the cosmological principal

7/30/2019 The Cosmological Principal

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Class 2 :

The Cosmological Principle This class

A reminder about Hubbles Law Definition of The Cosmological Principle Homogeneity and Isotropy

Definitions Observational motivation

CP, Relativity, and frames of reference

I : Crucial ASTR121 reminder

HUBBLES LAW!

Edwin Hubble discovered that theUniverse is expanding!

Specifically, he measured the distance andvelocity of (nearby) galaxies he found that

This is called Hubbles Law. The constantH0 is called Hubbles constant.

Current estimates are H0=71km/s/Mpc


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Example of a galaxy spectrum


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II : The Cosmological Principle Early history of cosmology is largely the

realization that we do not occupy a specialplace in the Universe Once though that Earth was at center of solar

system now we know were not.

Once thought that Solar System was at center of theGalaxy now we know were not.

Once thought that our Galaxy was the dominantstructure in the Universe now we know that its a

pretty typical galaxy Definition : The Cosmological Principle (or

Copernican Principle) states that the Universelooks the same where-ever you are and which-ever direction you look


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Two immediate consequences of theCosmological Principle

Universe is homogeneous : every place in theuniverse has the same conditions as every otherplace, on average.

Universe is isotropic : there is no preferreddirection in the universe, on average.

Questions (discussion in class):

Is it possible to have a space which is homogeneousbut not isotropic?

Is it possible to have a space which is isotropic butnot homogeneous?

Why do we need the Cosmological Principle? Cosmology involves using the machinery of General

Relativity to model our Universe

In detail, Universe is an incredibly complex placewould be impossible to analyze mathematically ifthere were no simplifying principle

Assumption of homogeneity and isotropy gives usthe simplification that we need

Of course, we would be foolish to use CP if itwasnt actually suggested by data!! Evidence for homogeneity and isotropy comes from

galaxy surveys, observations of Cosmic MicrowaveBackground, uniformity of elemental abundances


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CfA redshiftsurvey

Each point

is a brightgalaxy

z=0.033

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Sloan DigitalSky Survey

Galaxiescolor codedby the age oftheir starshttp://www.sdss.org


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Las CampanasRedshift survey

Max distance ~ 109 pc !

z=0.20

Almost uniform intensity of microwaves in

all directions (isotropic 2.7K black bodyradiation)


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Question : Hubble showed that (almost)all galaxies are moving away from uswith velocity proportional to distance...It seems that we are at the center ofthe expansion! How is this consistentwith the homogeneity assumption?

III : The Cosmological Principle, Relativity,

and frames of reference

Cosmology is based on Relativity Theory (Special andGeneral) which rests on the assumption that physics is thesame all (inertial) frames of reference.

Does that mean that there is no preferred frame ofreference in the Universe?

No! A preferred frame sneaks into the theory via theimposition of the homogeneity assumption

Homogeneity states that, at a moment, the Universe has thesame average properties no matter where you are so we areimposing uniformity across a spatial slice of the spacetime

(i.e. set of all points in spacetime that are simultaneous toeach other)

But the notion of simultaneity changes when once chancesframe of reference so, in expanding Universe, homogeneitycan only be true in some particular frame of reference

Thus, homogeneity picks out a cosmological rest frame


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Subtracting off the mean level leaves a dipole

pattern motion of Earth wrt cosmological rest frame

the cosmological principal

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