Objections to the Big Bang

According to the Big Bang model, the universe expanded from an extremely dense and hot state and continues to expand.

The Big Bang theory has become the prevailing cosmological model for the universe from a hypothetical "the beginning of time" and on through a theorized large-scale evolution. The theory rests on a number of additional physical theories, among them stellar evolution, special and general relativity, and quantum mechanics. Each of these supporting theories is also disputed if not falsified.

As new astronomical discoveries were made, the theory has been modified by the accretion of additional, unobservable entities and processes, to the point where the observable galaxies are said to be only 4.6% of the total. The other 95.4% is invisible and hypothetical, a ratio of over twenty to one of invisible to visible subject matter. As Bjørn Ekeberg puts it:

The crux of today's cosmological paradigm is that in order to maintain a mathematically unified theory valid for the entire universe, we must accept that 95 percent of our cosmos is furnished by completely unknown elements and forces for which we have no empirical evidence whatsoever. For a scientist to be confident of this picture requires an exceptional faith in the power of mathematical unification.

There are numerous observations of stars, quasars, and galaxies which cast serious doubt on the theory. It also suffers from a lack of necessary observations and from the problem of irreproducible results- there is no way to test it.

With almost every new discovery, its proponents have had to add language such as 'astronomers were surprised', 'puzzled', it 'challenges the existing theories', 'a conundrum'.

The Big Bang has been described by its critics in terms that meet the criteria of a disputed and censored science. It has been called a "religion", a "creation myth", and other similar epithets by both its critics and its promoters .

Overview

History of the Universe - gravitational waves are hypothesized to arise from cosmic inflation, a speculated faster-than-light expansion just after the Big Bang.

A graphical timeline is available at Graphical timeline of the Big Bang

Hubble observed that the light from faraway galaxies is redshifted in various amounts. Redshift has been interpreted in several ways. The Big Bang relies on the Doppler effect interpretation, that all distant galaxies and clusters are receding away from our vantage point with an apparent velocity proportional to their distance. The farther away they are, the faster they move away from us, regardless of direction. Hubble himself disavowed this interpretation.

The Big Bang theory has failed to explain a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background, the large scale structure, and Hubble's Law, without adding a large and growing number of unproven and unprovable assertions.

The framework for the Big Bang model relies on Albert Einstein's disputed theory of general relativity and on simplifying assumptions such as homogeneity and isotropy of space, all of which conflict with the observed large-scale structure. The governing equations were formulated by Alexander Friedmann, and similar solutions were worked on by Willem de Sitter. Since then, astrophysicists have incorporated observational and theoretical additions into the Big Bang model, and its parametrization as the Lambda-CDM model serves as the framework for current investigations of theoretical cosmology. Attempts to fit this type of expansion model to the observed Universe has led to the make-believe notions of Dark Energy and Dark Matter, such that over 90% of the subject matter is unobservable.

In general:

• Its proponents describe it as a science; its critics describe it as a state-sponsored religion, that its central tenants are irreproducible and untestable.
• Its practitioners receive government funding.
• The Big Bang is taught in all relevant institutions of higher learning which receive government funding and is heavily promoted in corporate media.
• Its publications are vetted in a secretive process by anonymous “Peer Reviewers” at the relevant journals of cosmology and astrophysics. No alternative models are allowed to be published in these same journals.
• It has acquired a substantial body of criticism from diverse sources.
• Its critics in general do not receive government funding.
• Its critics make numerous claims that the Big Bang theory has been shown to be false, that numerous observations conflict with the theory, that additional unproven hypotheses have been added on in an ad hoc fashion to cover new findings, that this has reached the point where 96% of its studies is unobservable Dark Energy and Dark Matter, a science without subject matter.
• A notable number of its critics have been damaged in career and reputation.
• There are one or more alternative theories which are not allowed state funding, such as the various Steady State, Plasma Cosmology, and Electric Universe models.

...the problem is pervasive throughout astronomy and, contrary to its projected image, endemic throughout most of current science. Scientists, particularly at the most prestigious institutions, regularly suppress and ridicule findings which contradict their current theories and assumptions. -Halton Arp

Arguments against the Big Bang

Criticism of the Big Bang theory has come from both its proponents as well as from its non-believers. There is a large and growing body of observations which contraindicate. There are a number of underlying hypotheses and theories that the Big Bang relies on which have also received criticism. Some critiques:

• Dark Energy requires continuous energy creation, violating conservation of energy.
• Type 1a supernovae and redshift distances don't agree. This was why dark energy was made up to save the theory.

