|
|
| Line 1: |
Line 1: |
| The '''particle horizon''' (also called the cosmological horizon, the light horizon, or the cosmic light horizon) is the maximum distance from which [[Elementary particle|particle]]s could have traveled to the [[observation|observer]] in the [[age of the universe]]. It represents the boundary between the observable and the unobservable regions of the universe,<ref name="books.google.com">{{cite book|author=Edward Robert Harrison|title=Cosmology: the science of the universe|url=http://books.google.com/books?id=kNxeHD2cbLYC&pg=PA447|accessdate=1 May 2011|year=2000|publisher=Cambridge University Press|isbn=978-0-521-66148-5|pages=447–}}</ref> so its distance at the present epoch defines the size of the observable universe.<ref>{{cite book|author1=Andrew R. Liddle|author2=David Hilary Lyth|title=Cosmological inflation and large-scale structure|url=http://books.google.com/books?id=XmWauPZSovMC&pg=PA24|accessdate=1 May 2011|date=13 April 2000|publisher=Cambridge University Press|isbn=978-0-521-57598-0|pages=24–}}</ref> The existence, properties, and significance of a cosmological horizon depend on the particular [[cosmological model]].
| | I would recommend giving this a try, as it only costs about $7 per bar, and comes with a money back guarantee from certain websites, such as. Eradicating freckles, birth marks and acne marks are other advantages of applying skin whitening cream. Stir it well to mix the beeswax thoroughly with the oil, then allow it to cool to about 90 degrees. These proteins are collectively known as Functional Keratin, and along with another unusual ingredient called Phytessence Wakame, will leave your skin virtually wrinkle free. You will probably have to zoom in even further later when working on the finer details, but for now, just pick a 'comfortable' range. <br><br>Many people spend a a lot of money on skin whitening lotion and skincare products that claim to remove impurities and lighten skin color. When it results to skin treatment, the one method to obtain permanent and long durable benefits is actually to utilize natural and organic and fresh substances that a person have to apply on a regular basis. This is an excellent way to treat canker sores to promote swift healing. Chloasma is generally used to describe skin discolorations caused by hormones. If you want to stay beautiful, keep your skin healthy, and feel good, drink lots of water. <br><br>Research thoroughly all products associated with skin lightening by reading up on each product including what's in it, how it actually works to solve your skin problems, adverse effects as well as the maintaining aspects and other qualities of the products. CSC further disclosed that some of these products do not include formaldehyde as ingredients in their labels but were substituted with other ingredients that served as formaldehyde-releasing preservatives. In fact, for many people, it is recommended that you shower twice daily to ensure freshness and to avoid odor. In order to improve the effect of whitening, people should deal with the accumulation of melanin. Stress is regarded as the biggest aspects within the spread of acne. <br><br>Sugar with honey applied to our skin can exfoliate them just as well as the salons can. Obagi Toner is a gentle, alcohol free toner that adjusts the p - H of the skin for increased penetration of the system ingredients. All you need is 1 egg, a teaspoon of olive oil, and 1 tissue. If you are like me you want to keep things as natural as possible for you and your environment. We all know that all complexions are wonderful and it matters not which skin color you have, nevertheless for those who have neglected their pale skin color in the past when you had been some sort of sunshine worshipper and also you are somebody who wants some sort of brighter skin color there is nothing wrong within wanting a brighter skin. <br><br>The obvious disadvantage of these chemical bleaching creams is definitely the unwanted side effects. Calcium helps hyperhidrosis by helping your body cope with stress and nervousness. Always rinse the mouth thoroughly to remove any lemon juice residue. The best cream to whiten skin has to be a cream made of all natural products. In the time of applying Yogurt on the skin for about ten minutes to a minimum of thirty minutes, the skin is going to be expected to turn into lighter and more vibrant and this really is recognized by many to include a great deal of lactic acid.<br><br>If you have any sort of inquiries pertaining to where and how you can utilize neostrata hq skin lightening gel [[http://stylax.info/ http://stylax.info]], you could contact us at our web page. |
| | |
| In terms of [[comoving distance]], the particle horizon is equal to the '''conformal time''' <math>\eta</math> that has passed since the [[Big Bang]], times the [[speed of light]] <math>c</math>. In general, the conformal time at a certain time <math>t</math> is given by,
| |
| | |
| :<math>\eta = \int_{0}^{t} \frac{dt'}{a(t')}</math>
| |
| | |
| where <math>a(t)</math> is the [[Scale factor (cosmology)|scale factor]] of the [[Friedmann–Lemaître–Robertson–Walker metric]], and we have taken the Big Bang to be at <math>t=0</math>. By convention, a subscript 0 indicates "today" so that the conformal time today <math>\eta(t_0) = \eta_0 = 1.48 \times 10^{18}\ {\rm s}</math>. Note that the conformal time is not the [[age of the universe]]. Rather, the conformal time is the amount of time it would take a photon to travel from where we are located to the furthest observable distance provided the universe ceased expanding. As such, <math>\eta_0</math> is not a physically meaningful time (this much time has not yet actually passed), though, as we will see, the particle horizon with which it is associated is a conceptually meaningful distance.
