Cosmological constant in the context of Quantum mechanics

The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components:

1. a cosmological constant, denoted by lambda (Λ), associated with dark energy;
2. the postulated cold dark matter, denoted by CDM;
3. ordinary matter.

It is the current standard model of Big Bang cosmology, as it is the simplest model that provides a reasonably good account of:

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness (a standard candle), and since objects that are further away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the further away an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.

The accelerated expansion of the universe is thought to have begun since the universe entered its dark-energy-dominated era roughly 5 billion years ago.Within the framework of general relativity, an accelerated expansion can be accounted for by a positive value of the cosmological constant Λ, equivalent to the presence of a positive vacuum energy, dubbed "dark energy". While there are alternative possible explanations, the description assuming dark energy (positive Λ) is used in the standard model of cosmology, which also includes cold dark matter (CDM) and is known as the Lambda-CDM model.

Current observations suggest that the expansion of the universe will continue forever. The prevailing theory is that the universe will cool as it expands, eventually becoming too cold to sustain life. For this reason, this future scenario popularly called "Heat Death" is also known as the "Big Chill" or "Big Freeze". Some of the other popular theories include the Big Rip, Big Crunch, and the Big Bounce.

If dark energy—represented by the cosmological constant, a constant energy density filling space homogeneously, or scalar fields, such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space—accelerates the expansion of the universe, then the space between clusters of galaxies will grow at an increasing rate. Redshift will stretch ancient ambient photons (including gamma rays) to undetectably long wavelengths and low energies. Stars are expected to form normally for 10 to 10 (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker. According to theories that predict proton decay, the stellar remnants left behind will disappear, leaving behind only black holes, which themselves eventually disappear as they emit Hawking radiation. Ultimately, if the universe reaches thermodynamic equilibrium, a state in which the temperature approaches a uniform value, no further work will be possible, resulting in a final heat death of the universe.

A non-standard cosmology is any physical cosmological model of the universe that was, or still is, proposed as an alternative to the then-current standard model of cosmology. The term non-standard is applied to any theory that does not conform to the scientific consensus. Because the term depends on the prevailing consensus, the meaning of the term changes over time. For example, hot dark matter would not have been considered non-standard in 1990, but would have been in 2010. Conversely, a non-zero cosmological constant resulting in an accelerating universe would have been considered non-standard in 1990, but is part of the standard cosmology in 2010.

Several major cosmological disputes have occurred throughout the history of cosmology. One of the earliest was the Copernican Revolution, which established the heliocentric model of the Solar System. More recent was the Great Debate of 1920, in the aftermath of which the Milky Way's status as but one of the Universe's many galaxies was established. From the 1940s to the 1960s, the astrophysical community was equally divided between supporters of the Big Bang theory and supporters of a rival steady state universe; this is currently decided in favour of the Big Bang theory by advances in observational cosmology in the late 1960s. Nevertheless, there remained vocal detractors of the Big Bang theory including Fred Hoyle, Jayant Narlikar, Halton Arp, and Hannes Alfvén, whose cosmologies were relegated to the fringes of astronomical research. The few Big Bang opponents still active today often ignore well-established evidence from newer research, and as a consequence, today non-standard cosmologies that reject the Big Bang entirely are rarely published in peer-reviewed science journals but appear online in marginal journals and private websites.

The Supernova Cosmology Project is one of two research teams that determined the likelihood of an accelerating universe and therefore a positive cosmological constant, using data from the redshift of Type Ia supernovae. The project is headed by Saul Perlmutter at Lawrence Berkeley National Laboratory, with members from Australia, Chile, France, Portugal, Spain, Sweden, the United Kingdom, and the United States.

This discovery was named "Breakthrough of the Year for 1998" by Science Magazine and, along with the High-Z Supernova Search Team, the project team won the 2007 Gruber Prize in Cosmology and the 2015 Breakthrough Prize in Fundamental Physics. In 2011, Perlmutter was awarded the Nobel Prize in Physics for this work, alongside Adam Riess and Brian P. Schmidt from the High-Z team.

Vacuum energy is an underlying background energy that exists in space throughout the entire universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.

The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect, and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10 joules (10 ergs), or ~5 GeV per cubic meter. However, in quantum electrodynamics, consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant suggests a much larger value of 10 joules per cubic meter. This huge discrepancy is known as the cosmological constant problem or, colloquially, the "vacuum catastrophe."

The heat death of the universe (also known as the Big Chill or Big Freeze) is a scientific hypothesis regarding the ultimate fate of the universe which posits the universe will evolve to a state of no thermodynamic free energy and, having reached maximum entropy, will therefore be unable to sustain any further thermodynamic processes. Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other processes may no longer be exploited to perform work. In the language of physics, this is when the universe reaches thermodynamic equilibrium.

If the curvature of the universe is hyperbolic or flat, or if dark energy is a positive cosmological constant, the universe will continue expanding forever, and a heat death is expected to occur, with the universe cooling to approach equilibrium at a very low temperature after a long time period.

