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Steady-state model

The steady-state model, also known as the steady-state theory, is a cosmological theory proposing that the universe is expanding but maintains a constant average density of matter over time through the continuous creation of matter.^[1] Developed in the late 1940s, it posits the "perfect cosmological principle," asserting that the universe appears the same at any time as well as any location, in contrast to the Big Bang theory's prediction of an evolving universe from a hot, dense state. Key proponents included Hermann Bondi, Thomas Gold, and Fred Hoyle, who refined the model with mechanisms like continuous matter creation at a rate of approximately one hydrogen atom per cubic meter every few billion years to offset expansion.^[2] The theory aimed to explain observations like the uniform distribution of galaxies without invoking a singular origin, using a modification of general relativity to incorporate matter creation.^[3] However, it faced significant challenges from mid-20th-century observations, including the discovery of the cosmic microwave background radiation in 1965, which supported the Big Bang model and led to the steady-state theory's decline by the 1970s.^[4] Modern variants, such as quasi-steady-state cosmology, have attempted to address these issues but remain outside mainstream cosmology.^[5]

Overview

Core concepts

The steady-state model is a cosmological theory proposing that the universe maintains a static appearance on large scales over time, despite undergoing expansion, through the continuous creation of matter. This model was independently formulated in 1948 by Hermann Bondi and Thomas Gold in their paper "The Steady-State Theory of the Expanding Universe," and by Fred Hoyle in "A New Model for the Expanding Universe," as an alternative to evolving universe models like the Big Bang or oscillating cosmologies prevalent at the time.^[6]^[7] Central to the steady-state model is the perfect cosmological principle, which extends the standard cosmological principle—positing that the universe appears homogeneous and isotropic from any spatial location—by asserting that it also looks the same at any epoch in time. Bondi and Gold described this as the universe being "homogeneous and stationary in its large-scale appearance as well as in its physical laws," implying no preferred origin or evolutionary phase.^[6] This principle leads to a universe without a beginning or end, where the large-scale structure and content remain invariant across cosmic history.^[7] To reconcile expansion with this timeless uniformity, the model incorporates continuous matter creation that precisely offsets the dilution of density caused by the universe's growth. Hoyle introduced a creation field, or C-field, as a mathematical entity in the field equations of general relativity that generates matter with zero momentum along geodesics, at a rate of approximately one hydrogen atom per cubic meter every 3 × 10^5 years, or about 10^{-43} g/cm³/s.^[7]^[8] This creation rate ensures that the mean matter density remains constant, as the influx of new matter balances the "loss" due to expansion, yielding dp/dt = 0 in the model's equations and preserving the universe's steady state.^[6]^[7]

Comparison to Big Bang theory

The steady-state model posits an eternal universe that remains fundamentally unchanged over time, adhering to the perfect cosmological principle which asserts uniformity in both space and time, in stark contrast to the Big Bang theory's depiction of a universe with a finite age of approximately 13.8 billion years that has undergone significant evolution from a hot, dense initial state.^[9] This philosophical divergence reflects broader debates on the nature of existence: the steady-state view avoids a singular "beginning," appealing to perspectives that favor an infinite, self-sustaining cosmos without a creation event, while the Big Bang implies a temporal origin that some interpreted as compatible with theological notions of divine initiation.^[9] Such contrasts influenced mid-20th-century cosmological discourse, where the steady-state model's emphasis on continuity resonated with those wary of extrapolating physical laws to an extreme singularity.^[10] Predictively, the steady-state model lacks a hot early phase, precluding mechanisms like primordial nucleosynthesis that the Big Bang successfully explains, such as the observed abundance of helium-4 at about 24-25% by mass in the universe's primordial composition.^[11] In the Big Bang framework, this helium arises from fusion processes in the first few minutes after the universe's inception, when temperatures allowed neutrons and protons to combine into light nuclei, a prediction corroborated by observations of low-metallicity dwarf galaxies where helium content plateaus independently of heavier elements produced in stars. The steady-state model, by contrast, cannot account for this uniform primordial helium "floor" without ad hoc stellar production assumptions, highlighting its inability to replicate key elemental signatures of cosmic evolution.^[12] A core distinction lies in density evolution: the steady-state universe maintains a constant average matter density despite expansion through continuous creation of new matter, whereas the Big Bang predicts a decreasing density as the universe expands, with all baryons conserved from the initial epoch.^[13] To achieve this constancy (using 1948-era estimates of expansion rate), the steady-state model requires matter creation at a rate of approximately one hydrogen atom per cubic meter every 3 × 10^5 years; with modern estimates of the expansion rate (as of 2025), this would be closer to one per cubic meter every 3 billion years, a minuscule flux that preserves the overall matter-energy balance without violating local conservation laws on observable scales.^[14] This contrasts sharply with the Big Bang's adherence to baryon number conservation, where no such ongoing creation is needed, underscoring the steady-state approach's reliance on novel physical processes to sustain its timeless structure.^[15]

