The universe is a strange place – hyper-massive black holes are hidden in the frigid hearts of all galaxies, stars boil in the violent cauldrons of gamma-ray bursts, multi-solar mass rogue planets wander between the stars, and hot super-Earths cohabit with their dark cousins. But more astonishingly, in one of every five cubic centimeters, twenty-three percent of the universe is composed of pressureless, invisible stuff called dark matter, having only gravitational interaction but not interacting with electromagnetic force. Seventy-three percent of the universe is composed of a strange fluid endowed with a negative equation of state, expanding the universe onward and outward, and blowing galaxies apart. It was labeled dark energy, because it cannot radiate upon telescopes [1]. To believe the existence of such exotic entities is hard; to learn its nature exactly is even harder.
1. Introduction to the Universe
Nevertheless, it is a worthwhile endeavor to explore dark matter and dark energy with astronomical probes and particle physics experiments, since they are crucial for understanding the formation of the large-scale structure of the universe, the formation and evolution of galaxies, and the thermodynamic evolution of the early universe [2]. In the beginning, the universe was hot and dense. Very shortly after the Big Bang, the universe was composed of an exotic state of matter composed of elementary particles, colliding with one another at energies far beyond the reach of even the most powerful particle accelerators today. A broken symmetry caused quarks and gluons to combine into protons and neutrons, and then protons and neutrons later formed primitive nuclei with the help of light elements (deuterium, helium-3, and lithium-7). The subsequently expanding universe began to cool down, and three hundred thousand years later atomic recombination took place (H and He atoms). The photons thus freed decoupled from matter and continued to fly through the universe. The greyness of the universe was established, about 380,000 years after the Big Bang, by a vast quantity of fossil relics – the cosmic microwave background radiation (CMB) – an afterglow of the hot dense and opaque universe.
1.1. The Nature of Dark Matter and Dark Energy
The universe, according to current models of cosmology, consists of: i) ordinary matter, gas, stars, galaxies, etc., of which planets, trees, and people are made, ii) dark matter, which is not visible but is expected to exist in large amounts, or about 25% of the energy density of the universe, and iii) dark energy, an exotic entity suggested to take the form of vacuum energy associated with empty space, or about 70% of the energy density of the universe [3]. The nature of dark matter and dark energy is among the most fundamental issues of modern cosmology, as it involves the most basic properties of space and time, and matter as well [4]. In order to understand, or speculate about, the dark part of the universe, it is necessary to begin with the bright part; i.e. the part of the universe that emits electromagnetic radiation.
Despite its complexity, the visible universe has been successfully described, to a degree that is surprising also to experts, by the simple Friedman-Robertson-Walker (FRW) type cosmological models. It is assumed to be very homogeneous and isotropic on large scales, and time-dependent, expanding, and cooling. The FRW cosmological models predict cosmic structure formation and evolution. Initially homogeneous and isotropic setups develop density fluctuations due to gravitational instability. Over time, in regions where density has been enhanced by random perturbations, matter collapses into condensed virialized structures such as galaxies, clusters of galaxies, and larger cosmic structures. At the current epoch, the nonlinear structures of the visible universe are observed, and their properties related to the growth of coherent structure on the basis of the FRW model are often analyzed.
Given the FRW model as an input, it is possible to compute the motions of visible matter in the universe represented by galaxies, clusters, and larger structures, and to directly compare the results with observations. Dark matter appears to be needed in current best-fit models of cosmic structure formation based on the FRW picture in order to explain the observed motions of galaxies and larger structures, as well as the motions of the visible parts of these structure. However, the nature of this dark matter is presently unknown. The isotropic cosmic microwave background (CMB) radiation is a remarkable property of the universe; it has been precisely studied astrophysically and cosmologically, and it can be understood theoretically as a product of the Big Bang, the beginning of the expansion in FRW cosmology. To a good approximation, CMB observations only depend on fundamental cosmological parameters such as temperatures, densities, and Hubble constant.
2. Historical Background
In the early 1920s, the spectacular new ceaseless flow of starlight from galaxies beyond the Milky Way led Edwin Hubble to apply the growing concept of the distance ladder to extragalactic nebulae, and to measure a distance to the Andromeda nebula, more than 2 million light years away. The distance ladder relies on the determination of accurate distances to some nearby stellar beacons. For instance, one can measure the parallax angle for nearby stars, which appers to move with respect to more distant stars as the earth orbits the Sun. The parallax angle is directly related to the distance in parsecs (pc): d=1/p (in arcseconds) [5].
