1. THE LARGE SCALE CMB CUT-OFF AND THE TENSOR-TO-SCALAR RATIO Gavin Nicholson Imperial College London with Carlo Contaldi Imperial College London (astro-ph/0701783) Cosmo 07, University of Sussex 1 03 October 2015

2. Large Scale CMB Anomalies 03 October 2015 2 Large Scale Defects ‘Missing Power’ (Tegmark et al 2003, Contaldi et al 2003) A preferred axis (Land & Magueijo 2005, Copi et al 2006) C l ’s are different in different hemispheres (Eriksen et al 2004, Hansen 2004) Large scale features in the map are largely unaffected by WMAP1 to WMAP3 transition. What might be a cause of these defects? Foregrounds? Large-scale systematic errors? Topology? Unknown Physics?

3. Short Inflation Here we have ‘just enough’ inflation to produce what we see, and no more Models of inflation on the string theory landscape seem to predict a highly suppressed probability of long inflation (Freivogel et al. 06) Others (Gibbons and Turok 06) also argue that long inflation is unlikely Generically this produces a spectrum with a cut-off 3 (Tocchini-Valentini et al. 05)

4. Short Inflation 03 October 2015 4 Resultant spectra for TT is inconclusive as we are Cosmic Variance dominated one large scales Can we probe the pre-inflationary period? Aim: To use the BB power spectrum to ‘see’ pre- inflationary physics.

5. Pre-Inflationary Epochs Initially the kinetic energy of the inflaton is much greater than the potential energy – i.e.  ’  Includes scenarios with stochastic initial conditions Chaotic Inflation Inflation tunnelling from a stable landscape minima We start with a significant radiation energy density Kinetic energy of the inflaton is negligible These scenarios include models with ‘bouts’ of inflation interspersed with reheating periods 03 October 2015 5 Kinetic Dominated Regime (KD)Radiation Dominated Regime (RD)

6. Initial Conditions We chose two simple potentials V(  )= m 2   /2 and V(  )=  /4   = 18 and   = 24  0 ’ = 10m   We chose these initial values so the number of efolds obtained is approximately equivalent Choosing a simple potential V(  )= m 2   /2 We assume that the inflaton is already in the slow roll regime when the inflaton’s energy density begins to dominate. i.e.  0 ’ = 0   = 16 03 October 2015 6 Kinetic Dominated Regime (KD)Radiation Dominated Regime (RD)

7. Inflationary Perturbations (Outline) 03 October 2015 7 Perturb the FRW metric Recast the perturbations into the gauge invariant Mukhanov variable, u or v Plane wave expand the evolution equation for each wavenumber k giving us uk or vk This gives us oscillator equations with a time dependant mass Evolve these equations to late times until uk/a and vk/a become constant

8. The initial conditions for the u k modes can be set by taking the limit  ’ >>  and z ’’ /z ~ a ’’ /a, where So we get the solution Normalising so that we obtain correct adiabatic vacuum in the small scale limit Assumes modes larger than horizon at start of evolution were once much smaller (and approached the Bunch Davis vacuum) This is justified if for example, there was a previous inflationary stage. Initial Conditions 03 October 2015 8 Kinetic Dominated Regime (KD)

9. The initial conditions for the u k and v k modes again involve an assumption about the pre-inflationary physics The model we use is the same as in Powell and Kinney (astro-ph/0612006) which chooses the vacuum such that +ve frequency on all scales and asymptotes to the Bunch-Davis vacuum in the UV Initial Conditions 03 October 2015 9 Radiation Dominated Regime (RD)

10. Kinetic Dominated Results Tensor modes show the same suppression, however it is not as strong Thus r rises. Start evolution at fixed time and evolve until u k /a and v k /a have reached their constant values 03 October 2015 10

11. Why? 03 October 2015 11 Qualitatively the super horizon tensor modes are not suppressed as strongly In slow roll, P T /P S  ’ 2 Although this is only valid for small  ’, the scalar perturbation is always damped by an extra  ’  1/H ’

12. Radiation Dominated Results Again both scalar and tensor spectra show a cut-off Cut-off is almost identical in form Thus here r = const NOTE: This is due to different ICs for the kinetic term, it is quite insensitive to the exact choice of normalisation 03 October 2015 12

13. Is This Observable? 03 October 2015 13 Possibly! The difference between KD and RD ICs is pronounced in the amplitude of r Since this is effect is on large scales so we are limited by Cosmic Variance The next generation of CMB polarisation experiments will aim to survey the whole sky. Can these experiments distinguish between these scenarios and the standard cosmological model?

14. Hypothetical Experiment 80% sky coverage Sample variance limited for l < 100 n s = 0.967   differences No cut off and KD 5.03 No cut off and RD 8.17 The spectra are normalised so that the power at the first acoustic peak matches that of WMAP 03 October 2015 14

15. Detecting the Effect 03 October 2015 15 The dependence is degenerate with  (we have assumed  =0.9 ) However, this value will be fixed to high accuracies by E-mode and TE cross correlation spectra in such an experiment Thus it is reasonable to expect that this degeneracy will have been broken So the cut-off would show up as a mismatch between the  required by E and B

16. Conclusions 03 October 2015 16 Both KD and RD initial conditions modify the primordial power spectrum on large scales in ‘short inflation’ The scalar power spectra are similar, however there are important differences in the tensor spectra and hence the form of r To detect a drop in r on large scales requires many observational obstacles to have been overcome Can the naïve sample variance limited result be reached? Level of polarised foreground is yet to be determined If we have achieved this then its possible that this effect may be observed, however distinguishing between KD and RD initial conditions will be more difficult.