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Deceleration Parameter I a Few Others… Definition 2017‐09‐17 Outline Covers chapter 6 in Ryden Cosmological parameters I Cosmological parameters II The most important ones in this course: An endless number of subpopulations can M: Matter be introduced if necessary… : Radiation R CDM: Cold dark matter or DE: Cosmological constant or dark energy bar: Baryons tot (or just ): Sum of the other s stars: Stars : Curvature (+1,0,-1) – related to tot CMBR: CMBR photons R0: Curvature radius of the Universe : Neutrinos wDE: Equation of state of dark energy H0: Hubble parameter at current time BH: Black holes -1 -1 (often expressed as h: H0=100h km s Mpc ) Robots: Robots (see exercises) t0: Current age of the Universe Deceleration parameter I A few others… Definition: 1 2017‐09‐17 Deceleration parameter II Cosmological distances I Acceleration equation Radiation, matter & Benchmark model: D(z) depend on cosmological parameters H0, M, etc. can be extracted from measurements of D(z) Acceleration! Problem: In an expanding and/or curved Universe, there are many ways to define D(z) Cosmological distances II Intermission: What is this? The proper distance is important for theoretical reasons, but impossible to measure in practice, since you cannot halt the expansion of space! In a static Euclidian (flat) Universe, these would all be equivalent – but in our Universe, they’re not! Luminosity distance I Luminosity distance II In a static, flat Universe, the brightness Why does the inverse square law of a light source is determined by not hold at cosmological distances? the inverse-square law. However, in an expanding and/or curved Universe, this is not the case. 2 2017‐09‐17 Luminosity distance III Luminosity distance IV Angular‐diameter distance I Luminosity distance V In a static, flat Universe, Flat, only Benchmark objects of a fixed length appear smaller if they are further away. In an expanding and/or dL Flat, matter only curved Universe, this is not the case. l 036 z Angular‐diameter distance II Angular diameter distance III Bizarre: After a certain redshift, distant objects start appearing larger in the sky – not smaller! Flat, only Problematic as a cosmological probe… No good standard rods/yardsticks have yet dA been discovered at cosmological distances Benchmark Flat, matter only 036 z 3 2017‐09‐17 How to use the luminosity distance as a Intermission: What’ s going on here? probe of cosmology • Standard candles: Light sources for which L can be derived through some independent means Standard candles must be observable at Standard candles I: Cepheid Variables substantial redshifts to be useful 10000 Luminosity Luminosity (Lsolar) 100 1 10 50 Time Period (days) Standard candles II: Supernovae Type Ia Suggestion for Literature Exercise: Gamma‐ray bursts as probes of cosmology Peak luminosity almost constant! -19 Absolute -17 magnitude -15 -12 0 100 300 Days after maximum May be detectable up to z~10 But: Are they good standard candles? 4 2017‐09‐17 The magnitude system I The magnitude system II In astronomy, one often measures the flux of light sourcs using photometry – i.e. the flux received within a well-defined filter Filter profiles Spectrum of light source The magnitude system III Luminosities are often given as absolute magnitudes, Complications I: K‐correction i.e. the apparent magnitude a light source of intrinsic For two identical objects at different z, a given filter luminosity L would have at a fixed distance of 10 pc probes different parts of the spectrum (and different physical processes) Low-z magnitudes cannot be directly compared to high-z magnitudes z=0 z=high Flux B Flux B Wavelength Wavelength Complications I: K‐correction Complications II: Dust extinction K-correction: An attempt to correct from observed (redshifted) to intrinsic (non-redshifted) spectrum What are these black stripes? Often a complicated function, based on assumptions about the shape of the source spectrum… 5 2017‐09‐17 Wavelength dependence of dust Wavelength dependence of extinction dust extinction II Before contact with dust After contact Flux with dust Wavelength Photons at infrared and radio wavelengths are less affected by dust than optical or ultraviolet photons are Extinction correction Intermission: What’s this? Supernova cosmology I Supernova cosmology II Supernova cosmology III > 0! Major breakthrough! 6 2017‐09‐17 2011 Nobel prize in Physics ”for the discovery of the accelerating expansion of the Universe through observations of distant supernovae“ Saul Perlmutter Brian P. Schmidt Adam G. Riess A few other probes of Combined constraints cosmological parameters Lecture 7 Benchmark model Lecture 9 M=0.3, =0.7 H =72 km s-1 Mpc-1 Suitable for 0 literature exercises Suggestion for Literature Exercise: Gravitational lensing Weak gravitational lensing Distortion of background images by foreground matter More on this also in the dark matter lecture… Unlensed Lensed 7 2017‐09‐17 The Big Rip I Dark energy and other alternatives Phantom energy with equation of state w <-1 Dark energy grows over time Alternative fate of the Universe in which currently bound structures will get disassembled in the future Suitable for literature exercises The Big Rip II Caldwell et al. (2003) 8.
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