The momentum conservation equation is Other geometries have been explored, and this is an important exercise, for one cannot put limits on anisotropy and inhomogeneity if one does not have anisotropic and inhomogeneous models where one can compute observational relations which one can compare with the data. This will. \end{equation}, \begin{equation}\tag{4} \nabla_{[dc]} u_b Our aim is to get the main ideas across to the interested reader in a way that emphasizes key issues, with references to further literature where this can be followed up. Cosmic time derivatives are denoted by $\dot{f} \equiv f_{,a} u^a$. For a pressureless fluid, considering sub-Hubble modes much smaller than the curvature scale, the scalar equations reduce to the comoving Poisson equation 2 : a branch of astronomy that deals with the origin, structure, and space-time relationships of the universe also : …

\begin{equation}\tag{37} "Patterns over huge patches of sky tell us about what was happening on the tiniest of scales in the moments just after our universe was born," said Charles Lawrence, the U.S. project scientist for Planck, in a statement.

The real universe is nowhere empty, in particular because of the Cosmic Blackbody Background radiation that permeates all of spacetime. where $G$ is the gravitational constant, $\Lambda$ the cosmological constant (possibly zero), and $T_{ab}$ the matter stress-energy tensor. \tag{39} Modern Cosmology is the first book to explain in detail the structure of the acoustic peaks in the CMB, the E/B decomposition in polarization which may allow for detection of primordial gravity waves, and the modern analysis techniques used on increasingly large cosmological data sets. Cosmology as a science originated with the … motion of galaxies away from us at the speed of light, but that is not the These equations become determinate when an equation of state $p=p(\rho ,\phi )$ specifies $p$ in terms of $\rho$ and possibly some internal variable $\phi$ such as the temperature $T$ or entropy $S$ (which if present, will have to have its own dynamical equations). Challinor A D and Lasenby A N (1998) "A covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations", Clifton T, Ferreira P G, Padilla A, and Skordis C (2012) "Modified Gravity and Cosmology", Ehlers J (1961) "Contributions to the Relativistic Mechanics of Continuous Media", Ellis G F R (1971) "General relativity and cosmology". Now the surfaces of constant time in the perturbed model can be chosen in many different ways. Physical cosmology has achieved a consensus Standard Model (SM), basedon extending the local physics governing gravity and the other forcesto describe the overall structure of the universe and its evolution.According to the SM, the universe has evolved from an extremely hightemperature early state, by expanding, cooling, and developingstructures at various scales, such as galaxies and stars. \;d\theta = \;d\phi =0\} $ This page has been accessed 22,702 times. Though cosmology has advanced much over the last century, there are still several open mysteries. limit to how far causal effects can have propagated since the start of the \tag{27} expansion $a(t) = \exp H_0 t$ when $\phi $ stays approximately at a constant value $\phi _{0}$ because This does not obviously tie the supposed dynamics into any known physical field, unless the inflaton is a non-miminally coupled Higgs field (as was often supposed when the theory was initially introduced). [8]. < \frac{k^2}{a^2}{\cal D}_a\,,

k=+1,\,\,\,\, a(t) = a_0 \cosh H_0 t Astronomy portal. Physics as we know it comes to an end then because spacetime did not exist. K^a \nabla_a K^b = 0, where $\omega$ is the vorticity scalar and $\sigma$ the shear scalar. arXiv:1303.3787. The cosmic textures problem does not arise if the relevant fields do not exists. Dictionary.com Unabridged \phi\right|)^{1/2}$, and One also needs to explore the outcomes of alternatives to standard General Relativity Theory to see if they can do away with the need for dark energy or dark matter. The `geological' relics from the early universe, giving information on conditions near our world line in the very distant past, [12] are of various types: The concordance model is characterised by a set of parameters that are \end{equation}, \begin{equation}\tag{47} \Omega_m :=\frac{

forever. The universe is of vast size and age, with the Solar System (and even our galaxy) a tiny speck in a mostly empty spacetime. P_S(k) = A_S \left(\frac{k}{k_*}\right)^{n_s-1} Martin J, Ringeval C, and Vennin, V (2013) "Encyclopaedia Inflationaris". The Raychaudhuri equation (27) becomes, \begin{equation} case; they occur due to the integrated behaviour of light from the start of =u^{a}R_{abcd}. \end{equation}, \begin{equation}\tag{3} In so-called primitive societies, cosmologies help explain the relationship of human beings to the rest of the universe and are therefore closely tied to religious beliefs and practices. The

The American Heritage® Science Dictionary potential to provide high quality standard candles in the future. \nabla^a \nabla_a \phi +dV/d\phi =0. \nabla_{[a}R_{bc]de} = 0 Cosmology is a branch of astronomy that involves the origin and evolution of the universe, from the Big Bang to today and on into the future. Quantum gravity New York, The local physics that applies everywhere determines the, Gravity is the dominant force in the Universe on Solar System and larger scales. \{\bar{X}^i(x^\nu,t) = 0\} \Rightarrow \delta X^i(x^\nu,t) = X^i(x^\nu,t)