Objections to the proponent's history of the Big Bang

Predictions of temperature of space using Big Bang and Steady State models

Year	Men	Temperature, T	Model	Method	Remarks
1896	C. E.Guillaume	< 5.6 K	Steady State	stellar irradiance using S-B Law
1926	Arthur Eddington	3.18 K	Steady State	stellar irradiance using S-B Law	'father' of stellar evolution model
1933	Erich Regener	2.8 K	Steady State	Cosmic ray energy balance	First use of rockets to measure cosmic rays
1938	Walther Nernst	0.75 K	Steady State	Tired Light	Nobel Laureate Chemistry, 1920, 3rd law of thermodynamics
1941	Gerhard Herzberg	2.3 K	Steady State	CN rotation spectrum	Nobel Laureate, Chemistry, 1971
1948	Alpher & Herman	~ 5.0 K	Big Bang	ideal gas expansion	Colleagues of George Gamow
1949-50	Alpher & Herman	> 5.0 K; 28 K	Big Bang	ideal gas expansion
1954	Finlay-Freundlich	1.9 K < T < 6.0 K	Steady State	Tired light	Colleague of Eddington, Einstein
1953	George Gamow	7.0 K	Big Bang	Thermodynamics	Big Bang popularizer
1961	George Gamow	50 K	Big Bang	Thermodynamics
1964	Penzias & Wilson	2.7 K	none	observation in microwave band	Bell Labs technicians testing a horn

• Its practitioners failed to predict the temperature of space (the cosmic background radiation), Gamow by over an order of magnitude.
• Its proponents faked the history of the CMB, by claiming that the Big Bang theory had predicted it better than the Steady State theory.
• Hubble disavowed the expansion-velocity interpretation of red shift and presented arguments against it.
• To claim to have proven General Relativity, Arthur Eddington faked his 1919 solar eclipse photographic evidence "when he cherry-picked among his observations of an eclipse". His camera didn't have the requisite resolution. A Fake News PR campaign was used to promote it.

Failures of prediction

Local filamentary structure, partly based on redshift distance. Dark Matter is said to cause this deviation from a radial explosion.

• It has failed to account for the large-scale structure of the universe, the Great Voids, Great Walls, Great Attractor, and the filamentary structure seen at all scales.
• Filaments, such as the ones seen around the Milky Way in the infrared and microwave bands, cannot be assembled using the forces of gravity and rotation.
• The large-scale structure could not have been assembled from a radial, point explosion.
• The large-scale structure could not have been assembled in the allotted time period.

Inconsistencies of the hubble constant of expansion

The Hubble Constant, which is presumed to measure the expansion rate of the Universe, is a constantly shifting value.

Measured one way, the universe appears to be expanding at a certain rate; measured another way, the universe appears to be expanding at a different rate. And... those discrepancies have gotten larger in recent years, even as the measurements have gotten more precise.

Objections to cosmic background microwave data

• COBE measured microwave emissions from the oceans of the Earth. http://www.sjcrothers.plasmaresources.com/COBEwmap-3.pdf
• There was no way to test and calibrate the COBE instruments for noise floor and discrimination.
• There was no way to test the COBE microwave horn antennas for diffraction at the lip.

Objections to cosmic inflation

Without the hypothetical inflation field, the big bang does not predict the smooth, isotropic cosmic background radiation that is observed, because there would be no way for parts of the universe that are now more than a few degrees away in the sky to come to the same temperature and thus emit the same amount of microwave radiation. - An Open Letter to the Scientific Community

I have not been surprised to hear some scientists openly talking about a crisis in cosmology. In the big “inflation debate” in Scientific American a few years ago, a key piece of the big bang paradigm was criticized by one of the theory's original proponents for having become indefensible as a scientific theory. Why? Because inflation theory relies on ad hoc contrivances to accommodate almost any data, and because its proposed physical field is not based on anything with empirical justification. This is probably because a crucial function of inflation is to bridge the transition from an unknowable big bang to a physics we can recognize today. - Bjørn Ekeberg, April 30, 2019

Quasar and redshift observations which counter-indicate

There is evidence that the high-redshift quasar is interacting with the material of the low-redshift galaxy and is in front of it.

