IX. The Cosmological Constant. ASTR378 Cosmology : IX. The Cosmological Constant 96

Transcription

1 IX. The Cosmological Constant ASTR378 Cosmology : IX. The Cosmological Constant 96

2 Einstein s Greatest Blunder At the time (~1915), Universe believed static, supported by observational data Universe containing only matter must be expanding or contracting the only static Universe is an empty one introduce a fudge factor,, with constant density and pressure Friedmann Equation with : 2 a + kc 2 a a 2 c 2 Λ 3 = 8πG 3 ρ ASTR378 Cosmology : IX. The Cosmological Constant 97

3 Problems with Acceleration Equation with acts as a repulsive force: a a = 4πG ρ + 3P + Λc 2 3 c 2 3 If has constant P, then infinitesimal expansion / contraction of the Universe would lead to runaway expansion / contraction unstable (Inelegant took away from formal beauty of theory ) 1929: Hubble paper on redshift-distance relation Universe expanding, no need for (although sometimes invoked when the age of the Universe appeared less than the ages of astronomical objects...) ASTR378 Cosmology : IX. The Cosmological Constant 98

4 1998: The Rehabilitation of Type Ia Supernovae (SNe Ia): thermonuclear explosion of a white dwarf > ~ 1.4 M (single/ double degenerate scenarios) Standard Candles: SNe Ia have ~same luminosity can get distances to host galaxies, calibration improved by taking shape of light curve into account In 1998, two competing teams observing SNe Ia found that for z 1, SNe Ia were too faint ASTR378 Cosmology : IX. The Cosmological Constant 99

5 28 April 4 April SN How to Find Supernovae ASTR378 Cosmology : IX. The Cosmological Constant 100

6 Two Competing Teams, Same Result S. Perlmutter, G. Aldering, S. Deustua, S. Fabbro, G. Goldhaber, D. Groom, A. Kim, M. Kim, R. Knop, P. Nugent, (LBL & CfPA) N. Walton (Isaac Newton Group) A. Fruchter, N. Panagia (STSci) A. Goobar (Univ of Stockholm) R. Pain (IN2P3, Paris) I. Hook, C. Lidman (ESO) M. DellaValle (Univ of Padova) R. Ellis (CalTech) R. McMahon (IofA, Cambridge) B. Schaefer (Yale) P. Ruiz-Lapuente (Univ of Barcelona) H. Newberg (Fermilab) C. Pennypacker Brian Schmidt (ANU) Nick Suntzeff, Bob Schommer, Chris Smith (CTIO) Mark Phillips (Carnegie) Bruno Leibundgut and Jason Spyromilio (ESO) Bob Kirshner, Peter Challis, Tom Matheson (Harvard) Alex Filippenko, Weidong Li, Saurabh Jha (Berkeley) Peter Garnavich, Stephen Holland (Notre Dame) Chris Stubbs (UW) John Tonry, Brian Barris (University of Hawaii) Adam Reiss (Space Telescope) Alejandro Clocchiatti (Catolica Chile) Jesper Sollerman (Stockholm) ASTR378 Cosmology : IX. The Cosmological Constant 101

7 The Accelerating Universe What else could make the SNe Ia at high z too faint? Dust? Are today s SNe the same as those at z~1? Are the various observational corrections (e.g., K-correction) causing systematic errors?...? Eleven years later, however, the general consensus is that the SN Ia data are best fit by an accelerating expansion, parameterised as ASTR378 Cosmology : IX. The Cosmological Constant 102

8 Adding to the Mix Can define a density parameter for, Ω : Ω Λ = Λc 2 ; Ω + Ω 3H 2 Λ 1 = kc 2 a 2 H 2 So, to have a flat Universe: open Universe: closed Universe: Ω + Ω Λ =1 0 < Ω + Ω Λ <1 Ω + Ω Λ >1 ASTR378 Cosmology : IX. The Cosmological Constant 103

9 Ω vs Ω ASTR378 Cosmology : IX. The Cosmological Constant 104

10 as a Fluid We can define as a fluid with energy density and pressure P. Rewriting the Friedmann Equation: ρ Λ Λ 8πG H 2 = 8πG 3 Rewriting the Fluid Equation: a ρ Λ + 3 a ρ + P Λ Λ c 2 ( ρ + ρ ) Λ kc 2 a 2 = 0 P Λ = ρ Λ c 2 since is constant by definition. has a negative effective pressure: as the Universe expands, work is done on the fluid, so energy density can remain constant even though a increasing ASTR378 Cosmology : IX. The Cosmological Constant 105

11 Equations of State Revisited Friedmann Equation, Fluid Equation, Acceleration Equation: 2 a + kc 2 = 8πG a a 2 3 ρ ; a ρ + 3 a ρ + P a = 0 ; c 2 a = 4πG ρ + 3P 3 c 2 Equation of State: P = P( ), for cosmological components can write in the form P = w (w dimensionless) For non-relativistic gases, w <v 2 >/3c 2 << 1 For photons and relativistic gases, P rel = 1/3( rel ) ; mildly relativistic gases have 0 < w < 1/3 A cosmological constant has w < 0, e.g., w=-1/3 ( dark energy ; experimentally w appears to be ~ -1 ASTR378 Cosmology : IX. The Cosmological Constant 106

12 ASTR378 Cosmology : IX. The Cosmological Constant 107

13 Living with Current observational constraints on Ω mat and Ω from three different sources: Type Ia supernovae (SNe, blue) Sound waves in the Cosmic Microwave Background (CMB, orange) Large-scale structure in the distribution of galaxies (Baryon Acoustic Oscillations=BAO, green) They all overlap at the same location (!) They all overlap where Ω mat + Ω 1 (!); best guess Ω mat ~ 0.3, Ω ~ 0.7 From Kowalski et al Contours: 68.3%, 95.4% and 99.7% confidence levels k < 0 k > 0 ASTR378 Cosmology : IX. The Cosmological Constant 108

14 So What is? What has an energy density that remains constant as the Universe expands or contracts? One idea: vacuum energy the energy density of virtual particle pairs that appear and annihilate each other in empty vacuum Vacuum energy would not be affected by the expansion of the Universe, so vac would be constant with time and independent of the expansion / contraction of the Universe However, the expected vacuum energy density has not been successfully calculated one guess is the Planck energy E P per Planck volume (l P3 ), but this yields vac ~ ev m -3, roughly 124 orders of magnitude > crit!...? ASTR378 Cosmology : IX. The Cosmological Constant 109