The present is the period of time that is occurring now. The present is contrasted with the past , the period of time that has already occurred, and the future , the period of time that has yet to occur.
94-438: It is sometimes represented as a hyperplane in space-time , typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely for observers in relative motion. The present may also be viewed as a duration . Contemporary history describes the historical timeframe immediately relevant to the present time and is a certain perspective of modern history . You shouldn't chase after
188-413: A ). This can be understood intuitively: for an ordinary particle in a cube-shaped box, doubling the length of an edge of the box decreases the density (and hence energy density) by a factor of eight (2 ). For radiation, the decrease in energy density is greater, because an increase in spatial distance also causes a redshift. The final component is dark energy: it is an intrinsic property of space and has
282-400: A Euclidean space or more generally an affine space , or a vector space or a projective space , and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can be given in coordinates as the solution of a single (due to the "codimension 1" constraint) algebraic equation of degree 1. If V
376-445: A subspace whose dimension is one less than that of the ambient space . Two lower-dimensional examples of hyperplanes are one-dimensional lines in a plane and zero-dimensional points on a line. Most commonly, the ambient space is n -dimensional Euclidean space , in which case the hyperplanes are the ( n − 1) -dimensional "flats" , each of which separates the space into two half spaces . A reflection across
470-616: A constant energy density, regardless of the dimensions of the volume under consideration ( ρ ∝ a ). Thus, unlike ordinary matter, it is not diluted by the expansion of space. The evidence for dark energy is indirect but comes from three independent sources: In 1998, the High-Z Supernova Search Team published observations of Type Ia ("one-A") supernovae . In 1999, the Supernova Cosmology Project followed by suggesting that
564-411: A different associated light cone. One has to conclude that in relativistic models of physics there is no place for "the present" as an absolute element of reality, and only refers to things that are close to us. Einstein phrased this as: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion" . In physical cosmology ,
658-533: A direct estimate of the Hubble parameter The reliance on a differential quantity, Δ z / Δ t , brings more information and is appealing for computation: It can minimize many common issues and systematic effects. Analyses of supernovae and baryon acoustic oscillations (BAO) are based on integrals of the Hubble parameter, whereas Δ z / Δ t measures it directly. For these reasons, this method has been widely used to examine
752-470: A given event, can not be in direct cause-effect relationship . Such collections of events are perceived differently by different observers. Instead, when focusing on "now" as the events perceived directly, not as a recollection or a speculation, for a given observer "now" takes the form of the observer's past light cone . The light cone of a given event is objectively defined as the collection of events in causal relationship to that event, but each event has
846-399: A hyperplane does not divide the space into two parts; rather, it takes two hyperplanes to separate points and divide up the space. The reason for this is that the space essentially "wraps around" so that both sides of a lone hyperplane are connected to each other. In convex geometry , two disjoint convex sets in n-dimensional Euclidean space are separated by a hyperplane, a result called
940-413: A hyperplane is a kind of motion ( geometric transformation preserving distance between points), and the group of all motions is generated by the reflections. A convex polytope is the intersection of half-spaces. In non-Euclidean geometry , the ambient space might be the n -dimensional sphere or hyperbolic space , or more generally a pseudo-Riemannian space form , and the hyperplanes are
1034-503: A non-standard form of kinetic energy such as a negative kinetic energy . They can have unusual properties: phantom energy , for example, can cause a Big Rip . A group of researchers argued in 2021 that observations of the Hubble tension may imply that only quintessence models with a nonzero coupling constant are viable. This class of theories attempts to come up with an all-encompassing theory of both dark matter and dark energy as
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#17327724493051128-508: A profound effect on the universe, making up 68% of universal density in spite of being so dilute, is that it is believed to uniformly fill otherwise empty space. The vacuum energy , that is, the particle-antiparticle pairs generated and mutually annihilated within a time frame in accord with Heisenberg's uncertainty principle in the energy-time formulation, has been often invoked as the main contribution to dark energy. The mass–energy equivalence postulated by general relativity implies that