Hubble subsequently shifted attention from closer naked eye galaxies to objective prism surveys of fainter galaxies, which involved the use of photographic plates and large telescopes. In a survey of 1,000 galaxies, he plotted a crude approximation to his now famous “Hubble curve,” at variance with Laplace and Milne and with the canonical static Newton-le-Sherif-Klein cosmology, where distances did not have to be taken into account in the dynamics. A heroic effort over the next 20 years resulted in the assembly of perhaps a few hundred, very incomplete, distance estimates, Josh’s cosmological resonator, and in Hubble’s publication of The Realm of the Nebulae, a compendium of the discoveries of the new field of extragalactic astronomy. Nevertheless, the only simple, plausible, and rigorous interpretation of Hubble’s curve, based on observational redundancy utilizing the distance ladder, is that it carries with it the unravelling of the great misconceptions of cosmology [4].
2.1. Early Observations and Discoveries
The discovery of the first galaxies and galaxy clusters, along with the brightening of the early Universe at temperatures above 10⁴K (redshift 1 < z < 10) due to ionized hydrogen filaments observed in 1965, established cosmology as a modern and testable science. The structures we observe today match these early phases. To reconcile the formation of cosmic structures across 60 scales (from 10¹⁰-⁷K stars to the recombination era at 3000K), models such as the Zeldovich pancake (~10¹²M⊙) were introduced. Additionally, the equation governing galaxy cluster number density, N(>mass, z), along with constant brightness and intrinsic GFD temperature TD ~ 2.8K, became essential. This theory eventually converged with the AGN hypothesis as metallicity growth from Population III stars at z>10 was better understood.
In 1914, Einstein introduced the cosmological constant (K₀) by adding a “cosmological term” to his equations, suggesting that these equations should apply not only to condensed matter but also to a homogeneous distribution of matter and energy. Mathematically and cosmologically, a dynamic, homogeneous, and isotropic “Friedmann-Lemaître-Robertson-Walker” (FLRW) Universe is identical to a static K=0 Einstein-de Sitter (dS) Universe. This concept has driven over a century of interest in exotic phenomena such as Visser tau fluctuations, Zeldovich pancakes, and the mass density parameter Ωₘ = 1, with dN/dz = 0 remaining constant over time.
3. Theoretical Framework
The theoretical framework section delves into the foundational theories that underpin our understanding of dark matter and dark energy, particularly emphasizing the role of general relativity and cosmology in shaping our theoretical models and interpretations of these enigmatic cosmic constituents.
Astrophysical and cosmological observations are commonly treated in the context of the theoretical framework provided by Einstein’s General Relativity and the standard cosmological model. Within cosmology, most of what is observationally known or inferred about the universe is analytically and computationally dealt with in the context of the Friedmann-Lemaître-Robertson-Walker (FLRW) homogeneous and isotropic metric, i.e. the hot big bang Friedmann-Robertson-Walker model [7]. In this framework, surface observations at widely different redshifts involving clusters, galaxies, supernova, microwave background anisotropies and many others, are presently being copiously used to constrain the cosmological parameters describing the standard cosmological model. The methodology involves integrating the appropriate differential equations along suitable paths with imposed boundary conditions, given the observational variables, and fits with analytic parametric functions. As the observational data is compiled in the FLRW framework, average properties of various observables computed in cosmological models are directly compared to the orbital cosmological parameters via statistical procedures. The cosmological parameters hence describe the orbital motion through the universe, and most of the theoretical musings on the form and content of the universe are firmly grounded into these parameters and their effects on the dynamics of the observables [2].
3.1. General Relativity and Cosmology
The standard cosmological model describes the large-scale structure and evolution of the universe based on a non-rotating, homogeneous, and isotropic space-time; taking as its simplest form the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies of general relativity (GR) [8]. This model is well tested; in particular, observations from the cosmic microwave background (CMB) provide evidence for an inflationary epoch. Despite its successes, this standard picture raises fundamental questions, the most pressing of which concerns the challenges posed by the so-called dark sector of the universe. Observations indicate that only ∼4% of the energy density of the full universe is contained in the abundantly baryonic (visible) cosmos powered by stars, and that the majority components are of exotic nature. One of them, whose presence has been known since the mid-1930s, is the so-called dark matter (DM). Nowadays it is known that the DM content of the universe must be non-baryonic and cold. Another poorly understood ingredient of the cosmos is the dark energy (DE), which emerged as the most plausible source of the observed late-time acceleration of the universe [9].
4. Observational Evidence
Observational evidence for dark matter and dark energy is presented on a variety of cosmic scales. The evidence for dark matter includes rotation curves of galaxies, mass-to-light ratios from clusters, large-scale galaxy clustering, weak lensing, and cosmic microwave background data. Evidence for dark energy comes from the isotropy of the cosmic microwave background, the large-scale structure of the universe, and from the distance-redshift relation of high-redshift supernovae. The observational data are presented and compared to the predictions of a spatially flat, homogeneous, and isotropic Friedmann-Lemaή tre-Robertson-Walker Universe that is filled with baryonic matter, dark matter that is consistent with a cold dark matter scenario, and a smooth dark energy component that is consistent with a cosmological constant. The concordance cosmology model is summarized in terms of its ingredients and key predictions. The current status of the confrontation between the predictions of this model and observations is presented [1]. The success of this concordance model and future directions for the exploration of dark energy and dark matter are discussed.
