The Standard Model of Cosmology Chad A. Middleton, Ph.D. Mesa State College October 11, 2007 “The most incomprehensible thing about the world is that it is comprehensible.” -A. Einstein

Cosmology is the scientific study of the large scale properties of the Universe as a whole. addresses questions like: Is the Universe (in)finite in spatial extent? Is the Universe (in)finite in temporal extent? What are the possible geometries of the Universe? What is the fate of the Universe?

Ancient Greek Worldview: A Geocentric Cosmos Rotating spheres carry the moon, sun, planets, & stars around a stationary Earth Perfect, eternal & unchanging celestial region Universe is finite

Keplerian Orbits Based on Tycho Brahe’s astronomical measurements Copernican circular Heliocentric orbits must be abandoned

Kepler’s 3 Laws of Planetary Motion 1. The planets move in elliptical orbits with the Sun at one focus. 2. A line drawn from the Sun to any planet sweeps out equal areas in equal time intervals. 3. The square of the period of a planet is proportional to the cube of the semi-major axis of its orbit.

Olbers’ Paradox Kepler believed: space must be finite # of stars must be finite space surrounded by some kind of dark wall If the Universe in infinite, unchanging, and everywhere the same, shouldn’t the entire night sky be bright?

Newton’s Universal Law of Gravitation Successes Described the motion of massive bodies… …on earth …in the heavens

So what keeps the stars fixed? Newton’s view of the Cosmos: a perfect balance? Newton envisioned an infinitely large universe stars were placed at just the right distances so their attractions cancelled.

In 1915, Einstein gives the world his General Theory of Relativity describes the curvature of space describes the matter & energy

Space is not an empty void but rather a dynamical structure whose shape is determined by the presence of matter and energy. Matter tells space how to curve Space tells matter how to move

Einstein’s Static Universe General Relativity does NOT allow for a static cosmological model  Einstein introduces a Cosmological Constant  Static Universe if: vacuum energy

In 1929, Edwin Hubble discovers that the Universe is expanding! Einstein calls  the “greatest blunder” of his life!

Doppler Shift allows for determining the velocity of approaching/receding galaxies!

Cosmological Principle On sufficiently large distance scales, the Universe is 1. Isotropic 2. Homogeneous  Maximally Symmetric Space

For a Homogeneous & Isotropic Universe… … 3 possible Geometries Recent data indicates that the Universe is flat

Friedmann-Robertson-Walker (FRW) Cosmology Choose the Robertson-Walker metric * 3 non-interacting components:  pressureless matter  radiation  vacuum * the Robertson-Walker metric describes a spatially homogeneous, isotropic Universe evolving in time

The FRW Equations are… density (  ) & pressure (p) of the Universe determine the evolution of the scale factor (a)

Solutions for the scale factor when  = 0 Radiation dominated: Matter dominated: Vacuum dominated: NOTICE: As t  0, a(t)  0 Solutions for a non-static Universe: an abstract theoretical curiosity?

Georges Lemaître suggests the Universe had a temporal beginning.. Belgian Astrophysicist/ Catholic Priest 1927 paper in Annals of the Brussels Scientific Society Lemaître… showed that the universe had to be either contracting or expanding. suggested that the Universe had a definite beginning in which all its matter and energy were concentrated at one point.

Did the Universe begin with a “ Big Bang ”??  is not an explosion that happened at one point in space Big Bang - a time of infinite density, infinite temperature, and infinite spacetime curvature The “Big Bang”...  occurred at every place in one moment in time

In the early 1960’s, the Princeton group in gravitational physics… finds that the Universe should be uniformly bathed in a background microwave radiation predicts a blackbody spectrum of the background radiation w/ T ~ 10K

In 1965, observational evidence for the Big Bang!! Arno Penzias & Robert Wilson Bell Lab Physicists calibrating the Bell Labs microwave antenna designed for satellite communications Awarded the 1978 Nobel Prize in physics for discovery of the Cosmic Microwave Background Radiation

Yeah, but does this microwave background radiation have a Blackbody Spectrum? In Nov ‘89, NASA launches the Cosmic Background Explorer (COBE) to measure… the spectrum the anisotropies of the cosmic background radiation.

Spectrum of the Cosmic Microwave Background Radiation The excellent agreement with Planck’s law is the best fit ever measured! John Mather & George Smoot Awarded the 2006 Nobel Prize in physics “for their discovery of the blackbody form and anisotropy discovery of the CMB”

COBE image of the Cosmic Microwave Background Radiation Light from when the Universe was 380,000 years old… Map of  K anisotropies

Conclusions Theory & observational evidence indicate that:  the Universe is infinite in spatial extent  the Universe began w/ a “Big Bang” ~ 13.7 billion years ago  the Universe is flat  the Universe will continue to expand indefinitely

Models of the Expansion of the Universe

An Alternative: “Steady State” Cosmology Proposed by Hoyle, Bondi, & Gold Perfect Cosmological Principle - Universe is not only homogeneous in space but also in time Universe has NO beginning or end to time new matter is continuously being created as Universe expands Expansion rate is constant

Steady State vs Big Bang Big Bang Predicts the correct abundance of H (~75%) & He (~25%) Universe only ~few Billion years old? Steady State Space & Time treated symmetrically What about Olbers’ Paradox?

Inflation Why is the Universe so spatially flat homogeneous & isotropic Where did the temperature anisotropies come from?

The Standard Model of Cosmology Chad A. Middleton, Ph.D. Mesa State College October 11, 2007 “The most incomprehensible thing about the world is that it is comprehensible.” -A. Einstein