1222-430: A single phenomenon that modifies the laws of gravity at various scales. This could, for example, treat dark energy and dark matter as different facets of the same unknown substance, or postulate that cold dark matter decays into dark energy. Another class of theories that unifies dark matter and dark energy are suggested to be covariant theories of modified gravities. These theories alter the dynamics of spacetime such that
1316-435: A universe which contracts slightly will continue contracting. According to Einstein, "empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands. As more space comes into existence, more of this energy-of-space would appear, thereby causing accelerated expansion. These sorts of disturbances are inevitable, due to the uneven distribution of matter throughout
1410-400: A vector space, a vector hyperplane is a subspace of codimension 1, only possibly shifted from the origin by a vector, in which case it is referred to as a flat . Such a hyperplane is the solution of a single linear equation . Projective hyperplanes , are used in projective geometry . A projective subspace is a set of points with the property that for any two points of the set, all
1504-420: Is an affine subspace of codimension 1 in an affine space . In Cartesian coordinates , such a hyperplane can be described with a single linear equation of the following form (where at least one of the a i {\displaystyle a_{i}} s is non-zero and b {\displaystyle b} is an arbitrary constant): In the case of a real affine space, in other words when
1598-621: Is a vector space, one distinguishes "vector hyperplanes" (which are linear subspaces , and therefore must pass through the origin) and "affine hyperplanes" (which need not pass through the origin; they can be obtained by translation of a vector hyperplane). A hyperplane in a Euclidean space separates that space into two half spaces , and defines a reflection that fixes the hyperplane and interchanges those two half spaces. Several specific types of hyperplanes are defined with properties that are well suited for particular purposes. Some of these specializations are described here. An affine hyperplane
1692-401: Is called "cosmological coupling" because the black holes couple to a cosmological requirement. Other astrophysicists are skeptical, with a variety of papers claiming that the theory fails to explain other observations. The evidence for dark energy is heavily dependent on the theory of general relativity. Therefore, it is conceivable that a modification to general relativity also eliminates
1786-414: Is close to flat . For the shape of the universe to be flat, the mass–energy density of the universe must be equal to the critical density . The total amount of matter in the universe (including baryons and dark matter ), as measured from the cosmic microwave background spectrum, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for
1880-423: Is defined to be a "face" of the polyhedron. The theory of polyhedra and the dimension of the faces are analyzed by looking at these intersections involving hyperplanes. Dark energy In physical cosmology and astronomy , dark energy is a proposed form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe . Assuming that
1974-478: Is known. This allows the object's distance to be measured from its actual observed brightness, or apparent magnitude . Type Ia supernovae are the best-known standard candles across cosmological distances because of their extreme and consistent luminosity . Recent observations of supernovae are consistent with a universe made up 71.3% of dark energy and 27.4% of a combination of dark matter and baryonic matter . The theory of large-scale structure , which governs
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#17327724493052068-409: Is measured as a function of cosmological redshift . OHD directly tracks the expansion history of the universe by taking passively evolving early-type galaxies as "cosmic chronometers". From this point, this approach provides standard clocks in the universe. The core of this idea is the measurement of the differential age evolution as a function of redshift of these cosmic chronometers. Thus, it provides
2162-434: Is minimally coupled to gravity, and does not feature higher order operations in its Lagrangian. No evidence of quintessence is yet available, nor has it been ruled out. It generally predicts a slightly slower acceleration of the expansion of the universe than the cosmological constant. Some scientists think that the best evidence for quintessence would come from violations of Einstein's equivalence principle and variation of
2256-417: Is more hypothetical than that of dark matter, and many things about it remain in the realm of speculation. Dark energy is thought to be very homogeneous and not dense , and is not known to interact through any of the fundamental forces other than gravity . Since it is rarefied and un-massive—roughly 10 kg/m —it is unlikely to be detectable in laboratory experiments. The reason dark energy can have such