Observational Evidence for Dark Matter. Price and History of Dark-Matter Research. The standard way to obtain the total mass of an object from its Newtonian dynamics, say, its velocity dispersion, is to determine the radius at which Newtonian gravitational force balances the outward centrifugal or pressure gradient force. Mass estimates made in this way based on the rotation curves of spiral galaxies pointed to the existence of additional unseen mass beyond the optical galaxy disks. The structural details of this mass — mostly rotationally-cooling, gaseous and later-on virializing halos of cold dark matter — came to be known as the “NFW profiles”. Modeling the dynamics of cluster mergers with N-body simulations, it became clear that the collision-less nature of dark matter was key for the cluster formation process and its relative insensitivity to phenomena such as baryonic cooling. Analyses of the cluster mass distribution as function of radius, inferred from strong lensing, weak lensing and X-ray observations, became possible [10].
4.1. Galaxy Rotation Curves
A paradigm for deep space astrophysics and cosmology is that of visible matter and one or more kinds of hidden or dark matter. Eddington (1921) appreciated that one way to know about the presence of invisible mass is to observe its gravitating effect. For spiral galaxies, these early Kitt Peak observations in the infrared, supported by radio and visual observations, show large regions of invisible mass beyond the visible mass. More than 95% of the mass in galaxies and clusters of galaxies is in the form of an unknown kind of dark matter [11]. Despite decades of observations and active searches across wavelengths, this dark matter has not yet been detected and this situation hopefully may change in the near future. On galaxy-wide scales, a consensus picture has emerged, in which the dark matter contributes Ωdm – 0.23 of the overall energy density of the universe. The rest is made up of baryonic matter Ωb – 0.043. Within the framework of Standard Cosmological Model (λCDM), the nature of this dark matter is unknown. These discrepancies between observed and expected surface brightness and resulting rotation-curve profiles indicate there must be more mass present than can be accounted for in the visible baryonic matter in these galaxies. In large part based on the comprehensive rotation curves data of more than two hundred spiral galaxies, a paradigm has emerged, in which the bulk of the gravitating mass in spiral galaxies (and clusters of galaxies) is in the form of an unseen nonbaryonic, weakly interacting particle called “dark matter” [12]. This putative dark matter halo has large central-to-total mass ratio, exponentially declining central mass density, and steeply rising rotation curves in the outskirts compared to their near flat response in the baryonic mass case. Baryonic mass in each galaxy is visible in large part in stars and in the gas, which reside in a thin disk. Current understanding is that this baryonic disk is immersed in a massive, non-baryonic and non-visible dark matter halo which extends far beyond the optical disk. Galaxy rotation curves, inferred from the dynamics of gas and stars in the disk of a spiral galaxy, measure the effective mass distribution M(r) around the galaxy as a function of distance r from its center. For a flat, slowly rotating galaxy disk of mass MD, that is perfectly spherical, isotropic, and at rest with respect to the observer, consideration of Newton’s laws yields that the harvest of mapping of galaxy surface mass density is given by a delicate equilibrium condition between the gravitational field created by the mass of the galaxy and the centrifugal forces caused by its rotation.
5. Cosmic Microwave Background
The primeval hot, ionized // 3.82 million years : the diffusion of atoms accommodated the formation of the cosmic web, favored the clumping of matter deformed by the gravitational instability, and switched on the primordial atmosphere’s regime of the universe. Over the ages, the potential wells produced the hierarchical formation of structures that started building the large-scale structures observable today. However, Flatness-Temperature; Horizon-Initial Singularity; Structure Formation; Cosmological Constant; Entropy; Primordial Magnetic Field; Why QCD Phase Transition?; Reheating | quantum fluctuations and vacuum energy density | triggers inflation’s end damped | until q = 1
Temperature homogeneity of large angular scale anisotropies and the black body spectrum have been studied spectroscopically. Constraints on Harrison’s 16′ oscillations indicate synchronous Doppler fluctuations suppressed during 1 sec-baryogenesis, while Silk-90′ (quadrupole ratio = 1/66; 23; 0.003) predicted it but were rejected with 10^4 correl. Events scanned within 3; 0our l = 277,000 km on timescales larger than that era. Scanning spots and lenses have changed the perspectives, with spherical harmonics E(L) showing variance with P(l) in subharmonics in Fourier space and limit sharpness in flat A(L) with decompositions into quantifying invariants of fiducial geometries, including topological features. The fractal scales and continuous curvature have also been studied, with Goodman ’93 ‘universal aB dimensions’ and Eisenberg ‘N body systems’ contributing to star formations and the dark presence, along with non-smooth dimensions varying versus time. Additionally, Effron ’87, ‘94 discusses available quantum strat and limits. Proofs for achieving a sectorial myriatic division and N exp. density have been presented, along with non-diffusive material branches, better enacting demand, shifting, and st. sym.modules-neutral curv sf’s with a broad band spectrum. Medicine #14 and Helionatch ‘chaos res.’ have also been explored. Orbital paths, ranging from 900K -2;10^27, and limit auto comp are areas of interest in the study.