• Redshifts are affected by gravity (van Flandern); redshifted light from a hi-z object could be a result.
• Redshifts can vary over time, which would would imply a large acceleration of the object. ("galaxy STIS 123627, also referred to as "Sharon". Sharon it was announced just a few years ago, is the most distant galaxy every discovered, over 12.5 billion light years away scientists proudly proclaimed. However, by 2007 Sharon no longer exhibited the same red shift previously observed, and is now estimated to be maybe 9 billion light years away.")
• High redshift quasars are found in front of and/or connected to low-redshift galaxies. Halton Arp
• Quantization of redshift.
• Large percentage of quasars, AGN's, etc are found along the axes of lower-redshift galaxies, statistically improbable.
• There are "holes" in space (in the celestial sphere) with no quasars.
• The quasars aligned with a galaxy show an ordered redshift quantization, with higher redshift QSO's closer to the lower-redshift galaxy.
• Quasars further away are too big and too bright. Either they age 'just so' or the redshift-distance relation is wrong.
• High redshift quasars have higher-than-solar metallicities. The iron-to-magnesium ratio increases at higher redshifts (earlier Big Bang epochs).
• The number density of optical quasars peaks at z=2.5-3, and declines toward both lower and higher redshifts. At z=5, it has dropped by a factor of about 20.
• Quasars claimed to be 13 billion years old did not have enough time to collect a supermassive Black Hole.

[T]hese quasars have the mass of about a billion suns, yet have been collecting matter for less than 100,000 years. Conventional wisdom says quasars of that mass should have needed to pull in matter a thousand times longer than that...

Halton Arp's observations and objections

Arp was denied telescope time as a result of publishing these counterindicative findings.

• Objects which appear young are aligned on either side of eruptive objects. This implies ejection of protogalaxies.
• The youngest objects appear to have the highest redshifts. This implies that intrinsic redshift decreases as the object ages.
• As distance from the ejecting central object increases, the quasars increase in brightness and decrease in redshift. This implies that the ejected objects evolve as they travel outward.
• At about z= .3 and about 400 kpc from that parent galaxy the quasars appear to become very bright in optical and X-ray luminosity. This implies there is a transition to BL Lac Objects.
• Few BL Lac objects are observed implying this phase is short-lived.
• Clusters of galaxies, many of which are strong X-ray sources, end to appear at comparable distances to the BL Lac's from the parent galaxy. This suggests the clusters may be a result of the breaking up of a BL Lac.
• Clusters of galaxies in the range z= .4 to .2 contain blue, active galaxies. It is implied that they continue to evolve to higher luminosity and lower redshift.
• Abell clusters from z= .01 to .2 lie along ejection lines from galaxies like CenA. Presumably they are evolved products of the ejections.
• The strings of galaxies which are aligned through the brightest nearby spirals have redshifts z= .01 to .02. Presumably they are the last evolutionary stage of the ejected protogalaxies before they become slightly higher redshift companions of the original ejecting galaxies. (p166-7)

Objections to the mathematics of the Big Bang

• Special Relativity is false math. The variables for time and distance are being used in algebraically illegal ways.
• General Relativity is false math. The GR pseudo-tensor is a mathematically-illegal construct.
• Gravity has to both act instantaneously and move at the finite speed of light.
• A singularity does not arise in Schwartzchild's solution for a Black Hole, Hilbert made that mistake [Crothers].

Objections to the thermodynamics of the Big Bang

• The initial Big Bang could not have cooled off because it was a closed system without a cold sink.
• The Universe is not a black body, so black body equations do not apply [Pierre-Marie Robitaille]
• Kirchhoff's law of thermal emission is incorrect.[Pierre-Marie Robitaille http://vixra.org/abs/1403.0935 On the Equation which Governs Cavity Radiation]
• Before the proton-antiproton annihilation event the mass of the Universe was at least 1 billion times greater than now. All estimates assume that the energy of the Big Bang can found by converting the present accepted mass into energy. If this is done, then the matter-antimatter annihilation would produce more energy than the Big Bang itself.
• The redshifting of primordial photons violates conservation of energy.