Historical development

Origins in the 1940s

The discovery of the universe's expansion by Edwin Hubble in 1929, based on observations of distant galaxies receding at velocities proportional to their distances, fundamentally altered cosmological thinking but left open the question of whether this expansion implied a finite beginning or an eternal process. By the late 1940s, there was no consensus on the implications, with some models suggesting an evolving universe from a hot, dense state—often associated with Georges Lemaître's earlier ideas—while others sought alternatives to avoid singularities or creation events deemed philosophically or scientifically problematic.^[9] In 1948, Hermann Bondi and Thomas Gold published their formulation of the steady-state model in the Monthly Notices of the Royal Astronomical Society, emphasizing the "perfect cosmological principle" that the universe appears identical at all points in space and time on large scales.^[6] This philosophical stance motivated their rejection of evolutionary models with a singular origin, which they viewed as introducing an unscientific "creation event," and instead proposed a framework where expansion is balanced by continuous matter creation to maintain uniformity and constant density. Independently, Fred Hoyle introduced a similar model in the same journal later that year, incorporating a creation field within general relativity to achieve the same steady-state conditions without violating conservation laws.^[7] These works briefly referenced the need for ongoing matter creation as a core assumption to reconcile expansion with observed large-scale homogeneity.^[9] The steady-state proposals garnered initial interest as an elegant alternative amid the post-World War II recovery of scientific research, when cosmology was revitalized by new observational tools like radio telescopes and a desire for testable, philosophically coherent theories.^[9] Published in a leading astronomical journal during a period of renewed international collaboration, the ideas appealed to those seeking a timeless universe that aligned with empirical uniformity in galaxy distributions, though they soon sparked debates over their compatibility with emerging evidence.^[6] Hermann Bondi and Thomas Gold, both Austrian-born scientists who emigrated to Britain in the 1930s, were pivotal in developing the steady-state model, drawing from their wartime experiences in radar research at the Admiralty.^[16]^[17] Their 1948 paper emphasized the model's observational implications, positing that the universe's large-scale appearance remains unchanged over time due to continuous matter creation compensating for expansion, aligning with then-current redshift data without requiring evolutionary changes in cosmic density.^[9] Fred Hoyle, a British astronomer and collaborator with Bondi and Gold during their radar work, provided the mathematical foundation for the model in his concurrent 1948 publication, introducing the C-field—a scalar field with negative pressure—to account for the continuous creation of matter at a rate proportional to the expansion.^[18] Hoyle further challenged the Big Bang through his later work on stellar nucleosynthesis, co-authoring the seminal 1957 B²FH paper that demonstrated heavy elements form in stellar interiors and supernovae, undermining Big Bang predictions limited to light elements like hydrogen and helium. In the 1950s, proponents refined the model by adjusting the matter creation rate to match evolving estimates of the Hubble constant, which ranged from about 250 to 500 km/s/Mpc during that decade, ensuring the model's predicted density remained consistent with radio galaxy counts and expansion observations.^[9] By the 1960s, Hoyle incorporated quasi-stellar objects (quasars) into the framework, interpreting their high redshifts and luminosities as evidence of localized, explosive events in a steady-state universe rather than distant, early phenomena.^[19] Collaborative efforts extended the model's reach through public engagement, including Hoyle's 1949 BBC radio series "The Nature of the Universe," which popularized steady-state ideas and famously coined the term "Big Bang" to critique the rival theory.^[19] These broadcasts, along with debates at the Royal Society and Royal Astronomical Society involving Hoyle, Bondi, and critics like Martin Ryle over radio source distributions, highlighted the model's emphasis on empirical testability.^[9] Signals of the model's decline emerged as Hoyle persisted in defending and refining it into the 1970s, proposing alternatives like iron whiskers to explain infrared background radiation despite mounting evidence from cosmic microwave background measurements favoring the Big Bang.^[18]