2350-515: Is no concept of half-planes. In greatest generality, the notion of hyperplane is meaningful in any mathematical space in which the concept of the dimension of a subspace is defined. The difference in dimension between a subspace and its ambient space is known as its codimension . A hyperplane has codimension 1 . In geometry , a hyperplane of an n -dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V . The space V may be
2444-420: Is not a hyperplane, and does not separate the space into two parts (the complement of such a line is connected). Any hyperplane of a Euclidean space has exactly two unit normal vectors: ± n ^ {\displaystyle \pm {\hat {n}}} . In particular, if we consider R n + 1 {\displaystyle \mathbb {R} ^{n+1}} equipped with
2538-500: Is possible to investigate the effect of dark energy in the history of the universe, and constrain parameters of the equation of state of dark energy. To that end, several models have been proposed. One of the most popular models is the Chevallier–Polarski–Linder model (CPL). Some other common models are Barboza & Alcaniz (2008), Jassal et al. (2005), Wetterich. (2004), and Oztas et al. (2018). Researchers using
2632-400: Is sometimes labeled "gravitational repulsion". In standard cosmology, there are three components of the universe: matter, radiation, and dark energy. This matter is anything whose energy density scales with the inverse cube of the scale factor, i.e., ρ ∝ a , while radiation is anything whose energy density scales to the inverse fourth power of the scale factor ( ρ ∝
2726-462: Is that it is an intrinsic, fundamental energy of space. This is the cosmological constant, usually represented by the Greek letter Λ (Lambda, hence the name Lambda-CDM model ). Since energy and mass are related according to the equation E = mc , Einstein's theory of general relativity predicts that this energy will have a gravitational effect. It is sometimes called vacuum energy because it
2820-525: Is the stress–energy tensor , which contains both the energy (or matter) density of a substance and its pressure. In the Friedmann–Lemaître–Robertson–Walker metric , it can be shown that a strong constant negative pressure ( i.e., tension) in all the universe causes an acceleration in the expansion if the universe is already expanding, or a deceleration in contraction if the universe is already contracting. This accelerating expansion effect
2914-415: Is the energy density of empty space – of vacuum . A major outstanding problem is that the same quantum field theories predict a huge cosmological constant , about 120 orders of magnitude too large. This would need to be almost, but not exactly, cancelled by an equally large term of the opposite sign. Some supersymmetric theories require a cosmological constant that is exactly zero. Also, it
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3008-414: Is thought to have completely ended when the universe was just a fraction of a second old. It is unclear what relation, if any, exists between dark energy and inflation. Even after inflationary models became accepted, the cosmological constant was thought to be irrelevant to the current universe. Nearly all inflation models predict that the total (matter+energy) density of the universe should be very close to
3102-399: Is unknown whether there is a metastable vacuum state in string theory with a positive cosmological constant, and it has been conjectured by Ulf Danielsson et al. that no such state exists. This conjecture would not rule out other models of dark energy, such as quintessence, that could be compatible with string theory. In quintessence models of dark energy, the observed acceleration of
3196-580: The Australian Astronomical Observatory scanned the galaxies to determine their redshift. Then, by exploiting the fact that baryon acoustic oscillations have left voids regularly of ≈150 Mpc diameter, surrounded by the galaxies, the voids were used as standard rulers to estimate distances to galaxies as far as 2,000 Mpc (redshift 0.6), allowing for accurate estimate of the speeds of galaxies from their redshift and distance. The data confirmed cosmic acceleration up to half of
3290-647: The Dark Energy Spectroscopic Instrument (DESI) to make the largest 3-D map of the universe as of 2024, have obtained an expansion history that has greater than 1% precision. From this level of detail, DESI Director Michael Levi stated: We're also seeing some potentially interesting differences that could indicate that dark energy is evolving over time. Those may or may not go away with more data, so we're excited to start analyzing our three-year dataset soon. Some alternatives to dark energy, such as inhomogeneous cosmology , aim to explain
3384-534: The Friedmann-Robertson-Walker metric (which describes the isotropic and homogeneous universe that is the basic assumption of modern cosmology), then one finds that black holes gain mass as the universe expands. The rate is measured to be ∝ a , where a is the scale factor . This particular rate means that the energy density of black holes remains constant over time, mimicking dark energy (see Dark_energy#Technical_definition ). The theory