| |
| | |
| The particle horizon recedes constantly as time passes and the conformal time grows. As such, the observed fraction of the universe always increases.<ref name="books.google.com"/><ref>{{cite book|author1=Michael Paul Hobson|author2=George Efstathiou|author3=Anthony N. Lasenby|title=General relativity: an introduction for physicists|url=http://books.google.com/books?id=xma1QuTJphYC&pg=PA419|accessdate=1 May 2011|year=2006|publisher=Cambridge University Press|isbn=978-0-521-82951-9|pages=419–}}</ref> Since proper distance at a given time is just comoving distance times the scale factor<ref name="expandingconfusion">{{cite journal|last = Davis|first = Tamara M.|coauthors = Charles H. Lineweaver |title=Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe|journal = Publications of the Astronomical Society of Australia|volume = 21|issue = 1|page = 97|year = 2004|doi = 10.1071/AS03040 |arxiv=astro-ph/0310808|bibcode = 2004PASA...21...97D }}</ref> (with [[comoving distance]] normally defined to be equal to proper distance at the present time, so <math>a(t_0) = 1</math> at present), the proper distance to the particle horizon at time <math>t</math> is given by<ref name="Giovannini">{{cite book|author=Massimo Giovannini|title=A primer on the physics of the cosmic microwave background|url=http://books.google.com/books?id=4ziIOYR1qZQC&pg=PA70|accessdate=1 May 2011|year=2008|publisher=World Scientific|isbn=978-981-279-142-9|pages=70–}}</ref>
| |
| | |
| :<math>H_p(t) = a(t) \int_{0}^{t} \frac{cdt'}{a(t')}</math>
| |
| | |
| and for today <math>t = t_0</math>
| |
| | |
| :<math> H_p(t_0) = c\eta_0 = 14.4\ {\rm Gpc}</math>.
| |
| | |
| ==Existence and Evolution of the Particle Horizon==
| |
| | |
| In this section we consider the [[FLRW]] cosmological model. In that context, the universe can be approximated as composed by non-interacting constituents, each one being a perfect fluid with density <math>\rho_i</math>, partial pressure <math>p_i</math> and state equation <math>p_i=\omega_i \rho_i</math>, such that they add up to the total density <math>\rho</math> and total pressure <math>p</math>.<ref>{{cite journal
| |
| |last=Berta Margalef-Bentabol
| |
| |coauthors=Juan Margalef-Bentabol; Jordi Cepa
| |
| |title=Evolution of the cosmological horizons in a concordance universe
| |
| |journal=Journal of Cosmology and Astroparticle Physics
| |
| |date=21 December 2012
| |
| |volume=2012
| |
| |issue=12
| |
| |doi=10.1088/1475-7516/2012/12/035
| |
| |url=http://iopscience.iop.org/1475-7516/2012/12/035
| |
| |arxiv=1302.1609}}</ref> Let us now define the following functions:
| |
| | |
| * Hubble function <math>H=\frac{\dot a}{a}</math>
| |
| | |
| * The critical density <math>\rho_c=\frac{3}{8\pi}H^2</math>
| |
| | |
| * The i-th dimensionless energy density <math>\Omega_i=\frac{\rho_i}{\rho_c}</math>
| |
| | |
| * The dimensionless energy density <math>\Omega=\frac{\rho}{\rho_c}=\sum \Omega_i</math>
| |
| | |
| * The redshift <math>z</math> given by the formula <math>1+z=\frac{a_0}{a(t)}</math>
| |
| | |
| Any function with a zero subscript denote the function evaluated at the present time <math>t_0</math> (or equivalently <math>z=0</math>). The last term can be taken to be <math>1</math> including the curvature state equation.<ref name="Evolution2">{{cite journal
| |
| |last=Berta Margalef-Bentabol
| |
| |coauthors=Juan Margalef-Bentabol; Jordi Cepa
| |
| |title=Evolution of the cosmological horizons in a universe with countably infinitely many state equations
| |
| |journal=Journal of Cosmology and Astroparticle Physics
| |
| |date=8 February 2013
| |
| |volume=2013
| |
| |series=015
| |
| |issue=02
| |
| |doi=10.1088/1475-7516/2013/02/015
| |
| |url=http://iopscience.iop.org/1475-7516/2013/02/015
| |
| |arxiv=1302.2186}}</ref> It can be proved that the Hubble function is given by
| |
| | |
| :<math> H(z)=H_0\sqrt{\sum \Omega_{i0}(1+z)^{n_i}}</math>
| |
| | |
| where <math>n_i=3(1+\omega_i)</math>. Notice that the addition ranges over all possible partial constituents and in particular there can be countably infinitely many. With this notation we have:<ref name="Evolution2" />
| |
| | |
| :<math> \text{The particle horizon } H_p \text{ exists if and only if } N>2</math>
| |
| | |
| where <math>N</math> is the largest <math>n_i</math> (possibly infinite). The evolution of the particle horizon for a expanding universe (<math>\dot{a}>0</math>) is:<ref name="Evolution2" />
| |
| | |
| :<math> \frac{dH_p}{dt}=H_p(z)H(z)+c</math>
| |
| | |
| where <math>c</math> is the speed of light and can be taken to be <math>1</math> (natural units). Notice that the derivative is made with respect to the FLRW-time <math>t</math>, while the functions are evaluated at the redshift <math>z</math> which are related as stated before. We have an analogous but slightly different result for [[Event Horizon]].