As the universe expanded, space itself stretched and, in turn, stretched the wavelength of the photons, causing their energy to decrease and the universe to cool. The cooling of the universe is sometimes confusingly attributed to the universe expansion from the standpoint that as a gas expands it cools. But this cause-effect logic doesn't work. While adiabatic expansion in a piston does lead to cooling, this is caused by the fact that the piston is doing work, thereby meaning that the gas molecules rebound from the retracting piston at a slower rate than when they struck the piston. But there is no such piston at work in the universe. There is no boundary that the universe is expanding against. So why then did the universe cool? The increasing wavelength of photons with increasing expansion of the universe follows from application of Einstein’s General Theory of Relativity. And this naturally begs another question: how does the resulting energy balance work? Where does the energy lost by the photons end up going ? It appears that Einstein’s equations are not consistent with the conservation of energy. The actual mechanism by which stretching of space causes the stretching of photons wavelength is unknown and not currently consistent with the conservation of energy. - Robert T. Hanlon, in The Historical and Theoretical Foundations of Thermodynamics

Objections to spacetime expansion

• If space is expanding, then zero-point energy is created from nowhere to fill in the newly-expanded space.
• Expanded time cannot be created in the same manner as expanded space is created. The space creation is a local event, but the time creation is always an event which must reverberate throughout the entire universe.

Other observations which counter-indicate

An animation of the Einstein Rings which should be observed around the claimed black hole at the center of the Milky Way galaxy but are not.

• There are no Einstein Rings around Sag A*, which General Relativity would predict.
• General Relativity fails its tests, e.g. it does not account for starlight bending around the Sun's limb.
• The measure of distance based on Standard candles is disputed.
• Some observed stars and globular clusters are, according to the stellar evolution model, older than the Universe of the Big Bang model.
• The Hubble Ultra Deep-field experiment found fully-formed galaxies where none should exist- these would have formed too close to the beginning of time. "...they gazed into infinity, and were so frightened by the visage, they stopped looking."

Miscellaneous objections to the theory

• The Big Bang relies on only 1/3rd of the velocity data. We can't measure transverse velocities of distant galaxies, which could be just as large as the inferred radial velocities.
• Since we can't measure the total proper motion, we can't know if all the galaxies radiated from a point source.
• Only 1/20th of its subject matter is observable, the other 19/20ths is completely made up.
• "Hot gas" is a linguistic dodge to avoid the complications of the word "plasma".

Objections to other supporting theories

• The speed of light is not a constant. In particular, measurements over the course of the past few centuries have shown a secular reduction.
• The accepted Stellar evolution model fails for several reasons, both theoretical and observational.
• The Nebular hypothesis fails for several reasons, including the observed distribution of angular momentum in the Solar System.
• No one knows what happens to matter over large time scales. This is beyond the limits of human knowledge.

Objections to mixing religion with science

In the 1920s and 1930s almost every major cosmologist preferred an eternal steady state Universe, and several complained that the beginning of time implied by the Big Bang imported religious concepts into physics; this objection was later repeated by other supporters of the steady state theory, who rejected the implication that the universe had a beginning.

Underlying assumptions

The Big Bang theory depends on several major assumptions, many of which cannot be tested or proven. One is the universality of physical laws, yet the model itself violates these laws, energy conservation in particular. Another assumption is the cosmological principle, reasonable but untestable. The cosmological principle states that on large scales the universe is homogeneous and isotropic.

These ideas were initially understood to be unfounded assumptions, but today there are efforts to test each of them. For example, the first assumption has been tested by observations showing that largest possible deviation of the fine structure constant over much of the age of the universe is of order 10⁻⁵.

Also, general relativity has failed stringent tests on the scale of the Solar System and binary stars.

Expansion of space

Main articles: Friedmann–Lemaître–Robertson–Walker metric and Metric expansion of space

General relativity purports to describe spacetime by a metric, which determines the distances that separate nearby points. The points, which can be galaxies, stars, or other objects, themselves are specified using a coordinate chart or "grid" that is laid down over all spacetime. The cosmological principle implies that the metric should be homogeneous and isotropic on large scales, which uniquely singles out the Friedmann–Lemaître–Robertson–Walker metric (FLRW metric). This metric contains a scale factor, which describes how the size of the universe changes with time. This enables a convenient choice of a coordinate system to be made, called comoving coordinates. In this coordinate system the grid expands along with the universe, and objects that are moving only because of the expansion of the universe remain at fixed points on the grid. While their coordinate distance (comoving distance) remains constant, the physical distance between two such comoving points expands proportionally with the scale factor of the universe.

The Big Bang is not an explosion of matter moving outward to fill an empty universe. Instead, space itself expands with time everywhere and increases the physical distance between two comoving points. In other words, the Big Bang is not an explosion in space, but rather an expansion of space. Because the FLRW metric assumes a uniform distribution of mass and energy, it applies to our universe only on large scales—local concentrations of matter such as our galaxy are gravitationally bound and as such do not experience the large-scale expansion of space.