3478-635: The Lambda-CDM model . Some people argue that the only indications for the existence of dark energy are observations of distance measurements and their associated redshifts. Cosmic microwave background anisotropies and baryon acoustic oscillations serve only to demonstrate that distances to a given redshift are larger than would be expected from a "dusty" Friedmann–Lemaître universe and the local measured Hubble constant. Supernovae are useful for cosmology because they are excellent standard candles across cosmological distances. They allow researchers to measure
3572-715: The Planck spacecraft and the Supernova Legacy Survey. First results from the SNLS reveal that the average behavior (i.e., equation of state) of dark energy behaves like Einstein's cosmological constant to a precision of 10%. Recent results from the Hubble Space Telescope Higher-Z Team indicate that dark energy has been present for at least 9 billion years and during the period preceding cosmic acceleration. The nature of dark energy
3666-654: The accelerating expansion of the universe has removed the local supercluster beyond the cosmological horizon (at about 150 billion years). In radiocarbon dating , the "present" is defined as AD 1950 . In English grammar , actions are classified according to one of the following twelve verb tenses: past ( past , past continuous , past perfect , or past perfect continuous ), present (present, present continuous , present perfect , or present perfect continuous ), or future ( future , future continuous , future perfect , or future perfect continuous ). The present tense refers to things that are currently happening or are always
3760-436: The critical density . During the 1980s, most cosmological research focused on models with critical density in matter only, usually 95% cold dark matter (CDM) and 5% ordinary matter (baryons). These models were found to be successful at forming realistic galaxies and clusters, but some problems appeared in the late 1980s: in particular, the model required a value for the Hubble constant lower than preferred by observations, and
3854-471: The equation of state had possibly crossed the cosmological constant boundary (w = −1) from above to below. A no-go theorem has been proved that this scenario requires models with at least two types of quintessence. This scenario is the so-called Quintom scenario . Some special cases of quintessence are phantom energy , in which the energy density of quintessence actually increases with time, and k-essence (short for kinetic quintessence) which has
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3948-400: The expansion of the universe are required to understand how the expansion rate changes over time and space. In general relativity, the evolution of the expansion rate is estimated from the curvature of the universe and the cosmological equation of state (the relationship between temperature, pressure, and combined matter, energy, and vacuum energy density for any region of space). Measuring
4042-424: The hyperplane separation theorem . In machine learning , hyperplanes are a key tool to create support vector machines for such tasks as computer vision and natural language processing . The datapoint and its predicted value via a linear model is a hyperplane. The dihedral angle between two non-parallel hyperplanes of a Euclidean space is the angle between the corresponding normal vectors . The product of
4136-447: The lambda-CDM model of cosmology is correct, dark energy dominates the universe, contributing 68% of the total energy in the present-day observable universe while dark matter and ordinary (baryonic) matter contribute 26% and 5%, respectively, and other components such as neutrinos and photons are nearly negligible. Dark energy's density is very low: 7 × 10 g/cm ( 6 × 10 J/m in mass-energy ), much less than
4230-431: The redshift (which measures the speed at which the supernova is receding) shows that the universe's expansion is accelerating . Prior to this observation, scientists thought that the gravitational attraction of matter and energy in the universe would cause the universe's expansion to slow over time. Since the discovery of accelerating expansion, several independent lines of evidence have been discovered that support
4324-540: The Lambda-CDM model then became the leading model. Soon after, dark energy was supported by independent observations: in 2000, the BOOMERanG and Maxima cosmic microwave background experiments observed the first acoustic peak in the cosmic microwave background, showing that the total (matter+energy) density is close to 100% of critical density. Then in 2001, the 2dF Galaxy Redshift Survey gave strong evidence that
4418-473: The Universe began when it did. If acceleration began earlier in the universe, structures such as galaxies would never have had time to form, and life, at least as we know it, would never have had a chance to exist. Proponents of the anthropic principle view this as support for their arguments. However, many models of quintessence have a so-called "tracker" behavior, which solves this problem. In these models,
