STTPWKSP-PSahoo ppt for modified gravity

Presentation

1. STTP-Applied Mathematics in Science and Engineering KJCOEMR, Pune Dr. Parbati Sahoo Assistant Professor Dept. of Mathematics, Bhadrak Autonomous College, Odisha. Email: [email protected] Modified gravity theories and its cosmological implications

2. contents: Relativity and Cosmology Background Mathematics Standard Cosmological model Modified gravity theories Cosmological models in the framework of modified gravity theories

3. Relativity and Cosmology General Relativity is the theory of gravity proposed by Einstein in 1916, that supercedes the Newtonian theory of gravity which dates back to the seventeenth century. General Relativity forms the basis for the disciplines of cosmology (the structure and origin of the Universe on the largest scales) and relativistic astrophysics (the study of galaxies, quasars, neutron stars, etc.), and has led to a number of dramatic predictions concerning the physical world: We wish to derive, and then solve, the equation governing the evolution of the entire Universe. This is possible because, on large scales, the Universe is homogeneous and isotropic, and therefore allows for a simple mathematical description.

4. Principle of relativity not a new idea! Basic concepts of special relativity …an idea whose time had come… Basic concepts of general relativity a genuinely new idea Implications for cosmology Curved spacetime and implications for cosmology General Relativity implies spacetime is curved in the presence of matter since universe contains matter, might expect overall curvature (as well as local “gravity wells”) how does this affect measurements of large-scale distances? what are the implications for cosmology?

5. Background Mathematics Differential geometry Tensor Calculus Lie algebra Differential Equation Statistics Numerical Simulations

6. Curved spacetime Curved Spacetime:

7. 3D curved spacetime

8. first wave crest next wave crest

9. Note: in general relativity universe can be infinite (if k = −1 or 0) or finite but unbounded (if k = +1) universe can expand or contract (if overall scale factor a ( t ) is not constant) if universe expands or contracts, radiation emitted by a comoving source will appear redshifted or blueshifted respectively 20 th century: birth of observational cosmology Hubble’s law ~1930 Development of astrophysics 1940s – 1950s Discovery of the CMB 1965 Inflation 1981 CMB anisotropies: COBE ~1990

10. Expanding Universe Hubble’s law ~1930 from antiquity Universe had been assumed to be static relativity naturally expects universe to expand or contract, but very few people took this literally Alexander Friedmann Georges Lema ître not Einstein! expansion eventually discovered by observation The expanding universe At z << 1 all cosmological models expect a linear behaviour, z  d first evidence: Edwin Hubble 1929

11. Relativistic models General relativity allows one to calculate the behaviour of space-time in the presence of mass-energy R S

12. relativistic form

13. Modified gravity theories

14. Go through the google scholar link given below for more details on cosmological models in the framework of modified gravity theories. https://scholar.google.com/citations?user=iXPGeIcAAAAJ&hl=hi&oi=ao