| |
| | |
| ==Horizon problem==
| |
| {{main|Horizon problem}}
| |
| The concept of a particle horizon can be used to illustrate the famous horizon problem, which is an unresolved issue associated with the [[Big Bang]] model. Extrapolating back to the time of [[recombination (cosmology)|recombination]] when the [[cosmic microwave background]] (CMB) was emitted, we obtain a particle horizon of about | |
| | |
| :<math> H_p(t_{\rm CMB}) = c\eta_{\rm CMB} = 284\ {\rm Mpc} = 8.9 \times 10^{-3} H_p(t_0) </math>.
| |
| | |
| which corresponds to a proper size at that time of:
| |
| | |
| :<math> a_{\rm CMB}H_p(t_{\rm CMB}) = 261\ {\rm kpc} </math>
| |
| | |
| Since we observe the CMB to be emitted essentially from our particle horizon (<math>284\text{ Mpc} \ll 14.4\text{ Gpc}</math>), our expectation is that parts of the [[cosmic microwave background]] (CMB) that are separated by about a fraction of a [[great circle]] across the sky of
| |
| | |
| :<math>f = H_p(t_{\rm CMB})/H_p(t_0)</math>
| |
| | |
| (an [[angular size]] of <math>\theta \sim 7.1^\circ</math>) should be out of [[causal contact]] with each other. That the entire CMB is in [[thermal equilibrium]] and approximates a [[blackbody]] so well is therefore not explained by the standard explanations about the way the [[expansion of the universe]] proceeds. The most popular resolution to this problem is [[cosmic inflation]].
| |
| | |
| == References ==
| |
| {{reflist}}
| |
| | |
| [[Category:Physical cosmology]]
| |
| [[Category:Universe]]
| |
I would recommend giving this a try, as it only costs about $7 per bar, and comes with a money back guarantee from certain websites, such as. Eradicating freckles, birth marks and acne marks are other advantages of applying skin whitening cream. Stir it well to mix the beeswax thoroughly with the oil, then allow it to cool to about 90 degrees. These proteins are collectively known as Functional Keratin, and along with another unusual ingredient called Phytessence Wakame, will leave your skin virtually wrinkle free. You will probably have to zoom in even further later when working on the finer details, but for now, just pick a 'comfortable' range.
Many people spend a a lot of money on skin whitening lotion and skincare products that claim to remove impurities and lighten skin color. When it results to skin treatment, the one method to obtain permanent and long durable benefits is actually to utilize natural and organic and fresh substances that a person have to apply on a regular basis. This is an excellent way to treat canker sores to promote swift healing. Chloasma is generally used to describe skin discolorations caused by hormones. If you want to stay beautiful, keep your skin healthy, and feel good, drink lots of water.
Research thoroughly all products associated with skin lightening by reading up on each product including what's in it, how it actually works to solve your skin problems, adverse effects as well as the maintaining aspects and other qualities of the products. CSC further disclosed that some of these products do not include formaldehyde as ingredients in their labels but were substituted with other ingredients that served as formaldehyde-releasing preservatives. In fact, for many people, it is recommended that you shower twice daily to ensure freshness and to avoid odor. In order to improve the effect of whitening, people should deal with the accumulation of melanin. Stress is regarded as the biggest aspects within the spread of acne.
Sugar with honey applied to our skin can exfoliate them just as well as the salons can. Obagi Toner is a gentle, alcohol free toner that adjusts the p - H of the skin for increased penetration of the system ingredients. All you need is 1 egg, a teaspoon of olive oil, and 1 tissue. If you are like me you want to keep things as natural as possible for you and your environment. We all know that all complexions are wonderful and it matters not which skin color you have, nevertheless for those who have neglected their pale skin color in the past when you had been some sort of sunshine worshipper and also you are somebody who wants some sort of brighter skin color there is nothing wrong within wanting a brighter skin.
The obvious disadvantage of these chemical bleaching creams is definitely the unwanted side effects. Calcium helps hyperhidrosis by helping your body cope with stress and nervousness. Always rinse the mouth thoroughly to remove any lemon juice residue. The best cream to whiten skin has to be a cream made of all natural products. In the time of applying Yogurt on the skin for about ten minutes to a minimum of thirty minutes, the skin is going to be expected to turn into lighter and more vibrant and this really is recognized by many to include a great deal of lactic acid.
If you have any sort of inquiries pertaining to where and how you can utilize neostrata hq skin lightening gel [http://stylax.info], you could contact us at our web page.