4512-464: The accelerated cosmic expansion and study properties of dark energy. Dark energy's status as a hypothetical force with unknown properties makes it an active target of research. The problem is attacked from a variety of angles, such as modifying the prevailing theory of gravity (general relativity), attempting to pin down the properties of dark energy, and finding alternative ways to explain the observational data. The simplest explanation for dark energy
4606-411: The age of the universe (7 billion years) and constrain its inhomogeneity to 1 part in 10. This provides a confirmation to cosmic acceleration independent of supernovae. The existence of dark energy, in whatever form, is needed to reconcile the measured geometry of space with the total amount of matter in the universe. Measurements of cosmic microwave background anisotropies indicate that the universe
4700-511: The case and no easy answer to the question. Buddhism and many of its associated paradigms emphasize the importance of living in the present moment—being fully aware of what is happening, and not dwelling on the past or worrying about the future . This does not mean that they encourage hedonism , but merely that constant focus on one's current position in space and time (rather than future considerations, or past reminiscence) will aid one in relieving suffering. They teach that those who live in
4794-399: The case. For example, in the sentence, "she walks home everyday," the verb "walks" is in the present tense because it refers to an action that is regularly occurring in the present circumstances. Verbs in the present continuous tense indicate actions that are currently happening and will continue for a period of time. In the sentence, "she is walking home," the verb phrase "is walking" is in
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#17327724493054888-418: The competing theories successfully explain observations to the same level of precision as standard dark energy. Cosmologists estimate that the acceleration began roughly 5 billion years ago. Before that, it is thought that the expansion was decelerating, due to the attractive influence of matter. The density of dark matter in an expanding universe decreases more quickly than dark energy, and eventually
4982-862: The conventional inner product ( dot product ), then one can define the affine subspace with normal vector n ^ {\displaystyle {\hat {n}}} and origin translation b ~ ∈ R n + 1 {\displaystyle {\tilde {b}}\in \mathbb {R} ^{n+1}} as the set of all x ∈ R n + 1 {\displaystyle x\in \mathbb {R} ^{n+1}} such that n ^ ⋅ ( x − b ~ ) = 0 {\displaystyle {\hat {n}}\cdot (x-{\tilde {b}})=0} . Affine hyperplanes are used to define decision boundaries in many machine learning algorithms such as linear-combination (oblique) decision trees , and perceptrons . In
5076-405: The coordinates are real numbers, this affine space separates the space into two half-spaces, which are the connected components of the complement of the hyperplane, and are given by the inequalities and As an example, a point is a hyperplane in 1-dimensional space, a line is a hyperplane in 2-dimensional space, and a plane is a hyperplane in 3-dimensional space. A line in 3-dimensional space
5170-508: The cosmic microwave background aligned with vast supervoids and superclusters. This so-called late-time Integrated Sachs–Wolfe effect (ISW) is a direct signal of dark energy in a flat universe. It was reported at high significance in 2008 by Ho et al. and Giannantonio et al. A new approach to test evidence of dark energy through observational Hubble constant data (OHD), also known as cosmic chronometers, has gained significant attention in recent years. The Hubble constant, H ( z ),
5264-437: The dark energy dominates. Specifically, when the volume of the universe doubles, the density of dark matter is halved, but the density of dark energy is nearly unchanged (it is exactly constant in the case of a cosmological constant). Projections into the future can differ radically for different models of dark energy. For a cosmological constant, or any other model that predicts that the acceleration will continue indefinitely,
5358-400: The density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space. The first observational evidence for dark energy's existence came from measurements of supernovae . Type Ia supernovae have constant luminosity, which means that they can be used as accurate distance measures. Comparing this distance to
5452-399: The diagram on the right was to portray a 3-dimensional object having access to the past, present, and future in the present moment (4th dimension). It follows from Albert Einstein 's Special Theory of Relativity that there is no such thing as absolute simultaneity . When care is taken to operationalise "the present", it follows that the events that can be labeled as "simultaneous" with
5546-446: The equation of state for dark energy is one of the biggest efforts in observational cosmology today. Adding the cosmological constant to cosmology's standard FLRW metric leads to the Lambda-CDM model, which has been referred to as the " standard model of cosmology " because of its precise agreement with observations. As of 2013, the Lambda-CDM model is consistent with a series of increasingly rigorous cosmological observations, including