Theoretical framework

Fundamental assumptions

The steady-state model is grounded in the perfect cosmological principle, which posits that the universe is homogeneous and isotropic not only in space but also across all epochs of time, ensuring that its large-scale structure and physical laws remain unchanged indefinitely.^[20] This assumption implies no evolutionary processes on cosmic scales, distinguishing it from models that allow for temporal variations in density or composition. Central to the model is the postulate of uniform expansion, where the universe expands perpetually with recession velocities strictly proportional to distance, as encapsulated in Hubble's law, which holds eternally without alteration.^[20] To counteract the dilution of matter density that would otherwise result from this expansion, the theory incorporates a matter creation hypothesis, whereby new matter—primarily in the form of hydrogen—is continuously generated at a rate precisely proportional to the expansion rate, thereby preserving a constant average density throughout space and time.^[20] The model eschews any singular origin, envisioning the universe as infinite in both spatial extent and temporal duration, with no initial conditions or "beginning" required to explain its current state.^[20] This framework necessitates a modification to traditional energy conservation principles: while the continuous creation of matter appears to violate strict local conservation of energy, it is formulated such that overall momentum is conserved, and the total energy within any observable volume remains balanced by the influx of newly created material.^[20]

Mathematical formulation

The mathematical formulation of the steady-state model derives from Einstein's field equations of general relativity, augmented by an additional source term representing the continuous creation of matter via a scalar "C-field" or creation tensor. This modification, introduced by Hoyle, preserves local conservation of energy-momentum while permitting a non-zero global creation rate, enabling a universe with unchanging density despite expansion. The resulting equations describe exponential expansion with constant Hubble parameter, distinguishing the model from standard Friedmann-Lemaître-Robertson-Walker (FLRW) solutions. The core dynamical equation is the standard first Friedmann equation:

\left( \frac{\dot{a}}{a} \right)^2 = \frac{8\pi G}{3} \rho - \frac{k c^2}{a^2} + \frac{\Lambda}{3}

Here, a(t) is the scale factor, \dot{a} = da/dt, H = \dot{a}/a is the Hubble parameter, \rho is the matter energy density, k is the spatial curvature parameter, \Lambda is the cosmological constant, G is Newton's gravitational constant, and c is the speed of light. The C-field contributes to the stress-energy tensor with zero energy density but negative pressure, effectively acting to sustain the expansion. For the steady-state solution, H is constant, leading to the scale factor evolving as

a(t) \propto e^{H t},

implying perpetual expansion without deceleration or singularity, and an infinite age for the universe.^[15] Matter density remains constant through a modified continuity equation, derived from the covariant divergence of the total stress-energy tensor (including the creation contribution):

\dot{\rho} + 3 H (\rho + p) = \Gamma,

where p is the pressure and \Gamma is the volumetric creation rate of matter-energy. In the steady-state regime with constant \rho and pressureless matter (p = 0), \Gamma = 3 H \rho balances the dilution due to expansion. For a flat universe (k = 0) without \Lambda, the Friedmann equation simplifies to the critical density relation \rho = \frac{3 H^2}{8 \pi G}, maintained indefinitely by the creation process. The model favors flat geometry (k = 0) to ensure uniformity and constant H, avoiding time-dependent curvature effects.

Observational predictions

Early tests with radio sources

In the steady-state model, the constant density of matter throughout cosmic history implies a uniform spatial distribution of extragalactic radio sources, yielding a Euclidean log N-log S relation where the slope is -1.5, meaning the number of sources with flux greater than S, denoted N(>S), scales as N(>S) \propto S^{-1.5} ^[21]. This prediction serves as a direct test of the model's uniformity, as any deviation would suggest either observational biases or violations of the steady-state assumptions, such as source evolution over time. Early observational tests in the 1950s, particularly the Cambridge 2C survey conducted by Martin Ryle and Peter Scheuer, revealed a steeper slope in the log N-log S distribution, approximately -2.5 at faint fluxes, indicating a substantial excess of weak (distant) radio sources compared to steady-state expectations ^[22]. The 1955 results specifically showed that source counts at the faint end exceeded the predicted Euclidean values by a factor of about 10, challenging the notion of a uniform source density and suggesting that radio sources were more numerous or luminous in the past ^[9]. Steady-state proponents, including Fred Hoyle, responded by proposing that the continuous creation of matter could influence source counts, potentially producing more faint sources through mechanisms tied to creation events, which initially allowed the model to fit the 1950s data reasonably well ^[23]. Hoyle argued that the observed excess might arise from local underdensities (a "local hole") rather than cosmic evolution, dismissing the need for time-varying source properties ^[24]. However, steady-state advocates also attributed discrepancies to measurement errors in early surveys, such as confusion from source blending or instrumental noise ^[21]. Subsequent refinements in the early 1960s, including deeper Cambridge 3C surveys, confirmed the steeper slope and excess, with slopes around -2.0, providing robust evidence for source evolution that the steady-state framework struggled to accommodate without ad hoc adjustments ^[25]. This debate highlighted the radio counts as a pivotal early challenge to the model's uniformity, though interpretations remained contentious until higher-precision data solidified the evolutionary picture ^[26].