5.1. Planck Satellite Data
The Planck satellite, launched on May 14, 2009, is the third mission in ESA’s Horizon 2000 Science Programme and Europe’s first mission dedicated to the investigation of the Cosmic Microwave Background (CMB). The main goal of Planck is to map the anisotropies of the CMB from scales determined by primordial acoustic oscillations in the early Universe (about 0.1degree angular separation on the sky) to the largest angular scales on which the temperature fluctuations have been limited by the noise associated with the last scattering surface (about 10 degrees) [13]. An unprecedented combination of sensitivity, angular resolution, and frequency coverage is essential to achieving the science goals for the Planck mission.
The most important of these goals is to provide stringent constraints on models of cosmology and structure formation based on precision measurements of the CMB anisotropies. The Planck scientific objectives encompass the different stages in the behind-the-scene evolution of the Universe, extending from observations at the very early epoch when it was only about 10–36 seconds old, to the structure and distribution of galaxies and clusters of galaxies formed when the Universe became less dense and cooler [14]. That relates back to the Copernican principle which considers that the Universe is isotropic and homogeneous on sufficiently large scales. Planck is expected to constrain the standard cosmological model and the associated cosmological parameters with accuracy never before attained. Based on the Wilkinson Microwave Anisotropy Probe (WMAP) observations, the cosmic mean density of baryonic (normal) matter is determined to be about 4.6 percent while all other contributions to the total mass–energy budget are unknown. Roughly 22.4 percent is attributed to an enigmatic component, called dark matter, and 73 percent to another mysterious component, called dark energy, which opposes gravity to accelerate the expansion of the Universe.
6. Gravitational Lensing
Being dazzled by a brilliant sparkly star ought to be side-tracked after an encounter, This twinkling warm celestial body in the night sky, is a kind of genie, a eye-twinkling feeling wish-maker, and day-dreaming companion. This pureness of nothing, these cold, dead, balls of gases, can even make cry a fierce Viking warrior and a brutal warlord. But across this heavenly vastness cannot be alone. Logically, this should have something counteract this sparkle in the darkness. To have something boring yet subtle to dim their brightness and keep them aside. To have something that does not permit them to fulfil their true potential of the stardom. Therefore, dimming this twinkling star from afar, making them envious of bright-neon colour, smooth-skinned and eye-soothing tilt-shifting selfies of these big-apple city minervas.
Darkness does nothing to forbade this dream from taking shape. Just as there are sparkle eye-twinklings in the bright day-broadness new-york city, the day beholder can be dielectric, not yearning for an awe. This memory-beaming enigma then faces at another question, neither the question of what is lighting a smile underneath a broad-waking gory green-yellow taro orange sky, nor what is bringing out misshaped glimpses using pOltR, fast ajar double-glass inhibited eyepiece but instead wandering to a remembering frosted glass cold quartz-sublimity star and etching this spectacle with tranquillity on the marble surface of this dark violet tight-nut skyscraper light beam storm surrounded with glassing satin window eyepiece of thousand scripted foretelling.
As visible light moves, everything in this schematic does likewise, translating the shift of everything else. In the shifting shifts schema, things at the edge do not do behaviours at the centre, and so things at the edge feel a slower, redder-shift time, bound to slow routine which ought to be galaxy feast, which perhaps in doubting converse beholder positions ought similarly blue but should not. Answering down to have nothing outside and stop thinking on just anything grand, picturing this shapeless dark, beyond empty canvass.
However, this sparkliness could not shine differently, be itself without being wild and bright outside of a gargantuan dark pomegranate. Things out there are incandescent at its core and cold dead throughout its vastness. No graveness but pulsar excitement, cracks void serenity, and black-and-white monkey painting humanity imaginations. Because bilirubin currently ticked passing this hopping through sun-fading holiday broad-lands project, with pop-coloured sandy tall-peaked abstract dark soaked yet widening golden & violet mirage sceneries. Perhaps imagining the imageless slowdown fringe peak surfing holdem galatta-scented schematically on the unviolated outskirts of an uproarious beluga abode, pondering on questioning nothing and asking for daring secrets would turn often wild and mad, but in remembrance and shimmering fun nativity tomfoolery does nothing more muscat stets a black sea and star pulled this surrounding brilliance away from pausing on solemn old clock-pulsushing screen-vaulted wandering.