5640-575: The existence of dark energy. The exact nature of dark energy remains a mystery, and possible explanations abound. The main candidates are a cosmological constant (representing a constant energy density filling space homogeneously) and scalar fields (dynamic quantities having energy densities that vary in time and space) such as quintessence or moduli . A cosmological constant would remain constant across time and space, while scalar fields can vary. Yet other possibilities are interacting dark energy, an observational effect, and cosmological coupling (see
5734-444: The expansion history of the universe by looking at the relationship between the distance to an object and its redshift , which gives how fast it is receding from us. The relationship is roughly linear, according to Hubble's law . It is relatively easy to measure redshift, but finding the distance to an object is more difficult. Usually, astronomers use standard candles: objects for which the intrinsic brightness, or absolute magnitude ,
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#17327724493055828-538: The expansion of the universe is accelerating . The 2011 Nobel Prize in Physics was awarded to Saul Perlmutter , Brian P. Schmidt , and Adam G. Riess for their leadership in the discovery. Since then, these observations have been corroborated by several independent sources. Measurements of the cosmic microwave background , gravitational lensing , and the large-scale structure of the cosmos , as well as improved measurements of supernovae, have been consistent with
5922-477: The formation of structures in the universe ( stars , quasars , galaxies and galaxy groups and clusters ), also suggests that the density of matter in the universe is only 30% of the critical density. A 2011 survey, the WiggleZ galaxy survey of more than 200,000 galaxies, provided further evidence towards the existence of dark energy, although the exact physics behind it remains unknown. The WiggleZ survey from
6016-480: The fundamental constants in space or time. Scalar fields are predicted by the Standard Model of particle physics and string theory , but an analogous problem to the cosmological constant problem (or the problem of constructing models of cosmological inflation ) occurs: renormalization theory predicts that scalar fields should acquire large masses. The coincidence problem asks why the acceleration of
6110-439: The future without us being determined to do it) since at least Boethius . Thomas Aquinas offers the metaphor of a watchman, representing God, standing on a height looking down on a valley to a road where past, present and future, represented by the individuals and their actions strung out along its length, are all visible simultaneously to God. Therefore, God's knowledge is not tied to any particular date. The original intent of
6204-406: The hypersurfaces consisting of all geodesics through a point which are perpendicular to a specific normal geodesic. In other kinds of ambient spaces, some properties from Euclidean space are no longer relevant. For example, in affine space , there is no concept of distance, so there are no reflections or motions. In a non-orientable space such as elliptic space or projective space , there
6298-413: The interstellar space'. The mechanism was an example of fine-tuning , and it was later realized that Einstein's static universe would not be stable: local inhomogeneities would ultimately lead to either the runaway expansion or contraction of the universe. The equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise,
6392-471: The matter density is around 30% of critical. The large difference between these two supports a smooth component of dark energy making up the difference. Much more precise measurements from WMAP in 2003–2010 have continued to support the standard model and give more accurate measurements of the key parameters. The term "dark energy", echoing Fritz Zwicky 's "dark matter" from the 1930s, was coined by Michael S. Turner in 1998. High-precision measurements of
6486-694: The model under-predicted observations of large-scale galaxy clustering. These difficulties became stronger after the discovery of anisotropy in the cosmic microwave background by the COBE spacecraft in 1992, and several modified CDM models came under active study through the mid-1990s: these included the Lambda-CDM model and a mixed cold/hot dark matter model. The first direct evidence for dark energy came from supernova observations in 1998 of accelerated expansion in Riess et al. and in Perlmutter et al. , and
6580-428: The modified dynamics stems to what have been assigned to the presence of dark energy and dark matter. Dark energy could in principle interact not only with the rest of the dark sector, but also with ordinary matter. However, cosmology alone is not sufficient to effectively constrain the strength of the coupling between dark energy and baryons, so that other indirect techniques or laboratory searches have to be adopted. It