Challenges from cosmic background radiation

The steady-state model, positing an eternal universe without a hot, dense origin, predicted no relic thermal radiation from an early evolutionary phase; instead, any cosmic background would arise from discrete sources such as integrated starlight or galactic emissions, lacking a uniform thermal spectrum.^[13] This expectation stemmed from the model's core assumption of unchanging physical conditions over infinite time, precluding the cooling of primordial plasma.^[9] The 1965 discovery by Arno Penzias and Robert Wilson fundamentally challenged this view, as their observations using a sensitive horn antenna at Bell Laboratories revealed an isotropic microwave signal with a temperature of approximately 2.7 K, exhibiting a near-perfect blackbody spectrum across the sky. Published in The Astrophysical Journal, their findings indicated a uniform radiation field incompatible with discrete, evolving sources, as it showed no directional variations beyond a small dipole due to Earth's motion. In contrast, the Big Bang theory had anticipated such relic radiation from the decoupling of photons at recombination.^[9] Proponents of the steady-state model, including Fred Hoyle, attempted to accommodate the discovery by proposing that the microwave background resulted from starlight—potentially from ancient Population III stars—scattered and thermalized by interstellar dust, producing a diffuse glow without invoking a primordial origin. However, this hypothesis failed empirical tests, particularly regarding isotropy; scattering mechanisms could not replicate the observed near-uniformity (to within 1 part in 10,000) without introducing directional biases from galactic structures, as later confirmed by high-precision mapping. Subsequent integration efforts, such as adjusting creation rates to mimic cooling, were dismissed as ad hoc and unable to match the blackbody form without violating the model's foundational principles.^[27] A key quantitative mismatch arose from the CMB's temperature, which implies a historical cooling from roughly 3000 K at the epoch of recombination—when the universe became transparent to photons—demanding a hot, dense early phase entirely absent in the steady-state framework. This relic signal, redshifted by cosmic expansion, directly contradicted the eternal uniformity of steady-state cosmology. By the 1970s, the CMB's properties had become decisive evidence against the steady-state model, tipping the balance toward the Big Bang paradigm among most cosmologists.^[27] Although the Cosmic Background Explorer (COBE) satellite in the 1990s provided definitive confirmation of the blackbody spectrum at 2.725 K with deviations less than 0.005%, this postdated the model's primary decline.

