Developing a basic explanatory manual for the Light cone 1.0 calculator. This is as a supplement to give a basic understanding on what the terms used in the calculator mean. The user manual is separate as is the advanced manual which shows the math forms used in the calculator.(adsbygoogle = window.adsbygoogle || []).push({});

The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformly. The CMB provides an excellent reference point in distance measurements and corresponds to a stretch of 1090

Doppler shift and redshiftare the same phenomenon in general relativity. However you will often see Doppler factored into components with different names used. In all cases of Doppler, the light emitted by one body and received by the other will be red or blueshifted i.e. its wavelength will be stretched. So the color of the light is more towards the red or blue end of the spectrum. As shown by the formula below.

[tex]\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}[/tex]

However the only form of redshift we need to concern ourselves with is called the cosmological redshift.

The Cosmological Redshiftis a redshift attributed to the expansion of space. The expansion causes a Recession Velocity for galaxies (on average) that is proportional to DISTANCE.

A key note is expansion is the same throughout the cosmos. However gravity in galaxy clusters is strong enough to prevent expansion. In other words galaxy clusters are gravitationally bound. In regards to expansion it is important to realize that galaxies are not moving from us due to inertia, rather the space between two coordinates are expanding. One way to visualize this is to use a grid where each vertical and horizontal joint is a coordinate. The space between the coordinates increase rather than the coordinates changing. This is important in that no FORCE is acting upon the galaxies to cause expansion. As expansion is homogeneous and isotropic then there is no difference in expansion at one location or another. In the [itex]\Lambda[/itex]CDM model expansion is attributed to the cosmological constant described later on. The rate a galaxy is moving from us is referred to as recession velocity. This recession velocity then produces a (red) shift proportional to distance. The further away an object is the greater the amount of redshift. This is given in accordance with Hubble’s Law. In order to quantify the velocity of this galactic movement, Hubble proposed Hubble's Law of Cosmic Expansion, aka Hubble's law, an equation that states:

Hubble’s Law: The greater the distance of measurement the greater the recessive velocity

Velocity = H_{0}× distance.

Velocity represents the galaxy's recessive velocity; H_{0}is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

The Hubble ConstantThe Hubble “constant” is a constant only in space, not in time,the subscript ‘0’ indicates the value of the Hubble constant today and the Hubble parameter is thought to be decreasing with time. Any measurement of redshift above the Hubble distance defined as H_{0}= 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity

z = (Observed wavelength - Rest wavelength)/(Rest wavelength) or more accurately

1+z= λ_{observed}/λ_{emitted}or z=(λ_{observed}-λ_{emitted})/λ_{emitted}

[tex]1+Z=\frac{\lambda}{\lambda_o}[/tex] or [tex]1+Z=\frac{\lambda-\lambda_o}{\lambda_o}[/tex]

λ_{0}= rest wavelength

Note that positive values of z correspond to increased wavelengths (redshifts).

Strictly speaking, when z < 0, this quantity is called a blueshift, rather than

a redshift. However, the vast majority of galaxies have z > 0. One notable blue shift example is the Andromeda Galaxy, which is gravitationally bound and approaching the Milky Way.

WMAP nine-year results give the redshift of photon decoupling as z=1091.64 ± 0.47 So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.

The scale factor, cosmic scale factor or sometimes the Robertson-Walker scale factor parameter of the Friedmann equations represents the relative expansion of the universe. It relates the proper distance which can change over time, or the comoving distance which is the distance at a given reference in time.

d(t)=a(t)d_{o}

where d(t) is the proper distance at epoch (t)

d_{0}is the distance at the reference time (t_{o})

a(t) is the comoving angular scale factor. Which is the distance coordinate for calculating proper distance between objects at the same epoch (time)

r(t) is the comoving radial scale factor. Which is distance coordinates for calculating proper distances between objects at two different epochs (time)

[tex]Proper distance =\frac{\stackrel{.}{a}(t)}{a}[/tex]

The dot above a indicates change in.

the notation R(t) indicates that the scale factor is a function of time and its value changes with time. R(t)<1 is the past, R(t)=1 is the present and R(t)>1 is the future.

[tex]H(t)=\frac{\stackrel{.}{a}(t)}{a(t)}[/tex]

Expansion velocity

[tex] v=\frac{\stackrel{.}{a}(t)}{a}[/tex]

This shows that Hubble's constant is time dependant.

Luminosity: absolute luminosity is the amount of energy emitted per second.

is often measured in flux where flux is

[tex]f=\frac{L}{4\pi r^2}[/tex]

However cosmologists typically use a scale called magnitudes. The magnitude scale has been developed so that a 5 magnitude change corresponds to a differents of 100 flux.

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# Lightcone 1.0 basic redshift article development

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