6674-475: The need for dark energy. There are many such theories, and research is ongoing. The measurement of the speed of gravity in the first gravitational wave measured by non-gravitational means ( GW170817 ) ruled out many modified gravity theories as explanations to dark energy. Astrophysicist Ethan Siegel states that, while such alternatives gain mainstream press coverage, almost all professional astrophysicists are confident that dark energy exists and that none of
6768-481: The observational data by a more refined use of established theories. In this scenario, dark energy does not actually exist, and is merely a measurement artifact. For example, if we are located in an emptier-than-average region of space, the observed cosmic expansion rate could be mistaken for a variation in time, or acceleration. A different approach uses a cosmological extension of the equivalence principle to show how space might appear to be expanding more rapidly in
6862-579: The original paper. Another study questioning the essential assumption that the luminosity of Type Ia supernovae does not vary with stellar population age was also swiftly rebutted by other cosmologists. This theory was formulated by researchers of the University of Hawaiʻi at Mānoa in February 2023. The idea is that if one requires the Kerr metric (which describes rotating black holes) to asymptote to
6956-455: The past and is finished as of the current reference to the action. Finally, verbs in the present perfect continuous tense refer to actions that have been continuing up until the current time, thus combining the characteristics of both the continuous and perfect tenses. An example of a present perfect continuous verb phrase can be found in the sentence, "she has been walking this route for a week now," where "has been walking" indicates an action that
7050-415: The past or place expectations on the future. What is past is left behind. The future is as yet unreached. Whatever quality is present you clearly see right there, right there. What we perceive as present is the vivid fringe of memory tinged with anticipation. "The present" raises the question: "How is it that all sentient beings experience now at the same time?" There is no logical reason why this should be
7144-453: The points on the line determined by the two points are contained in the set. Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added. An affine hyperplane together with the associated points at infinity forms a projective hyperplane. One special case of a projective hyperplane is the infinite or ideal hyperplane , which is defined with the set of all points at infinity. In projective space,
7238-415: The present continuous tense because it refers to a current action that will continue until a certain endpoint (when "she" reaches home). Verbs in the present perfect tense indicate actions that started in the past and is completed at the time of speaking. For example, in the sentence, "She has walked home," the verb phrase "has walked" is in the present perfect tense because it describes an action that began in
7332-428: The present moment are the happiest. A number of meditative techniques aim to help the practiser live in the present moment. Christianity views God as being outside of time and, from the divine perspective past, present and future are actualized in the now of eternity . This trans-temporal conception of God has been proposed as a solution to the problem of divine foreknowledge (i.e. how can God know what we will do in
7426-489: The present time in the chronology of the universe is estimated at 13.8 billion years after the singularity determining the arrow of time . In terms of the cosmic expansion history , it is in the dark-energy-dominated era , after the universe's matter content has become diluted enough for dark energy to dominate the total energy density. It is also in the universe's Stelliferous Era , after enough time for superclusters to have formed (at about 5 billion years), but before
7520-456: The problem remains unresolved. Independently of its actual nature, dark energy would need to have a strong negative pressure to explain the observed acceleration of the expansion of the universe . According to general relativity, the pressure within a substance contributes to its gravitational attraction for other objects just as its mass density does. This happens because the physical quantity that causes matter to generate gravitational effects
7614-400: The quintessence field has a density which closely tracks (but is less than) the radiation density until matter–radiation equality , which triggers quintessence to start behaving as dark energy, eventually dominating the universe. This naturally sets the low energy scale of the dark energy. In 2004, when scientists fit the evolution of dark energy with the cosmological data, they found that
7708-557: The remaining 70%. The Wilkinson Microwave Anisotropy Probe (WMAP) spacecraft seven-year analysis estimated a universe made up of 72.8% dark energy, 22.7% dark matter, and 4.5% ordinary matter. Work done in 2013 based on the Planck spacecraft observations of the cosmic microwave background gave a more accurate estimate of 68.3% dark energy, 26.8% dark matter, and 4.9% ordinary matter. Accelerated cosmic expansion causes gravitational potential wells and hills to flatten as photons pass through them, producing cold spots and hot spots on
