, the data do not contradict a nearly constant dark energy, but future measurements may detect small variations if dark energy is changing.
6. Measuring Heterogeneity: Methods and Observations
6.1 KFS Experiments
From COBE (1990s) to WMAP (2000s) and Planck (2010s), temperature anisotropy and polarization measurements have greatly improved in resolution (arcminutes) and sensitivity (few µK). This determined the amplitude of the primary power spectrum (~10-5) and the spectral slope ns ≈ 0.965. Additional ground-based telescopes (ACT, SPT) study small-scale anisotropies, lensing, and other secondary effects, further refining the power spectrum of the material.
6.2 Shift Reviews
Large galaxy surveys (SDSS, DESI, eBOSS, Euclid) analyze the 3D arrangement of galaxies, i.e. the current structure. By comparing this with linear predictions from the initial conditions of the CFS, cosmologists check the ΛCDM model or look for deviations. Baryon acoustic oscillations are also visible as a subtle "bump" in the correlation function or "waviness" in the power spectrum, linking these inhomogeneities to the acoustic scale from recombination.
6.3 Weak Lensing
Weak gravitational lensing of more distant galaxies, caused by large-scale matter, provides another direct measure of the amplitude (σ8) and a measure of growth in time. Surveys such as DES, KiDS, HSC, and in the future Euclid, Roman, will determine the cosmic shear, allowing for the reconstruction of the matter distribution. This provides additional constraints, complementing displacement surveys and KFS studies.
7. Current Issues and Tensions
7.1 Hubble Voltage
Combining KFS data with ΛCDM yields H0 ≈ 67–68 km/s/Mpc, while local ladder methods (with supernova calibration) indicate ~73–74. These measurements depend strongly on the amplitude of the heterogeneities and the expansion history. If the heterogeneities or initial conditions differ from the standard ones, this may change the derived parameters. Efforts are underway to see whether early new physics (early dark energy, extra neutrinos) or systematics could resolve this tension.
7.2 Small ℓ Anomalies, Large Scale Combinations
Some large-scale anomalies in the KFS anisotropies (cold spot, quadrupole alignment) may be statistical coincidences or hints of cosmic topology. Observations have not yet confirmed anything significant beyond the standard framework of inflationary seeds, but the search for non-Gaussianities, topological features, or anomalies continues.
7.3 Neutrino Mass and Other Questions
Small neutrino masses (~0.06–0.2 eV) suppress the growth of structures on scales <100 Mpc, leaving significant traces in the matter distribution. By analyzing the KFS anisotropies and large-scale structure data (e.g. BAO, lensing) together, it is possible to detect or constrain the total neutrino mass. In addition, the heterogeneities may indicate small effects of warm TM or self-acting TM. So far, cold TM with minimal neutrino masses does not contradict the data.
8. Future Perspectives and Missions
8.1 Next Generation KFS
CMB-S4 – a series of ground-based telescopes are planned that will measure temperature/polarization anisotropies with high precision, including fine lensing. This could reveal subtle signs of inflationary seeds or neutrino mass. LiteBIRD (JAXA) will be dedicated to large-scale searches for B-modes, possibly detecting primordial gravitational waves from inflation. This would confirm the quantum origin of anisotropies if it successfully finds B-modes.
8.2 Creating 3D Large-Scale Structure Maps
Reviews like DESI, Euclid and Roman The telescope will cover tens of millions of galaxy displacements, recording the distribution of matter down to z ∼ 2–3. They will allow us to refine σ8 and Ωm, and to "draw" the cosmic web in detail, thus connecting early heterogeneities with the present structure. 21 cm intensity maps from SKA will allow observing heterogeneities at even higher redshifts – both before and after reionization, providing a continuous picture of the formation of structures.
8.3 Search for Absences
Inflation usually predicts near-Gaussian initial fluctuations. However, a multi-field or non-minimum inflation scenario may yield small local or equipotential non-Gaussianities.KFS and large-scale structure data are increasingly reducing the limits of such effects (fNL ~ a few parts of a unit). The discovery of larger sparsenesses would significantly change our understanding of the nature of inflation. So far, no significant results have been found.
9. Conclusion
Universes anisotropy and heterogeneities – from small ΔT/T fluctuations KFS to the large-scale distribution of galaxies – are the essential beginnings and traces of the formation of structures. Initially, perhaps, inflation Quantum fluctuations that arose during the first billions of years, these small-amplitude perturbations, under the influence of gravity, grew into a cosmic web where we see clusters, filaments, and voids. Precise measurements of these heterogeneities are KFS anisotropies, galaxy shift reviews, weak lensing cosmic shear – provides fundamental insights into the composition of the Universe (Ωm, ΩL), the conditions of inflation and the role of dark energy in the late stage of acceleration.
Although the ΛCDM model successfully explains many features of the evolution of heterogeneities, unanswered questions remain: Hubble voltage, small discrepancies in the growth of structures or the influence of neutrino mass. As the precision of new surveys increases, we may either further establish the invulnerability of the inflation + ΛCDM paradigm, or we may detect subtle deviations that suggest new physics—whether in inflation or in dark energy or dark matter interactions. In any case, the study of anisotropies and heterogeneities remains a powerful force in astrophysics, connecting quantum fluctuations of early time with grand cosmic scale structures over billions of light-years.
Literature and Additional Reading
- Mukhanov, V. (2005). Physical Foundations of Cosmology. Cambridge University Press.
- Baumann, D. (2009). "TASI Lectures on Inflation." arXiv:0907.5424.
- Smoot, G. F., et al. (1992). "Structure in the COBE differential microwave radiometer first-year maps." The Astrophysical Journal Letters, 396, L1–L5.
- Eisenstein, DJ, et al. (2005). "Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies." The Astrophysical Journal, 633, 560–574.
- Planck Collaboration (2018). "Planck 2018 results. VI. Cosmological parameters." Astronomy & Astrophysics, 641, A6.