Theoretical implications of detecting gravitational waves

Transcription

1 Theoretical implications of detecting gravitational waves Ghazal Geshnizjani Department of Applied Mathematics University of Waterloo In collaboration with: William H. Kinney arxiv: [astro-ph.co] December 19, 2014 Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

2 Overview 1 Motivation: Are gravitational waves the smoking gun for Inflation? 2 The window of observability for primordial tensor modes 3 Freezing mechanism to produce tensor modes 4 Producing tensor power spectrum regardless of back ground cosmology 5 Number of e-folds is not enough for non-inflationary scenarios Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

3 What triggered the primordial fluctuations? There are different proposals! Planck Collaboration HH 2 Empirical evidence: scenarios but Inflation violate at least one of these 4 conditions: NEC, Cs 1 or ρ < MPL Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

4 Applying present observational constraints [Planck Collaboration] Basic Properties of Scalar Primordial perturbations I I I Nearly scale-invariant for 1 Mpc < λ < 3000 Mpc Adiabatic Super-Hubble at early times (1 Mpc 104 RH (zbbn )) Other constraints I Universe has become Radiation dominated by BBN ( T 1 MeV, z ) Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

5 In the following theoretical framework: 1 quantum field theory in 3 + 1D curved space time 2 Initial conditions: adiabatic vacuum 3 Conservation of energy in four dimensions (continuity equation) 4 Adiabatic perturbations We see that (GG and Ahmadi 2013, GG, Dizgah and Kinney 2011) There are infinite number of models that can do this! Any scenario but Inflation violates at least one of these conditions: NEC, C s 1 or ρ < MP 4! but violating these conditions may not be catastrophic... So what s next? Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

6 Can detection of primordial gravitational waves such as the one suggested by BICEP2 be more decisive? Empirical evidence: The alternative generically do not produce tensor modes. Inflationary models can produce tensor modes. Hence the statement: Detecting primordial gravitational waves is the smoking gun for Inflation Lets check out the merit of this statement and see in what sense this is the case Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

7 Sweet spot for potential detection [BICEP Collaboration] Detection of gravitational waves on large scales λ 580Mpc (comoving scale) P h Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

8 How does Inflation work? through freezing, it extracts tensor modes from vacuum fluctuations on small scales at early times! R H = 1 ah is the comoving Hubble radius Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

9 Freezing is needed to preserve the power The equation of motion for canonical variable v ( ) v k + k 2 a v k = 0. a h M pa Vacuum fluctuations : On small scales (k 2 a a ) amplitude decays ( ) k 2 [ ] 2 Pk h 4π 2 lp too small today! M p a aλ But on large scales (k 2 a a ), h k is conserved (v k a or h k const) Trick: make vacuum fluctuations go from (k 2 a a ) to (k2 a a ) before they decay Freezing! Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

10 Freezing freezing radius R fr R H 2 ɛ Modes have to cross this scale this Radius should shrink in comoving frame. The tensor power spectrum will freeze out with amplitude ( ) Pk h k 2 [ ] 2 4π 2 lp [1 + z fr (λ)] 2 M p a fr (k) λ Is inflation the only option: No! Transition from radiation universe, contracting scenarios, etc. For tensors it doesn t go in UV far enough Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

11 Number of e-folds in non-inflationary scenarios is not enough For λ 580Mpc (corresponding to l 150) P h k (1 + z fr ) 2. z 10 9 at Big Bang Nucleosynthesis! P h a lower bound on the number of e-folds of expansion between mode freezing and today: N tot = ln (1/a fr ) But in in a non-inflationary universe and ρ < M 4 p: N tot 122. (1) In expanding scenarios we need acceleration Contracting universe lose number of e-folds: N tot 122 N Contr Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

12 any other possibility for producing primordial tensor modes? Changing initial conditions? SKY IS THE LIMIT Topological defects Quantum gravity magics? in general h Horndeski theories: varying speed of sound Inflation or c T Hfr 2 > 10 M2 p Horava-Gravity: k3 ω k k + a 2 Λ 2 HL P h k Λ2 HL M 2 p The UV scale of the theory is Λ HL 10 5 M p but to make 580Mpc/a Λ HL we need again N tot (Inflation)! Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

13 Summary of Results for tensor Perturbations A tensor signal with amplitude P h for non-accelerating expansion histories (ɛ > 1) is not consistent within the framework of General Relativity In contracting alternatives, tensor modes cannot provides detectable signal. Tensor detectability in non-accelerating backgrounds for Honrndeski theories implies either a super-planckian energy density or superluminal propagation of gravitons. The scale of Horava-Gravity in the dispersion relation does not need to be super-planckian but setting adiabatic initial conditions for large scale modes requires super-planckian energy densities. Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14

14 The End Ghazal Geshnizjani (University of Waterloo) The smoking gun for Inflation December 19, / 14