Static Universe

Part of a series on Physical cosmology

Early universe

Inflation · Nucleosynthesis

Backgrounds

Expansion · Future

Components · Structure

Components

Dark energy · Dark matter
Photons · Baryons

Structure

Experiments

Scientists

Subject history

In the grand, often inconvenient, tapestry of cosmology, a static universe model stands as a testament to humanity's early, perhaps even desperate, desire for cosmic stability. This particular cosmological model, sometimes less imaginatively referred to as stationary, infinite, static infinite, or static eternal, posits a universe that is both boundless in space and without beginning or end in time. Crucially, within this framework, space itself engages in neither the drama of expansion nor the collapse of contraction. Such a universe, if it were to exist, would be devoid of what physicists refer to as spatial curvature; in simpler, and arguably more comforting, terms, it would be 'flat' or Euclidean. A rather neat and tidy picture, if only reality were so accommodating. The notion of a static infinite universe first found a voice in the work of the English astronomer Thomas Digges (1546–1595), who, in 1576, dared to suggest that the heavens might not be so neatly bounded after all. He extended the Copernican system to embrace an infinite cosmos, a truly radical thought for his era.

This early proposition contrasts sharply, yet ironically, with a later, more refined static model put forth by none other than Albert Einstein. In 1917, through his seminal paper, "Cosmological Considerations in the General Theory of Relativity," Einstein presented his preferred cosmology: a universe that was temporally infinite (eternal) but, quite significantly, spatially finite. He sought a universe that was stable, unchanging, and, above all, not prone to the awkward dynamism that his own equations seemed to suggest.

The scientific narrative took a rather inconvenient turn, however, with the burgeoning understanding of the redshift-distance relationship. This relationship, deduced from the inverse correlation of galactic brightness to their observed redshift, was painstakingly gathered through the observations of American astronomers Vesto Slipher and Edwin Hubble. It was the Belgian astrophysicist and priest Georges Lemaître who, with a perhaps unsettling clarity, interpreted this pervasive redshift as definitive evidence of universal expansion – a cosmic exhalation that directly pointed towards a primordial beginning, now famously known as the Big Bang.

Naturally, not everyone was quick to embrace such a dramatic narrative. The Swiss astronomer Fritz Zwicky, for instance, proposed an alternative, less disruptive explanation: that the observed redshift was merely an artifact, caused by photons losing energy as they traversed the vast, intergalactic reaches, interacting with the sparse matter and/or subtle forces found there. Zwicky's hypothesis, a desperate attempt to cling to a static cosmos, would later be rather tellingly, and somewhat pejoratively, dubbed 'tired light' – a term coined by one of the principal proponents of the Big Bang theory, Richard Tolman. The universe, it seemed, wasn't merely expanding; it was actively resisting humanity's preference for stasis.

The Einstein universe

For a more in-depth exploration of this particular cosmic cul-de-sac, one might consult the main article: Einstein's static universe.

In 1917, as he grappled with the implications of his own groundbreaking equations of general relativity, Albert Einstein found himself in a peculiar predicament. His elegant framework, when applied to the universe as a whole, suggested an inherent instability. Left unchecked, the attractive effects of gravity on ordinary matter would inevitably cause any static, spatially finite universe to either collapse inward under its own immense weight or, conversely, expand forever into an ever-thinning void. Neither scenario appealed to Einstein's philosophical predisposition for a stable, eternal cosmos. To counteract this gravitational imperative, he introduced a novel, and somewhat controversial, element: a positive cosmological constant into his field equations. This constant acted as a repulsive force, precisely balancing gravity's pull and, in theory, holding the universe in a state of delicate, unchanging equilibrium.

This particular rendition of the cosmos soon became known colloquially as the Einstein World, or more formally, Einstein's static universe. It was a universe where everything was perfectly balanced, a cosmic still life, utterly devoid of the messy dynamism that observations would soon unveil.

Einstein's motivation for this cosmic intervention, however, proved to be short-lived. The aforementioned work of Georges Lemaître, who first proposed that the universe was not static but actively expanding, coupled with Edwin Hubble's rigorous research into the observational data compiled by astronomer Vesto Slipher, firmly established the empirical relationship between redshift and distance. This crucial evidence formed the bedrock for the modern expansion paradigm that Lemaître had so presciently introduced. It was a paradigm shift that forced Einstein to confront the uncomfortable truth that his static model, despite its mathematical elegance, simply didn't reflect reality. According to the physicist George Gamow, this realization prompted Einstein to famously declare the introduction of the cosmological constant, and by extension, his entire static cosmological model, as his "biggest blunder." A rather humbling admission from a mind of such caliber, proving even geniuses can occasionally try to force the universe into a shape it simply refuses to take.