Criticisms and decline

Inconsistencies with observations

One major empirical challenge to the steady-state model arises from big bang nucleosynthesis (BBN), which successfully predicts the observed abundances of light elements like deuterium (D/H ≈ 2.5 × 10^{-5}) and helium-3 without requiring a hot, dense early phase absent in steady-state cosmology. In the steady-state framework, these elements are expected to form primarily through stellar processes over cosmic history, but stellar nucleosynthesis models fail to reproduce the primordial ratios observed in low-metallicity gas clouds, as deuterium is efficiently destroyed in stars, leading to an underprediction of its abundance, while helium-3 ratios also mismatch without a primordial hot phase.^[28] This discrepancy was evident by the 1960s, when detailed stellar calculations could not match the data, reinforcing the need for a brief, high-temperature epoch around 1 MeV, as proposed in the seminal αβγ paper. The distribution of quasars provides further inconsistency, with observations showing a strong clustering at high redshifts (z > 2) and a sharp decline at low redshifts, implying quasars were more prevalent in the early universe—a pattern incompatible with the steady-state prediction of uniform quasar density across all epochs due to continuous matter creation maintaining eternal uniformity. Early quasar surveys in the 1960s, following Maarten Schmidt's identification of 3C 273 at z = 0.158, revealed overabundant high-z sources, with counts exceeding steady-state expectations by factors of 10 or more at faint magnitudes, suggesting a finite-age universe with evolutionary phases. This look-back time issue implies quasars formed within the first few billion years, challenging the infinite, unchanging cosmos of the steady-state model. Observations of galaxy evolution similarly contradict the steady-state assumption of no large-scale temporal changes, as high-redshift galaxies (z > 1) appear systematically smaller, more irregular, and bluer—indicating higher star-formation rates and less mature structures—compared to nearby galaxies, pointing to progressive assembly over cosmic time. Deep imaging surveys from the 1960s onward, including those using the Palomar 200-inch telescope, quantified this evolution through metrics like surface brightness and morphological indices, showing distant galaxies dimmer and less luminous than predicted for a static density profile. For instance, the number counts of faint galaxies steepen beyond m ≈ 22, consistent with luminosity evolution but requiring ad hoc adjustments in steady-state interpretations to avoid implying a younger universe. The steady-state resolution to Olbers' paradox—via cosmic expansion redshifting distant starlight out of the visible band—avoids an infinitely bright sky but struggles with quantitative limits on the extragalactic background light (EBL), as the model's infinite extent and matter creation predict a higher integrated infrared flux from unresolved sources than observed by detectors like IRAS in the 1980s. This critique highlights that while expansion dilutes contributions from remote shells, the eternal star formation rate leads to an overprediction of cumulative light beyond the horizon, necessitating unverified absorption mechanisms to match the measured EBL at 100 μm ≈ 20 nW m^{-2} sr^{-1}.^[29] Data from the 1970s and 1980s, including baryon density constraints, further eroded steady-state viability; for example, BBN-limited baryon density (Ω_b h^2 ≈ 0.01–0.02) clashed with the model's required creation rate to sustain constant density during expansion, favoring a hot big bang origin without continuous matter injection.^[30] Subsequent observations of Type Ia supernovae in the 1990s confirmed time dilation effects due to cosmic expansion, providing additional evidence against an eternal, unchanging universe.^[31]

Shift to standard cosmology

The discovery of the cosmic microwave background (CMB) radiation in 1965 by Arno Penzias and Robert Wilson marked a pivotal turning point in cosmology during the 1960s, providing compelling evidence for a hot, dense early universe consistent with the Big Bang model and undermining the steady-state theory's prediction of no such relic radiation. This observation, interpreted as the cooled remnant of the primordial fireball, shifted scientific consensus rapidly, as it aligned with Big Bang predictions from earlier theoretical work while conflicting with steady-state expectations of a uniform, unchanging cosmos.^[32] Notably, Fred Hoyle, a key proponent of the steady-state model, had coined the term "Big Bang" in 1949 during a BBC radio broadcast as a pejorative to ridicule the idea of an explosive cosmic origin, yet by the late 1960s, this once-mocked framework gained dominance as steady-state lost ground.^[33] By the 1970s, the Big Bang model had solidified its position, and the introduction of cosmic inflation theory in 1980 by Alan Guth further resolved longstanding issues such as the horizon and flatness problems, explaining the universe's large-scale uniformity without invoking continuous matter creation as in steady-state cosmology.^[34] Guth's inflationary scenario posited a brief period of exponential expansion driven by a scalar field, which not only bolstered the Big Bang's explanatory power but also marginalized steady-state alternatives by accounting for observed cosmic structure formation more naturally. This development, building on 1970s nucleosynthesis successes, accelerated the transition, with steady-state increasingly viewed as incompatible with accumulating evidence.^[35] Institutional shifts followed suit, as cosmology textbooks and curricula by the 1980s began adopting the cold dark matter (CDM) paradigm as the standard framework, emphasizing a finite-age universe with dark matter dominating structure growth over steady-state's eternal expansion.^[36] Hoyle mounted final defenses of steady-state ideas in the 1990s through collaborations, culminating in the 1993 proposal of a quasi-steady-state model with Geoffrey Burbidge and Jayant Narlikar, which incorporated episodic matter creation to mimic observed expansion while avoiding a true singularity.^[37] Despite these efforts, the model failed to gain traction amid mounting Big Bang confirmations. The steady-state model's legacy endures in ongoing cosmological debates, particularly influencing discussions on dark energy and fine-tuning by highlighting the need for mechanisms to sustain cosmic density without exquisitely balanced initial conditions, concepts echoed in modern explorations of dynamical dark energy.^[38] As of 2025, the original steady-state theory remains a historical curiosity, with no active research programs supporting it, as observational data from missions like Planck continue to affirm the Lambda-CDM framework.^[39]