6.1. Strong and Weak Lensing
Light from a distant galaxy generally arrives at Earth without any distortion. However, if in its way there is another massive body like a star cluster or a galaxy, its gravity can bend the ray of light and deflect it from the original direction [15]. This phenomenon, also named lensing, is governed by Einstein’s General Theory of Relativity.
If the lens mass distribution is regular and the layout is well centered, an observer positioned on the far side may see a bright ring around the lens. This effect is known as strong lensing (SL). The light paths, also called caustics, are very sensitive to the detailed mass distribution of the lens. SL is usually applied to galaxy clusters because of their large masses and compactness.
When the mass distribution of the lens is not symmetric, the light from the background source is split into several images. Each of these images can reach an observer positioned on the near side of the lens, and therefore they usually arrive at different times [16]. Gravitational waves are also deflected by gravity the same way as light, therefore they can also be lensed by the same structure as the one producing lensing to light signals.
7. Large-Scale Structure of the Universe
With time, the distribution of matter in the Universe became more and more complex, as gravitation acted upon it. There are the formations of structures of a size of galaxy, cluster of galaxies, superclusters of galaxies, voids of large empty domains with no mass at all, great walls of galaxies. All this picture resembles the spider web and it is called the cosmic web.
The current understanding of the cosmic web is the outcome of the two important components of the Universe. These are the distributions of the baryonic matter, directly observable as the light from the galaxies formed of it, and the distributions of the invisible dark matter, revealed indirectly through its gravitational effects. Dark energy, the counterpart of which is a smooth repulsive energy, pushes all the matter structures apart and is responsible for the current acceleration of the expansion of the Universe [17].
The formation and evolution of the cosmic web are modeled mathematically with the help of cosmological simulations. A simple computer experiment is represented – simulating the matter distribution in the Universe, given the initial density perturbation, expanding under the influence of gravity with time. This simulates the evolution of the three-dimensional density field, calculated for matter dominated and cold dark matter scenarios.
7.1. Baryon Acoustic Oscillations
To discuss the large-scale structure of the universe is to argue for at least one specific model of such structure. That model invokes multiple complementary statistics at many epochs, chosen to highlight a collection of well-understood phenomena. The collection of such phenomena includes everything from ‘simple’ hierarchical clustering, galaxies merging together to build more massive galaxies under the influence of their gravity (initially smooth quantum fluctuation-induced perturbations in the density of Cold Dark Matter) to nursery simulations of large galaxy clusters accreting smaller companions along extended filaments of matter. Simple and straightforward matters are the cosmic microwave background (CMB). With respect to viewing other cosmological structures such as the cosmic web of galaxies, it provides theorists an early simple smooth and isotropic space to see last scattering surface snapshots of the distribution of modes. The (flat) space on such surface has a scale factor normalized to unity. Modes at such scale traverse stresses the ordinary matter before it can take shape of denser structures. The ‘forcing’ is due to the presence of baryons, who’s sound speed dominated the dynamics until recombination. Zooming in at a fixed angle on CMB temperature maps shows arcs of hot and cold spots: maxima and minima respectively of the gravitational potential wells. The spots’ size depends on space curvature. The comparison method has been extensively used to uncover basic properties of cosmological structure algorithmically [18]. So have Fourier transform methods.
Baryon Acoustic Oscillations (BAO) are the enigmatic oscillations in the distribution of baryonic matter in the present-day universe. In the linear regime of growth, present-day non-divergent density fluctuations δ are related to the present-day matter transfer function via δ = ∆CDM(k)/(1 + R) where ∆CDM(k) is the density contrast in a universe dominated by CDM only, and R = Ωb/Ωc. Mode amplitudes are determined by initial spectrum normalization. To obtain an initial set of δ, random Gaussian phases are assigned to the amplitudes in such a way that the resulting density field is isotropic [19]. Recent observations of large-scale structure in the universe have detected a key prediction of standard cosmology (that the universe is dominated by Cold Dark Matter and Compressed Baryons). The observations’ distribution of galaxies reveals, when averaged over large enough scales, a particular characteristic length (about 100 h-1 Mpc) corresponding to a well defined peak in the two-point correlation function. It is theorized that such a peak is a relic of the early universe: gravitational redshifted oscillations of primordial baryons trapped in a viscous fluid of relativistic plasma modes damped collisions of baryons with photons and supplied by adiabatic perturbations of matter. The multiple nature of the oscillations leads to periodic entrance into gravitational potential wells producing dense and sparse structures. BAO in the galaxy power spectrum are defined as the characteristic “wiggles’’ along a characteristic mode scale kBAO = 0.04 h Mpc-1: a peak at k = kBAO and an anticorrelated trough at k = 2kBAO. The width of the BAO peaks, determined by the sound speed at the time of decoupling, appears in k-space as a “conch-shell” sphere that progressively grows with time. The BAO technique is designed to be the “standard roder’’ in measurements of the unexplored part of the asymptotic expansion of the Universe, ie. the time-evolution of Dark Energy density.