Problems and related issues in physics

See also: List of unsolved problems in physics

As with any theory, a number of mysteries and problems have arisen as a result of the development of the Big Bang theory. Some of these mysteries and problems have been resolved while others are still outstanding. Proposed solutions to some of the problems in the Big Bang model have revealed new mysteries of their own. For example, the horizon problem, the magnetic monopole problem, and the flatness problem are most commonly resolved with inflationary theory, but the details of the inflationary universe are still left unresolved and alternatives to inflation are even still entertained in the literature. What follows are a list of the mysterious aspects of the Big Bang theory still under intense investigation by cosmologists and astrophysicists.

Baryon asymmetry

Main article: Baryon asymmetry

It is not yet understood why the universe has more matter than antimatter. It is generally assumed that when the universe was young and very hot, it was in statistical equilibrium and contained equal numbers of baryons and antibaryons. However, observations suggest that the universe, including its most distant parts, is made almost entirely of matter. A process called baryogenesis was hypothesized to account for the asymmetry. For baryogenesis to occur, the Sakharov conditions must be satisfied. These require that baryon number is not conserved, that C-symmetry and CP-symmetry are violated and that the universe depart from thermodynamic equilibrium. All these conditions occur in the Standard Model, but the effect is not strong enough to explain the present baryon asymmetry.

Dark energy

Main article: Dark energy

Chart shows the proportion of different components of one of the Big Bang universe theories – about 95% of this Big Bang theory is hypothetical dark matter and dark energy.

Measurements of the redshift–magnitude relation for type Ia supernovae led to speculation that the expansion of the universe has been accelerating since the universe was about half its present age. To explain this acceleration, general relativity requires that much of the energy in the universe consists of a component with large negative pressure, dubbed "dark energy". Dark energy, though speculative, solves numerous problems. Measurements of the cosmic microwave background indicate that the universe is very nearly spatially flat, and therefore according to general relativity the universe must have almost exactly the critical density of mass/energy. But the mass density of the universe can be measured from its gravitational clustering, and is found to have only about 30% of the critical density. Since theory suggests that dark energy does not cluster in the usual way it is the best explanation for the "missing" energy density. Dark energy also helps to explain two geometrical measures of the overall curvature of the universe, one using the frequency of gravitational lenses, and the other using the characteristic pattern of the large-scale structure as a cosmic ruler.

Negative pressure is believed to be a property of vacuum energy, but the exact nature and existence of dark energy remains one of the great mysteries of the Big Bang. Results from the WMAP team in 2008 are in accordance with a universe that consists of 73% dark energy, 23% dark matter, 4.6% regular matter and less than 1% neutrinos. According to theory, the energy density in matter decreases with the expansion of the universe, but the dark energy density remains constant (or nearly so) as the universe expands. Therefore, matter made up a larger fraction of the total energy of the universe in the past than it does today, but its fractional contribution will fall in the far future as dark energy becomes even more dominant.

The dark energy component of the universe has been explained by theorists using a variety of competing theories including Einstein's cosmological constant but also extending to more exotic forms of quintessence or other modified gravity schemes. A cosmological constant problem sometimes called the "most embarrassing problem in physics" results from the apparent discrepancy between the measured energy density of dark energy and the one naively predicted from Planck units.

Dark matter

Main article: Dark matter

Rotation curve of a typical spiral galaxy: predicted by Newtonian gravity (A) and observed (B). Dark matter was made up to explain the 'flat' appearance of the velocity curve out to a large radius

Dark matter is a hypothetical kind of matter that has an associated gravitational force but nothing else. It was originally proposed in the 1930's, long before the promotion of the Big Bang theory. From observations of light from the stars in nearby galaxies, these earlier astronomers realized that stars do not orbit galactic centers in the way that planets orbit the Sun. In the Solar System, planets further out move much more slowly than planets closer in. In a galaxy, stars further out move at almost the same speed as stars closer in. This is an enormous contradiction to Newton's Law of gravitation. The Dark Matter hypothesis was originally created to explain this contradiction without having to upset Newtonian gravity or bring in other forces. From orbital calculations of these galactic stars, it turns out that either this undetected dark matter would have to account for most of the matter in the universe, or that the basic theory of gravity is wrong, or that there is some other phenomenon involved in shaping the galaxies.

The anomalous motion of galactic stars was not discussed much in the ensuing decades. During the 1970s and 80s, various observations showed that there is not sufficient visible matter in the universe to account for the apparent strength of gravitational forces between galaxies. The assumption that the universe is mostly driven by normal, gravitating matter led to predictions that were strongly inconsistent with observations. This revived the Dark Matter hypothesis and led to the idea that up to 90% of the matter in the universe is this dark matter that does not emit light or interact with normal baryonic matter.