Modern variants

Quasi-steady state cosmology

Quasi-steady state cosmology (QSSC) represents a late modification to the steady-state model, proposed by Fred Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar in 1993 to reconcile the theory with key observations like the cosmic microwave background (CMB) radiation and primordial nucleosynthesis. Building briefly on the original steady-state idea of continuous matter creation via a scalar C-field, QSSC introduces episodic bursts to address shortcomings in explaining light element abundances and the uniform 2.7 K CMB without a singular Big Bang origin. The model posits an eternal universe that expands exponentially over long timescales while oscillating on shorter cycles, avoiding both singularities and a static state.^[40] A core feature of QSSC is the occurrence of periodic creation events, termed "mini-bangs," which happen roughly every 40 billion years (the model's Q-cycle period). These mini-bangs involve the sudden production of matter in localized regions near compact objects like black holes, generating Planck-mass particles that rapidly decay into quarks, gluons, and eventually nucleons and light elements. This process maintains a quasi-steady average matter density, compensating for dilution due to expansion, while the overall universe density remains near-constant at about $10^{-27} g/cm³ between events. The creation is driven by the negative-pressure C-field, which facilitates matter emergence without violating energy conservation in the model's framework.^[40]^[41] Mechanistically, QSSC describes an oscillating universe where the scale factor a(t) follows a form combining long-term exponential growth (e^{Pt}, with P \approx 10^{-11} yr⁻¹) and shorter oscillatory components ($1 + \eta \cos(\tau(t)), where \eta < 1), yielding cycles of expansion and contraction without reaching zero volume. This oscillation is influenced by quantum cosmology, particularly Hoyle's earlier concept of a varying gravitational constant G, which decreases over time and links to particle number creation, alongside a negative cosmological constant tied to the C-field's dynamics. Matter creation during mini-bangs occurs via quantum fluctuations amplified near singularities, producing the observed helium-4 abundance of approximately 0.24 without relying on non-baryonic dark matter.^[41] Among its predictions, QSSC attributes the CMB to the thermalization of starlight scattered by microscopic carbon and iron particles (whiskers) over cosmic history, yielding a blackbody spectrum at 2.7 K that remains quasi-constant but exhibits slight variations across cycles due to oscillatory density changes. The model also better explains the observed distribution of quasars and high-redshift sources (up to z \approx 5) as recurring phenomena from multiple creation epochs, avoiding the need for quasar evolution assumed in standard cosmology, and predicts the existence of ancient galaxies and stars aged 40–50 billion years. These features aim to resolve tensions in steady-state theory, such as radio source counts and element formation.^[41] Despite its ambitions, QSSC has achieved fringe status in cosmology, widely criticized for introducing ad hoc elements like mini-bangs and the C-field to fit observations, which complicates the model and hinders rigorous testing compared to the simpler Lambda-CDM framework. Specific critiques, including those from Edward L. Wright on inconsistencies with radio galaxy distributions and stability issues against perturbations, have been addressed by proponents, but the theory's complexity and lack of unique, falsifiable predictions beyond shared features with standard models have limited its adoption. Narlikar, a key proponent, passed away in May 2025, after which QSSC has seen no major advancements. Further developments, such as exact solutions for the metric, have not garnered broad empirical support.^[13]^[42]^[43] Several cosmological models have drawn inspiration from the steady-state concept of an eternal universe but diverge in key mechanisms, often avoiding continuous matter creation while emphasizing alternative dynamics for cosmic evolution. Cyclic models, such as the ekpyrotic universe proposed in 2001, echo the steady-state idea of avoiding a singular origin by positing a sequence of brane collisions in higher-dimensional space, leading to periodic hot big bangs without maintaining constant density across cycles.^[44] In this framework, the universe undergoes contraction and bounce phases driven by string theory-inspired potentials, resolving the initial singularity issue but introducing varying matter densities over cycles, unlike the uniform steady state.^[44] Plasma cosmology, developed by Hannes Alfvén in the 1960s, shares the steady-state preference for an eternal universe but prioritizes electromagnetic forces over gravity as the dominant driver of large-scale structure, rejecting cosmic expansion in favor of plasma instabilities and filamentary configurations.^[45] Collaborating with Oskar Klein, Alfvén envisioned a symmetric metagalaxy where matter and antimatter domains coexist, separated by plasma currents that shape cosmic filaments without invoking expansion or creation processes.^[45] This model aligns with steady-state eternity but critiques gravitational dominance, emphasizing observable plasma phenomena like magnetic reconnection for galaxy formation.^[45] Tired light theories, first articulated by Fritz Zwicky in 1929, offer another alternative to expansion-based redshift interpretation, proposing that photons lose energy gradually through interactions with interstellar medium, mimicking the uniform redshift-distance relation observed in steady-state contexts without requiring an evolving universe. Zwicky suggested mechanisms like Compton scattering or gravitational drag could cause this energy dissipation, preserving spatial uniformity but facing criticism for failing to explain time dilation in supernovae light curves and surface brightness inconsistencies. The Hoyle-Narlikar theory of conformal gravity, developed in the 1960s, incorporates variable fundamental constants to accommodate observational data like accelerating expansion while maintaining an eternal framework. In this approach, conformal transformations allow scale-invariant dynamics, enabling a steady-like universe without ad hoc matter creation by adjusting couplings like the gravitational constant over cosmic history. These alternatives distinguish themselves from the original steady-state model primarily by eschewing continuous matter creation, instead relying on cyclic bounces, plasma electromagnetism, photon energy loss, or variable gravitational laws to achieve apparent uniformity and eternity.^[44]^[45]

