1. Dark Energy & Cosmic Horizons Pim van Oirschot

2. Table of Contents Part I: The standard model of Cosmology and its problems Part II: Cosmic Horizons Part III: Melia’s Horizon

3. The standard model of Cosmology and its problems Part I

5. The Cosmological Constant Problem The cosmological constant can be interpreted as the energy density of the vacuum Quantum Field Theory can predict a value for this energy density We can compare this value with the value inferred from astronomical observations The latter is 120 orders of magnitude smaller than predicted by Quantum Field Theory

6. The Expert’s Opinion Frank Wilczek The biggest and most profound gap in our current understanding of the physical world Sean Carroll One of the most perplexing issues in theoretical physics Michael Turner The biggest embarrassment in theoretical physics

7. Dark Energy A component that causes the expansion of the Universe to accelerate is referred to as Dark Energy The cosmological constant is just one possibility Dark Energy is characterised by its equation of state, w w = -1 for the cosmological constant

8. Cosmic Horizons Part II

9. Particle Horizon Harrison, Cosmology - 1981 Event Horizon

10. Horizons in an expanding Universe The Robertson-Walker line element is conformally equivalent to the Minkowski metric The conformal time can converge, depending on a(t) For the concordance model:

11. Conformal Convergence

12. The Hubble sphere Hubble’s law V = H D The Hubble sphere marks the distance beyond which V exceeds the speed of light, c We can see beyond the Hubble sphere

13. A Conformal Diagram

14. Melia’s Horizon Part III

15. A new type of “horizon” Observations should indicate that the equation of state of Dark Energy, w = -1/3 The Robertson-Walker line element should be written in static coordinates:

16. Notes on the “cosmic horizon” 1. 1. The “cosmic horizon” has been defined before by Hawking as the apparent horizon of the Universe 2. 2. We can see beyond the “cosmic horizon”, like we can see beyond the Hubble sphere

17. Another coincidence? Only in a Universe with Only in such a Universe, is c times the age t always equal to the “cosmic horizon”

19. Conclusions A number of outstanding, fundamental questions concerning the standard model of cosmology remain unsolved. Exploring the nature of Dark Energy might help us finding an answer to these questions The theory of Cosmic Horizons is not in disagreement with the existence of a non- zero cosmological constant