Dark Matter has always been controversial, even between proponents of the various Big Bang theories. Today, it is invoked to explain a variety of anomalous observations: the anisotropies in the CMB, galaxy cluster velocity dispersions, large-scale structure distributions, gravitational lensing studies, X-ray measurements of galaxy clusters, and any other observations that don't fit a gravity-driven model. This is an untestable construct as there is no way to directly detect Dark Matter, by definition.

Indirect evidence for dark matter comes from non-gravitational motion of visible matter, as no dark matter particles have been observed in laboratories nor proposed in the Standard Model. Many particle physics candidates for dark matter have been proposed, and several projects are underway to attempt to detect them directly.

Additionally, there are outstanding problems associated with the currently-favored cold dark matter model which include the dwarf galaxy problem and the cuspy halo problem. Alternative theories have been proposed that do not require a large amount of undetected matter but instead modify the laws of gravity established by Newton and Einstein, but no alternative theory as been as successful as the cold dark matter proposal, which itself has numerous problems. These problems have led to a number of other kinds of dark matter- self-interacting, meta-cold, warm, and fuzzy dark matter, among other hypothetical entities.

Horizon problem

The horizon problem results from the premise that information cannot travel faster than light. In a universe of finite age this sets a limit—the particle horizon—on the separation of any two regions of space that are in causal contact. The observed isotropy of the CMB- if it is taken to be primordial- is problematic in this regard: if the universe had been dominated by radiation or matter at all times up to the epoch of last scattering, the particle horizon at that time would correspond to about 2 degrees on the sky. There would then be no mechanism to cause wider regions to have the same temperature.

A resolution to this apparent inconsistency is offered by inflationary theory, in which a homogeneous and isotropic scalar energy field of some sort dominates the universe at some very early period (before baryogenesis). During inflation, the universe undergoes exponential expansion at a speed greatly in excess of the speed of light. The particle horizon expands much more rapidly than previously assumed, so that regions presently on opposite sides of the observable universe are well inside each other's particle horizon. The observed isotropy of the CMB then follows from the speculation that this larger region was in causal contact before the beginning of inflation. Inflation theory adds two more non-physical ideas to the Big Bang- faster-than-light information and an unknown "scalar energy field"

Magnetic monopoles

The magnetic monopole objection was raised in the late 1970s. Grand unified theories predicted topological defects in space that would manifest as magnetic monopoles. These objects would be produced efficiently in the hot early universe, resulting in a density much higher than is consistent with observations, given that no monopoles have been found. This problem is also resolved by cosmic inflation, which removes all point defects from the observable universe, in the same way that it drives the geometry to flatness.

Flatness problem

Using General Relativity, the overall geometry of the Big Bang universe is determined by whether the cosmological density parameter is less than, equal to or greater than 1. Shown from top to bottom are a closed universe with positive curvature, a hyperbolic universe with negative curvature and a flat universe with zero curvature. The curving would have to occur in a fourth dimension of space, not shown.

The flatness problem (also known as the oldness problem) is both an observational and a theoretical problem associated with a Friedmann–Lemaître–Robertson–Walker metric in the Spacetime of General Relativity. "Flat" means Euclidean space, in which the angles of a triangle add up to the usual 180 degrees.

The General Relativity universe model may have positive, negative, or zero spatial curvature depending on its total energy density. Curvature is negative if its density is less than the critical density, positive if greater, and zero at the critical density, in which case space is said to be flat. One problem for the General Relativity versions of the Big Bang is that any small departure from the critical density grows with time, and yet the structure of space today appears to be exactly Euclidean. Another problem is that a curved three-dimensional space implies a fourth dimension to curve into. A fourth dimension, expanding or otherwise, would add other complications related to vector rotations and translations, which are not observed.

This problem has led to a number of additional attempts to keep the Big Bang as a viable scientific theory by making up new properties of the theorized, unobserved Dark Energy. In one version, Dark Energy in the form of a cosmological constant drives the universe towards a flat state; however, the universe remained close to flat for several billion years, before the Dark Energy density became significant. The fact that the universe has reached neither a Heat Death nor a Big Crunch after billions of years requires an explanation. For instance, even at the relatively late age of a few minutes the universe density would have to have been within one part in 10¹⁴ of its critical value.