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Inflationary universe: A possible solution to the horizon and flatness problems. Alan H. ... 1980 (unpublished) A. H. Guth and E. J. Weinberg, [17]. Omitted ...
[30]
[astro-ph/9703194] Inflation: From Theory to Observation and Back
Mar 28, 1997 · Alan Guth introduced cosmologists to inflation at the 1980 Texas Symposium. Since, inflation has had almost as much impact on cosmology as the ...<|separator|>
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[PDF] A Brief History of Dark Matter - UCSC Physics
1978 ApJ 219, 413. Page 10. Page 11. 1980 - Most astronomers are convinced that dark matter exists around galaxies and clusters - but is it Hot or Cold? It was ...Missing: primary | Show results with:primary
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A Quasi--Steady State Cosmological Model with Creation of Matter
A Quasi--Steady State Cosmological Model with Creation of Matter. Hoyle, F ... NUCLEOSYNTHESIS;; ABUNDANCES. full text sources. ADS. |. data products. SIMBAD ...
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[PDF] Quasi-Steady-State and Related Cosmological Models - arXiv
matter at a rate of 3ρH or about 10-43 g/cm3 s. This exceedingly small value, corresponding to the formation of three new hydrogen atoms per cubic meter per.
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Planck 2018 results - I. Overview and the cosmological legacy of ...
This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard ...
[35]
https://arxiv.org/abs/astro-ph/9703194
[36]
[PDF] The quasi-steady state cosmology: Some recent developments
The quasi-steady state cosmology (QSSC hereafter) was proposed in 1993 by Fred. Hoyle, Geoffrey Burbidge and myself (Hoyle et al. 1993).
[37]
quasi-steady-state cosmology: a note on criticisms by E. L. Wright
We answer criticisms made by Wright of the quasi-steady-state cosmology (QSSC). It is shown that none of his criticisms is valid, and the QSSC remains a viable ...
[38]
The Quasi-Steady State Cosmology: A Problem of Stability
Abstract. This paper examines the gravitational stability against small perturbations of the quasi-steady state cosmological model. This model was first ...Missing: 1990s | Show results with:1990s
[39]
[hep-th/0103239] The Ekpyrotic Universe: Colliding Branes ... - arXiv
Mar 29, 2001 · Authors:Justin Khoury, Burt A. Ovrut, Paul J. Steinhardt, Neil Turok. View a PDF of the paper titled The Ekpyrotic Universe: Colliding Branes ...Missing: original | Show results with:original
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The Klein-Alfvén cosmology revisited - IOPscience
The Klein-Alfvén model is based on the pragmatic belief that also cosmology, just like all other fields of physics, should be based on physical laws ...