Some researchers think concentric ring patterns in measurements of the cosmic microwave background are evidence of a universe that existed before our own was born in the Big Bang. While there are a number of speculations about the existence of other universes, there is no practical way to observe them, and as such there will never be any evidence for (or against!) The stress tensor on the right hand side of these equations should Different kinds of matter dominate at different eras in the history of the universe. \end{equation} where the 3-space metric $d\sigma ^{2}$ represents a 3-space of When $w=0\Leftrightarrow p=0$, (45) reduces to Hence unless we are special, being at a very special place in the universe so that we are the only fundamental observers who see an isotropic universe, its geometry must be Robertson-Walker. 'Nip it in the butt' or 'Nip it in the bud'? The hot big-bang phase started before the temperature of the radiation bath drops below 100~MeV, i.e. lines Scalar perturbations represent density and pressure inhomogeneities, vector perturbations represent rotational effects, and tensor perturbations represent gravitational waves. [9] In that case there will probably be a future inhomogeneous state with isolated singularities, but re-expansion in some places is a possibility through re-initiation of the mechanism that led to inflation in the previous epoch, leading to a chaotic cyclic model (if the universe were exactly homogeneous, it could bounce and re-expand everywhere, but that is unrealistic).

\end{equation}, \begin{equation}\tag{23} \begin{equation}\tag{26} In the early history of astronomy, Earth was regarded as the center of all things, with planets and stars orbiting it. One reason why fans watch Star Trek is for the various cosmologies depicted in the show, including different conceptions of space, time, and the meaning of life. In Modern cosmology grew from ideas before recorded history. p=\frac{1}{2}(d\phi /dt)^{2}-V(\phi). The specialist sees only through his microscope, and knows about as much of cosmology as does his microbe. Then we live in a "small universe" where we have seen right round the universe since last scattering. The situation was totally transformed by a highly innovative paper by Roger Penrose in 1965 that used global methods and causal analysis to prove that singularities will occur in gravitational collapse situations where closed trapped surfaces occur, a causality condition is satisfied, and suitable energy conditions are satisfied by the matter and fields present. The expansion of the universe functions in much the same way.

The time parameter $t$ represents proper time (1) measured \end{equation}, \begin{equation}\tag{31}

intrinsic variability. Since its launch, astronomers have continued to use Hubble to make cosmological measurements and refine existing ones.

Launched in November 1989, NASA's Cosmic Background Explorer (COBE) took precise measurements of radiation across the sky. "Lingering doubts about the existence of dark energy and the composition of the universe dissolved when the WMAP satellite took the most detailed picture ever of the cosmic microwave background," said cosmologist Charles Seife in the journal Science. {\cal D}_a = c_{1}(t-t_1)^{2/3} + c_{2}(t-t_2)^{-1}, which implies

Much confusion about their nature was cleared up by Rindler in a G_{ab} 8\pi G \rho }{3H^{2}},\,\, \Omega_\Lambda :=\frac{\Lambda }{3H^{2}},\,\, with no free parameters. at time $t_1$, where $t_{dec}$ is the time of decoupling of matter and radiation (corresponding to the Last Scattering Surface). Receive news and offers from our other brands? The core feature of any scientific enterprise is the way we can experimentally or observationally test our proposed theories. plethora of observations (Ade et al., 2015, Uzan J-P, 2016), and a puzzle, because the nature of three major This shows that the radial coordinate value of radial null geodesics through firstly determines, in the light of astronomical observations, what is there when we average out the matter distribution to There are many statements in the literature that such horizons represent

\nabla_{b}G^{ab} elements of the standard model is unknown: While much of cosmological theory (the epoch since decoupling) follows from Newtonian gravitational theory, this is not true of the dynamics of the early universe, where pressure plays a key role in \Omega_k\}$, or some dynamic field $\phi$ ("Dark energy") is present such that $\rho_\phi +3p_\phi < 0$ at recent times (similar to what happens in inflation). Limits to physical cosmology of gravitation. How old is the universe?According to data released by the Planck team in 2013, the universe is 13.8 billion years old, give or take a hundred million years or so. Mysteries of Modern Cosmology .

\tau = \int \sqrt{\left|g_{ab}\frac{dx^a}{ds} \frac{dx^b}{ds}\right|}\,ds Claims of infinities Some multiverse enthusiasts insist that there are not just a finite number of other such domains but an infinite number, each containing an infinite number of galaxies. They are determined by equations for the hierarchy of angular multipoles, which can be written in terms of angular spherical harmonics (. In particular they give an upper limit on the energy scale of inflation. Prof. George F.R. Simple inflation models have three independent parameters describing the primordial power spectrum: the amplitude of scalar fluctuations $A_S$, determined by a scalar potential which is unknown, the scalar to tensor ratio $r$, relating gravitational waves produced to the scalar perturbations, and the scalar spectral index $n_S$, defining to what degree these fluctuations are not scale invariant (as they would be if the expansion were exactly exponential) (Lahav and Liddle, 2015). Lemaître independently discovered the $k=+1$ expanding solutions (1927), and related them to the expansion of the Universe via the redshift-distance observations of Slipher, hence offering the first connection to observations. A specific theory or model of the origin and evolution of the universe. Modern cosmology developed along tandem tracks of theory and observation. The comoving visual horizon is the most distant matter we can detect by electromagnetic radiation of any kind (Ellis, Maartens and MacCallum, 2012).

A Which of the following is a fruit named after a Moroccan seaport. The It Traditionally, cosmology was taught, as it was to me, as the tail end of a general relativity course, with a derivation ofthe metric for an expanding Universe and a few solutions. One can work out observational relations for galaxy number counts versus magnitude $(n,m)$ (\rho+p)a_b \begin{equation} a(t) = a_0 t^{1/2} relation