8. Dark Matter Candidates
In the quest to understand the mysterious dark matter that comprises about 27% of the universe, scientists have proposed several candidates. Among the most prominent are Weakly Interacting Massive Particles (WIMPs) and axions. WIMPs are theoretical particles that interact through gravity and possibly weak nuclear forces, making them elusive in detection. Axions, on the other hand, are ultra-light particles that could explain certain quantum chromodynamics anomalies. These candidates are being intensely studied through various experimental approaches, including particle colliders, direct detection experiments, and astrophysical observations. Understanding the nature and origin of dark matter is crucial for unraveling the mysteries of cosmic evolution and structure formation.
8.1. WIMPs and Axions
There are two candidates for the most popular dark matter candidates, WIMPs and axions. Both candidates can be sought in a variety of experimental approaches, from terrestrial colliders to deep space. On the one hand, WIMPs have cross-sections and mass scales closely related to the SM. Thermal WIMPs are heavier than the Z mass, with cross-sections adjustable to achieve the observed abundance. On the other hand, axions only weakly couple to matter, becoming invisible to standard particle detection methods [20]. Previous cosmological observations are summarized briefly at the beginning.
WIMPs are normally referred to as those particles arising from SU(2) extensions of the SM with TeV mass scales or related to the SUGRA philosophy, which is supposed to keep the SUSY hierarchy problem under control. At the same time, they are producing a big tuning problem. Thus, very large scales of grand unification have to be adjusted to be equal to the relatively low SUSY mass scales. This is known as the WIMP miracle [21].
9. Dark Energy Phenomena
The most famous aspect of dark energy is, arguably, the cosmological constant. It is amazing how little is known about the cosmological constant. It is not known why it is as small as it is. [22] It is not known why it is positive and not negative. It is not known why it is so much smaller than other essential energy scales known in particle physics. Many explanations for the cosmological constant do exist, but none are universally accepted. Such candidate models range from invoking symmetry principles or string theory structures, to modifying gravity or proposing anthropic reasoning. Interestingly, most of these attempts are not falsifiable, i.e., they are hard to subject to experimental tests and observations [23].
Having acknowledged this embarrassing lack of confidence in the picture of dark energy, it was decided to change perspective and focus on the strange properties of the cosmological constant itself. It contains many surprises that, it is believed, hold valuable hints to understand dark energy—from very different angles.
9.1. Cosmological Constant
In 1998 astronomers discovered that the expansion of the universe is accelerating. A mysterious and hitherto unknown agent was invoked to explain this. This something was called dark energy; it is described by Einstein’s cosmological constant; and it amounts to about 70 of the total mass of the universe. The universe’s energy budget thus has more than 90 vacuum energy, amorphous matter, and possibly more than 98 nonbaryonic matter [22]. In a sense, the cosmological constant is the most successful term in Einstein’s equations. First derived as a mathematical trick, it was subsequently taken seriously and became the first significant indication of general relativity’s power beyond gravity. Once ridiculed, it was recently resurrected and is widely believed to control the infinite future of the universe. There are, however, much less specific expectations, e.g. that it is a constant—it may well take different values in different places (beyond the local group of galaxies) or times [24].
The origin of this macroscopic constant energy density is truly enigmatic. It has been conjectured that the cosmological constant is a form of vacuum energy. If true, it would be natural for to be as large as 10^(-120) times the Planck energy density, making it the worst theoretical prediction ever made. Most of the cosmological constant problems listed on this earth have no comparable formulation elsewhere in fundamental physics and are hence genuinely cosmological in character. Nevertheless, finding more with fewer particles, links to particle physics, or failure to construct Minkowski space in curved string background is less truly cosmological than one might naively think since its relation to particles stems from translations invariance and is a property of the vacuum’ (bons, etc.) rather than one of the substance delta. In string theory, this weight of ambiguity of has not diminished, but the offset from addressable address are big numbers has not changed either (the best b =760, although some find variables).
10. Modified Gravity Theories
The Einstein’s equations serve as a theoretical framework for investigating the dynamics of the geometrical degrees of freedom of the gravitational field. Supernova observations suggest that present Universe is velocity dominated and its expansion is accelerating; hence, a natural explanation for these results would invoke an additional negative pressure energy-momentum tensor, responsible for the acceleration. In this framework, geometric or topological nature of the additional sector should not change gravitational theory at local scales, leading to a linear structure of the energy density. In the infrared, the most effective theory to explore the presence of a negative pressure fluid is the cosmological constant (Λ) model. In this framework, a simple interpretation for the cosmological constant is that of constant vacuum energy density generated by some unknown mechanism of spontaneous symmetry breaking at a energy scale of 10^16 GeV [25].
