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dark matter and dark energy
- 2. Estimating Matter Density and Dark Energy Density Parameters Using Type I a SNe Photometric Data from the Supernova Cosmology Project
- 3. What is the fate of the univer
- 4. CONTENT An introduction to the expanding universe and Hubble’s Law Causes of the expansion? Structure of the universe Standard candle: type I a supernovae Theoretical and observational analysis
- 5. An introduction to the expanding universe and Hubble’s Law
- 6. • Matter tells space time how to curve and curved space time tells matter how to move • More curved the universe the more the current expansion will halt • Lesser the curvature the more the expansion will continue • A universe composed only of normal matter cannot expand • It will collapse back on itself as a big crunch due to gravity • Einstein introduced cosmological constant in order to maintain a stable static universe
- 8. Galaxies are receding away from us with a velocity that is proportional to their distance from us HUBBLE’ S LAW V = H0 × d
- 10. HUBBLE PARAMETER (H0 ) • The fractional rate of change of scale factor with time • It is roughly the reciprocal of the age of the universe and the age increases with time • H0 of present universe is about 72 km/sec/parsec
- 11. RELATION BETWEEN REDSHIFT AND BETA (V/C) No galaxy can recede with a velocity greater than the velocity of light since v/c=1 is the upper limit
- 12. Causes of the expansion?
- 13. • Observations of the explosions of the type 1a supernovae • Dark energy responsible for driving an acceleration in the expansion of the universe • What is dark energy?
- 14. Structure Of The Universe
- 15. FRIEDMANN EQUATION 𝒂 𝒂 𝟐 = 𝟖𝝅𝑮 𝟑 𝝆 − 𝒌𝒄 𝟐 𝒂 𝟐 Important in understanding the expansion and different models of the universe a -scale factor which measures the universal expansion rate 𝒂 -change of scale factor ρ -cosmic density k -curvature constant which tell us about the geometry of the universe
- 16. EVOLUTION OF S CALE FACTOR FOR VARIOUS VALUES OF k When k = -1 𝒂 𝒂 𝟐 ~ 𝒄 𝟐 𝑹 𝟐 universe is described as an open universe When k = 0 𝒂 𝒂 𝟐 = 𝟖𝝅𝑮 𝟑 𝝆 universe is described as flat universe When k = 1 a= universe is described as closed universe
- 17. Critical density (𝛒 𝐜) Fate of the universe is governed by density (ρ) 𝛒 𝐜 is the critical density which is the average density of material in the universe for it to be flat 𝝆 𝒄 = 𝟑𝑯 𝟐 𝟖𝝅𝑮 :Open universe :Flat universe :Closed universe
- 18. Density Parameters Baryonic matter density parameter 𝝆 𝒄 − baryonic matter density Radiation density parameter 𝝆 𝜸 − radiation density Dark matter density parameter 𝝆 𝑫𝑴 − dark matter density Dark energy density parameter 𝛒 𝚲 - dark energy density
- 19. Flat universe (k = 0 ) Closed universe (k>0 ) Open universe (k< 0)
- 20. Standard candle: type I a supe
- 21. • Source that has a known luminosity • Type 1a supernovae STANDARD CANDLE A white dwarf star in a binary pair with a red dwarf accretes mass from the red dwarf until it reaches Chandrasekhar limit of 1.4 solar mass Core collapses due to gravitational pressure A violent explosion called type 1a supernovae occurs Same luminosity of explosion
- 22. RELATION BETWEEN DISTANCE MODULUS AND LUMINOSITY DISTANCE m - apparent magnitude which measures the observed brightness of an object from any point. M - absolute magnitude which gives the brightness of an object as seen from 10 parsecs away.
- 23. REDSHIFT LUMINOSITY DISTANCE RELATION 𝒅 𝑳 = 𝒄(1 + 𝒛) 0 𝒛 𝒅𝒛 )𝑯(𝒛
- 24. Ωm = 1 and ΩɅ = 0 matter dominated universe Ωm = 0.5 and ΩɅ = 0.5 Ωm = 0 and ΩɅ = 1 dark energy dominated universe
- 26. ANALYSIS OF RED SHIFT V/S DISTANCE MODULU GRAPH
- 27. The minimum value of χ2 equal to 228.8539 is got for 𝜴 𝒎 = 𝟎. 𝟐𝟕 and 𝜴 𝜦 = 𝟎. 𝟕𝟑 Best fit model of our universe containing 27% of matter (both baryonic and dark matter) and 73% of dark energy
- 28. When the density parameters are added (Ωm + ΩΛ), it turns out to be 1! The condition for our universe to be Flat
- 29. REFERENCE ● http://hubblesite.org/hubble_discoveries/dark_energy/detype_ia_superno vae.php ● http://curious.astro.cornell.edu/about-us/85theuniverse/supernovae/gene ralquestions/404howdo- supernovaeshowusthattheuniversesexpansionisacceleratingadvanced ● https://www.universetoday.com/37105/fateoftheuniverse/ ● http://discovermagazine.com/2013/may/12whatdoesdarkenergymeanforthefateoftheuniverse ● https://www.eeducation.psu.edu/astro801/content/l10_p9.html ● http://www.smithsonianmag.com/sciencenature/darkenergythebiggestmysteryintheuniverse9482130/ ● http://www.sciencemag.org/news/2016/07/attemptexplainawaydarken ergytakeshit ● http://blogs.discovermagazine.com/cosmicvariance/2006/01/11/evolvingdarkenergy/#.WPmCVJThXqA ● https://en.m.wikipedia.org/wiki/Supernova_Cosmology_Project