The Einstein universe, in its ideal formulation, is a closed system. This implies a specific geometry: it possesses a hyperspherical topology and exhibits positive spatial curvature. Within this model, the universe is uniformly filled with "dust" (a simplification for matter) and is sustained by a precisely calibrated positive cosmological constant. The value of this constant, denoted as ΛE, is given by the equation:

$\Lambda _{E}=4\pi G\rho /c^{2}$

Here, $G$ represents the Newtonian gravitational constant, $\rho$ signifies the uniform energy density of the matter distributed throughout the universe, and $c$ is the ubiquitous speed of light. The spatial curvature of the Einstein universe is intrinsically linked to its radius of curvature, $R_E$ , which can be calculated as:

$R_{E}=\Lambda _{E}^{-1/2}={c \over {\sqrt {4\pi G\rho }}}.$

This precisely balanced universe is, in essence, one of Friedmann's solutions to Einstein's field equations. Specifically, it describes a universe filled with dust of density $\rho$ , endowed with the cosmological constant $\Lambda _{E}$ , and characterized by the radius of curvature $R_{E}$ . It holds a unique position as the only non-trivial static solution derivable from Friedmann's equations. A mathematical curiosity, perhaps, but one that ultimately proved to be an unstable mirage.

Indeed, the fatal flaw of the Einstein universe was soon recognized: it was inherently unstable. This instability implied that even the slightest perturbation – a minute deviation in the value of the cosmological constant, a subtle shift in the matter density, or an infinitesimal alteration in the spatial curvature – would irrevocably disrupt its delicate balance. Such a perturbation would inexorably drive the universe away from its static state, compelling it to either embark on an eternal path of expansion and acceleration or to inexorably re-collapse back into a primordial singularity. A cosmic tightrope walk, perpetually destined to fail.

Following Einstein's rather public renunciation of his cosmological constant and his subsequent embrace of the Friedmann-Lemaître model of an expanding universe, most physicists throughout the greater part of the twentieth century simply assumed that the cosmological constant held a value of zero. If this assumption were true (and in the absence of any other mysterious forms of dark energy), the expansion of the universe would, by natural consequence, be decelerating. However, the universe, in its infinite capacity for irony, had other plans. In 1998, a groundbreaking discovery by Saul Perlmutter, Brian P. Schmidt, and [Adam G. Riess] and their respective teams introduced the astonishing theory of an accelerating universe. This unexpected observation dramatically revived the concept of a positive cosmological constant, now serving as the simplest and most compelling explanation for the enigmatic phenomenon we call dark energy. It seems even "blunders" can find a second act.

In a less impactful, yet notable, attempt to resurrect the static universe model, Irving Segal introduced his chronometric cosmology in 1976. Much like Zwicky before him, Segal attributed the perplexing redshift of distant galaxies not to expansion, but to an intrinsic curvature within the cosmos itself. While Segal claimed that astronomical data vindicated his model, the broader scientific community ultimately found his results to be inconclusive, preferring the mounting evidence for an expanding universe. Some ideas, it seems, simply refuse to stay buried, even when they're demonstrably dead.

Requirements of a static infinite model

For any model of a static infinite universe to even begin to be considered viable, it must, at a minimum, provide coherent and empirically supported explanations for three fundamental cosmic observations. These are, essentially, the universe's non-negotiable terms for admission.

First, and perhaps most critically, it must offer a compelling explanation for the observed intergalactic redshift. The systematic shift of light from distant galaxies towards longer, redder wavelengths is a pervasive phenomenon that the expanding universe model explains with elegant simplicity: the space between us and those galaxies is literally stretching, drawing out the light waves as it does so. A static model, by definition, lacks this mechanism and must therefore invent an equally robust, yet fundamentally different, explanation for this omnipresent cosmic signature.

Second, such a model must account for the existence and characteristics of the cosmic microwave background radiation (CMB). This faint, ubiquitous glow of microwaves permeating all of space is widely interpreted as the residual heat from the Big Bang itself – the afterglow of a universe that was once incredibly hot and dense. For a universe that has existed eternally in a static state, without a hot, dense beginning, the origin of this remarkably uniform background radiation poses an almost insurmountable challenge. It's the universe's echo, screaming about its violent birth, and a static model simply has no ear for it.

Third, and perhaps the most existentially dire requirement, a static universe model must incorporate a credible mechanism for the continuous re-creation of matter, particularly hydrogen atoms, from radiation or other unspecified sources. This perpetual genesis of new matter is essential to counteract the inexorable 'running down' of the universe. Without such a mechanism, the second law of thermodynamics would inevitably lead to a gradual, but complete, conversion of all matter into energy through stellar processes and other cosmic phenomena. Over an infinite timescale, a static universe would, without this constant replenishment, eventually consist solely of dead, inert objects such as black holes and cold, collapsed black dwarfs, utterly devoid of the vibrant, self-organizing structures required for observation or, indeed, for life. It's a universe that, without constant, miraculous intervention, would simply cease to be interesting, or even observable, to itself. A rather dull fate, wouldn't you agree?

Static Universe

The Einstein universe

Requirements of a static infinite model

See also