Alternative theories, known as modified gravity candidates, have been proposed to account for the astrophysical phenomenologies associated with DM and DE, which range from galactic to cosmological distances. These theories aim to explain cosmic phenomena that are generally interpreted as gravitational effects of DM or DE without the need for any new matter component. The possibility that the inverse square law of gravitation is violated at galactic or cosmological scales is the most straightforward route to modify gravity and is a central tenet in most alternative theories [26]. However, this indirectly means the existence of very light additional scalar degrees of freedom beyond the metric. There is a distinction between two approaches to modified gravity theories: (1) metric theories, which only change the action without introducing any new degrees of freedom other than the metric; and (2) non-metric theories, which additionally changes the action and introduces new degrees of freedom beyond the metric.
10.1. f(R) Gravity
Galileon-like gravity theories are higher-order metric and Palatini gravity theories that are algebraically equivalent to scalar-tensor theories with a non-linear kinetic term, or equivalently as Brans-Dicke theories with a time- and scale-dependent Brans-Dicke parameter. In addition to their cosmological success and reasonable predictions for structure formation in the large scale, there are models of this class that admit a Minkowski de-Sitter limit in the early universe. If instead of the standard Einstein-Hilbert action one assumes the action of the form f(R), the modified gravity models violate the equivalence principle at the background or cosmological level, leading to a dimensional parameter controlling deviation from general relativity. Several models of this scenic group exhibit particular duality symmetries in the context of homogeneous and isotropic cosmological solutions restoring standard Einstein gravity, at the background level without perturbations.
Surveying the possible phenomena that could occur under these conditions at the instability level (kinetic terms control the propagation and non-linearity adds tuning effects to the model), f(R) theories are existing models of gravity post-processing background solutions of modified theories differing from general relativity at all levels and providing inflation and solutions explaining cosmic acceleration. After a brief account of dualities in cosmological settings, a class of f(R) theories of Dubois-Teissier-Sabatini type exhibiting mathematically scalefactor duality transformation is chosen. The effective theory of an anisotropic universe is employed to explore the dynamical system approach which is a related minimization of variables integration consisting of studying first integral relations of equations of motion written in terms of dimensionless scale-factor variables.
11. Future Prospects
The next generation of observations is poised to unravel the enigma. Current ground-based telescopes can reach redshift 10, the arrival time of the earliest massive galaxies predicted in LCDM. In space, the James Webb Space Telescope is expected to observe galaxies at redshifts larger than 15 and grasp the underlying formation mechanisms. The wide-angle surveys of ESA’s Euclid and NASA’s Wide Field Infrared Survey Telescope (WFIRST) will constrain the dark energy equation of state, exploring deviations from the cosmological constant. The next generation ground-based telescopes, the Large Synoptic Survey Telescope (LSST), will explore much deeper limits than the Sloan Digital Sky Survey (SDSS). The sensitivity of these observations to galactic structure formation and evolution will enable constraining modifications to the GR equations governing the expansion, critical for understanding the nature of dark energy. Coincident with these optical observations, the coming decades will witness the development of other observatories revealing the true 3D view on the universe and its contents. Currently operational, planned, and proposed experiments/technology related to the energy spectrum of 1 GeV–1 PeV are unlikely to explain the 10 TeV or sub-PeV diffuse background detected recently by the IceCube observatory. However, they can provide information on a large number of surprises associated with dark matter and the still poorly-understood physics at an energy frontier of several TeVs where cosmic rays are made. Spaced-based GRACE-Like missions can monitor GWs generated by massive planets and perturbed stars in the Milky Way (or nearby galaxies) that will allow breaking the current electromagnetic degeneracy for supermassive black holes [1].
A SUN-like star on a cD galaxy in a cluster halo was observed by numerous telescopes ranging from BARB to high-energy space observatories. It formed a planetary-system-like cometary structure (AGN68inAbell2667 brill61), sandy particles in the protostellar disk generated by the star accreted baryonic halos (through radiative cooling via H2 lines, leading to thermal Jeans collapse). Several thousand stellar systems were expected to form, some converging through dynamical friction to sink into the galaxies’ centers. GR, explicitly calculated for a galaxy cluster, predicted formation via dynamical instability modes that evolve to multiparty accretion disc systems. Solar-type stars need a few billion years to spiral in close to the galaxies’ centers, and the merger event between stars or their remnants with the central spacetime becomes GR deflected. Exotic kinematic signatures can be detected and tested independently with sufficiently high precision.