7802-417: The scale factor is caused by the potential energy of a dynamical field , referred to as quintessence field. Quintessence differs from the cosmological constant in that it can vary in space and time. In order for it not to clump and form structure like matter, the field must be very light so that it has a large Compton wavelength . In the simplest scenarios, the quintessence field has a canonical kinetic term,
7896-407: The section Dark energy § Theories of dark energy ). The " cosmological constant " is a constant term that can be added to Einstein field equations of general relativity . If considered as a "source term" in the field equation, it can be viewed as equivalent to the mass of empty space (which conceptually could be either positive or negative), or " vacuum energy ". The cosmological constant
7990-428: The statistical methods employed were flawed. A laboratory direct detection attempt failed to detect any force associated with dark energy. Observational skepticism explanations of dark energy have generally not gained much traction among cosmologists. For example, a paper that suggested the anisotropy of the local Universe has been misrepresented as dark energy was quickly countered by another paper claiming errors in
8084-496: The transformations in the two hyperplanes is a rotation whose axis is the subspace of codimension 2 obtained by intersecting the hyperplanes, and whose angle is twice the angle between the hyperplanes. A hyperplane H is called a "support" hyperplane of the polyhedron P if P is contained in one of the two closed half-spaces bounded by H and H ∩ P ≠ ∅ {\displaystyle H\cap P\neq \varnothing } . The intersection of P and H
8178-458: The ultimate result will be that galaxies outside the Local Group will have a line-of-sight velocity that continually increases with time, eventually far exceeding the speed of light. This is not a violation of special relativity because the notion of "velocity" used here is different from that of velocity in a local inertial frame of reference , which is still constrained to be less than
8272-438: The universe. Further, observations made by Edwin Hubble in 1929 showed that the universe appears to be expanding and is not static. Einstein reportedly referred to his failure to predict the idea of a dynamic universe, in contrast to a static universe, as his greatest blunder. Alan Guth and Alexei Starobinsky proposed in 1980 that a negative pressure field, similar in concept to dark energy, could drive cosmic inflation in
8366-438: The vacuum energy should exert a gravitational force. Hence, the vacuum energy is expected to contribute to the cosmological constant , which in turn impinges on the accelerated expansion of the universe . However, the cosmological constant problem asserts that there is a huge disagreement between the observed values of vacuum energy density and the theoretical large value of zero-point energy obtained by quantum field theory ;
8460-531: The very early universe. Inflation postulates that some repulsive force, qualitatively similar to dark energy, resulted in an enormous and exponential expansion of the universe slightly after the Big Bang . Such expansion is an essential feature of most current models of the Big Bang. However, inflation must have occurred at a much higher (negative) energy density than the dark energy we observe today, and inflation
8554-409: The voids surrounding our local cluster. While weak, such effects considered cumulatively over billions of years could become significant, creating the illusion of cosmic acceleration, and making it appear as if we live in a Hubble bubble . Yet other possibilities are that the accelerated expansion of the universe is an illusion caused by the relative motion of us to the rest of the universe, or that
8648-532: Was briefly theorized in the early 2020s that excess observed in the XENON1T detector in Italy may have been caused by a chameleon model of dark energy, but further experiments disproved this possibility. The density of dark energy might have varied in time during the history of the universe. Modern observational data allows us to estimate the present density of dark energy. Using baryon acoustic oscillations , it
8742-419: Was first proposed by Einstein as a mechanism to obtain a solution to the gravitational field equation that would lead to a static universe, effectively using dark energy to balance gravity. Einstein gave the cosmological constant the symbol Λ (capital lambda). Einstein stated that the cosmological constant required that 'empty space takes the role of gravitating negative masses which are distributed all over
8836-406: Was happening continuously in the past and continues to happen continuously in the present. [REDACTED] Quotations related to present at Wikiquote Hyperplane In geometry , a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension . Like a plane in space , a hyperplane is a flat hypersurface ,
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