In physics, quintessence is a hypothetical form of dark energy, more precisely a scalar field minimally coupled to gravity, postulated as an explanation of the observation of an accelerating rate of expansion of the universe. The first example of this scenario was proposed by Ratra and Peebles (1988) and Wetterich (1988). The concept was expanded to more general types of time-varying dark energy, and the term "quintessence" was first introduced in a 1998 paper by Robert R. Caldwell, Rahul Dave and Paul Steinhardt. It has been proposed by some physicists to be a fifth fundamental force. Quintessence differs from the cosmological constant explanation of dark energy in that it is dynamic; that is, it changes over time, unlike the cosmological constant which, by definition, does not change. Quintessence can be either attractive or repulsive depending on the ratio of its kinetic and potential energy. Those working with this postulate believe that quintessence became repulsive about ten billion years ago, about 3.5 billion years after the Big Bang.

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.

The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic microwave background (CMB) – the radiant heat remaining from the Big Bang. Headed by Professor Charles L. Bennett of Johns Hopkins University, the mission was developed in a joint partnership between the NASA Goddard Space Flight Center and Princeton University. The WMAP spacecraft was launched on 30 June 2001 from Florida. The WMAP mission succeeded the COBE space mission and was the second medium-class (MIDEX) spacecraft in the NASA Explorer program. In 2003, MAP was renamed WMAP in honor of cosmologist David Todd Wilkinson (1935–2002), who had been a member of the mission's science team. After nine years of operations, WMAP was switched off in 2010, following the launch of the more advanced Planck spacecraft by European Space Agency (ESA) in 2009.

WMAP's measurements played a key role in establishing the current Standard Model of Cosmology: the Lambda-CDM model. The WMAP data are very well fit by a universe that is dominated by dark energy in the form of a cosmological constant. Other cosmological data are also consistent, and together tightly constrain the Model. In the Lambda-CDM model of the universe, the age of the universe is 13.772±0.059 billion years. The WMAP mission's determination of the age of the universe is to better than 1% precision. The current expansion rate of the universe is (see Hubble constant) 69.32±0.80 km·s·Mpc. The content of the universe currently consists of 4.628%±0.093% ordinary baryonic matter; 24.02%+0.88%
−0.87% cold dark matter (CDM) that neither emits nor absorbs light; and 71.35%+0.95%
−0.96% of dark energy in the form of a cosmological constant that accelerates the expansion of the universe. Less than 1% of the current content of the universe is in neutrinos, but WMAP's measurements have found, for the first time in 2008, that the data prefer the existence of a cosmic neutrino background with an effective number of neutrino species of 3.26±0.35. The contents point to a Euclidean flat geometry, with curvature (${\displaystyle \Omega _{k}}$) of −0.0027+0.0039
−0.0038. The WMAP measurements also support the cosmic inflation paradigm in several ways, including the flatness measurement.

Quantum gravity (QG) is a field of theoretical physics that seeks unification of the theory of gravity with the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang.

Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction, the strong force, and the weak force; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of gravity is based on Albert Einstein's general theory of relativity, which incorporates his theory of special relativity and deeply modifies the understanding of concepts like time and space. Although general relativity is highly regarded for its elegance and accuracy, it has limitations: the gravitational singularities inside black holes, the ad hoc postulation of dark matter, as well as dark energy and its relation to the cosmological constant are among the current unsolved mysteries regarding gravity, all of which signal the collapse of the general theory of relativity at different scales and highlight the need for a gravitational theory that goes into the quantum realm. At distances close to the Planck length, like those near the center of a black hole, quantum fluctuations of spacetime are expected to play an important role. Finally, the discrepancies between the predicted value for the vacuum energy and the observed values (which, depending on considerations, can be of 60 or 120 orders of magnitude) highlight the necessity for a quantum theory of gravity.

In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916.

According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum (non-rotating). A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass.

In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and the much larger theoretical value of zero-point energy suggested by quantum field theory.

Depending on the Planck energy cutoff and other factors, the quantum vacuum energy contribution to the effective cosmological constant is calculated to be between 50 and as many as 120 orders of magnitude greater than has actually been observed, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "probably the worst theoretical prediction in the history of physics".

Mark M. Phillips (born March 31, 1951) is an American astronomer who works on the observational studies of all classes of supernovae. He has worked on SN 1986G, SN 1987A, the Calán/Tololo Supernova Survey, the High-Z Supernova Search Team, and the Phillips relationship. This relationship has allowed the use of Type Ia supernovae as standard candles, leading to the precise measurements of the Hubble constant H₀ and the deceleration parameter q₀, the latter implying the existence of dark energy or a cosmological constant in the Universe.

He is the past director of Cerro Tololo Inter-American Observatory of the National Optical Astronomy Observatory and is the Associate Director and Carnegie Staff Member at Las Campanas Observatory in Chile, part of the Observatories of the Carnegie Institution for Science.