11.1. Upcoming Experiments and Observations
There are a number of experiments on the horizon that may reveal important clues about the nature of dark matter and dark energy. In the first case, astrophysical, laboratory, and accelerator searches for WIMPS will go ahead [3]. The GLAST, CRESST, CDMS, and DAMA proposed experiments fall into the case where the WIMP scattering cross section with normal matter is mediated by ordinary Z exchange. Other alternatives indicate that the capture of dark astrophysical objects is a sensitive way of testing a variety of models. Observations of the internal structure of dwarf galaxies and the highest pregalactic objects can reveal much of the formation process of early structures and are a strong test of the cold dark matter hypothesis. The AGN and archival data from WMAP may reveal the existence of WIMPs or account for a significant fraction of the cosmic microwave background power spectrum.
On the cosmological side, a combination of observations of the CMB, large-scale structure, BAO, SNIa, and the formation of galaxies will be key to shed light on the nature of dark energy. There are hopes of significant improvements in accuracy with upcoming observations. GR by itself may perform well on cosmological scales taming the worries regarding its applicability at the high curvature GS regime [27]. However, GR alone cannot account for the observed low energy acceleration. A key question is whether the infrared modification proposed to achieve this to GR respects the principle of locality.
12. Implications for Cosmology and Astrophysics
The exploration of implications for cosmology and astrophysics discusses the wider implications of dark matter and dark energy for our understanding of the universe. At present, 27% of the matter-energy content of the universe is in the form of non-baryonic dark matter whereas 68% is made up of dark energy, with only the remaining 5% in the form of the visible cosmic constituents comprising atoms [2]. These enigmatic and novel components active at cosmological scales and partake in important effects on the evolution of the universe and on the formation of structure and collapse within it, even as their precise nature remains illusive. The past century of astronomical observations and laboratory studies have confirmed the prediction for a rising expansion velocity of the universe by the general relativistic Einstein equation. The cosmological constant, Λ, postulated in 1917, describing the repulsive force that could balance the attractive force of gravitation, is an excellent candidate for describing the effects of dark energy [3].
A more modern perspective of Λ is taken in terms of quantum field theories in space, and regarding its cosmological effects, in terms of scalar quintessence fields that accompany a cosmological potential. It is argued that from accelerator experiment, astrophysical, and cosmological observations this repulsive force exists and dominates the fate of the universe. On the largest scales probed, and as presently understood, the universe is flat, almost homogeneous, isotropic, composed of dark energy, dark matter and normal visible matter fluids with thermal fluctuations seeded nearly Gaussian adiabatic density perturbations.
12.1. Understanding the Fate of the Universe
The large amounts of unseen matter or energy, detected by indirect means, are termed dark. The two most famous examples of these are dark matter and dark energy. The former is made of particles which follow the same laws of physics as ordinary baryonic matter, such as protons and neutrons. However, they only participate in gravity and perhaps other unknown forces. On the other hand, dark energy, first suspected in the mid-1990s, is much more enigmatic. Constituting roughly 73% of the mass-energy content of the universe, dark energy appears to be a smooth form of energy, perhaps with negative pressure, which practically has no clumpiness on the relevant cosmological scales of 10s of Mpc [4].
The fate of the universe is determined by its scalar curvature and the composition of matter and energy. Friedmann-Lemaitre-Robertson-Walker cosmologies describe spatially homogeneous isotropic models capable of explaining the cosmological redshift of galaxies. Basic concepts like the scales of the universe, density parameter, expansion rate, age of the universe, Hubble parameter, deceleration parameter, critical density, equation of state, and solutions of the field equations of cosmology are introduced [3].
13. Conclusion and Summary
The current state of knowledge of dark matter and dark energy has been summarized in a single essay. Discussion ranges from the oldest evidence for the existence of unseen forms of mass and energy, to the most recent ideas about the nature of the unobservable && invisible constituents of the Universe. A variety of chilling models, in which life in the Cosmos eventually dies out, have been sketched, and the most baffling problems still confronting theoretical physicists and cosmologists have been highlighted. This essay is meant for an audience of non-specialists, but thorough familiarity with the basic results of mathematical physics, relativistic astrophysics, and, preferably, the modern quantum field theory formulation of particle physics is taken for granted. Personal bias is inevitable in an essay of this nature; it is hoped that comments on the significance of particular pieces of knowledge will be felt to be appropriate, that insights obtained in some areas will be found to be useful pointers to new avenues of research, and that the concerns of the writer regarding particular issues will be shared by many [1].
The present knowledge of dark matter and dark energy seems contradictory, and it would be nice to have independent confirmation of this knowledge — confirmation not based on astronomical observations which are subject to modelling, interpretation, and manipulation, but rather on results which can be reproduced in the laboratory under controlled conditions. Currently, there are no reasonable prospects of direct detection of dark matter particles, be they WIMPS or super-weakly-interacting heavy particles, due to the very small interaction cross-sections that have been calculated for these particles in the context of most proposed candidate models. Here, one obvious hope lies with the LHC collider, whose parameters and design were heavily influenced by the quest for ‘beyond the standard model’ physics such as possible supersymmetry as well as the common paradigm of `SuperWIMP’ dark matter candidates [2].
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