Observing Quantum Gravity in the Sky

Transcription

1 Observing Quantum Gravity in the Sky Mark G. Jackson Instituut-Lorentz for Theoretical Physics Collaborators: D. Baumann, M. Liguori, P. D. Meerburg, E. Pajer, J. Polchinski, J. P. v.d. Schaar, K. Schalm, E. Sefussati, X. Siemens, A. Yadav, 57 others National High-Energy Theoretical Physics Seminar March 26, 2010

2 The Crisis and Opportunity of Modern Cosmology Crisis: Cosmological observables sensitively depend upon high-energy physics, which are unknown. Crisis and opportunity are the same word. A. Einstein Opportunity: Use cosmological observables to learn about high-energy physics, which are unknown. This is a crisitunity. H. Simpson

3 Outline The Transplanckian Opportunity Power Spectrum Non-Gaussianity Polarization Cosmic (super)strings

4 Inflationary Cosmology Inflationary theory solves the flatness, monopole and horizon problems (Guth, Albrecht, Steinhardt, Linde ʻ81-ʼ83) Assuming V is sufficiently flat, the classical solution is This also implies that quantum fluctuations are responsible for all matter in the universe, i.e. why we are here to observe it Ideally an inflation model is embedded in a quantum theory of gravity, such as superstring theory. There have been several models inspired by string theory, such as DBI, KKLMMT, etc. We need a way to test these theories

5 The Cosmic Microwave Background CMBPol (2020?)

6 The Transplanckian Opportunity: Sensitivity to High Energies Though the observed fluctuations currently have low energy, they were once very high: p = k / a(t) Thus CMB observables should be sensitive to new physics at some ʻTransplanckianʼ scale M. Dimensional analysis suggests that these modifications to low-energy observables must scale as (H/M) n. Scale of inflation Scale of new physics

7 First Observable: The Primordial Power Spectrum The power spectrum is simply the 2-pt correlation function of inflaton field fluctuations: (Naively) interpreting this as a propagator, we expect that it encodes high-energy physics via virtual heavy χ-particles: δφ δφ <δφδφ> <χχ>

8 Inflaton Field Effective Action Consider the effective action for φ: The freezeout scale is p=h, thus the 2-pt function is Only even powers of p are allowed in S eff, so we have an expansion in (H/M) 2. Which is disastrous, since H/M ~ 0.01 (Burgess, Cline, Easther, Greene, Lemieux, v.d. Schaar, Schalm, Shiu, Kaloper, Kinney, Kleban, Lawrence, Shenker)

9 A Possible Solution: Vacuum State Modification Fortunately, there appears to be a loophole (Easther, Greene, Kinney, v.d. Schaar, Schalm, Shiu). First, note that this is not an in-out scattering amplitude, but rather an in-in correlation: Second, we need to specify this initial state. Previous analysis assumed a Bunch-Davies vacuum, De Sitter space allows for more general vacua:

10 Effect of Vacuum Choice on Power Spectrum The excited vacuum will add an oscillating term to the power spectrum, These ʻwigglesʼ are expected to be a generic, model-independent feature of quantum gravity, with all new physics encoded in β. P s (k) Easther, Greene, Kinney, Shiu ʻ01 Standard powerlaw result Transplanckian signal of order β ln k

11 General Vacuum Construction Procedure We (MGJ, Schalm ʻ10) have recently made progress in this direction. Note that a final state contains both light (observable) and heavy (unobservable) states: Correlation requires summing over all initial heavy states: Note that this summation is present in all backgrounds, but only in expanding backgrounds will the energy scales mix, allowing interaction

12 An Example Consider a heavy field χ coupled to the inflaton, as in The power spectrum is then simply a sum over χ-vacua, Note that this cannot be factored into an effective action for φ, and necessarily implies a modified φ -vacuum (MGJ, Schalm ʻ10)

13 Effective Action vs Vacuum State Corrections Effective Action Corrections: Virtual χ-exchange Vacuum Corrections: Real χ-exchange Stationary phase at u = 1/2k, when pair production occurs (MGJ, Schalm ʻ10) This is exactly the form we expected (and desired)! Unfortunately, there are two vertices, and most of the effect gets washed out by loop integration. Work in progress...

14 Second Observable: Non-Gaussianity We may then consider the 3-pt correlation, k 3 k 2 k 1 A free field theory will produce a vanishing 3-pt correlation, and so ng measures interactions: (Creminelli ʻ03) Very small Adding Potentially very large The shape of the momenta triangle indicates when it was produced (Babich, Creminelli, Zaldarriaga ʻ04) and can serve to easily differentiate models (eg Khoury and Piazza ʻ08)

15 Types of Non-Gaussianity WMAP7: Enfolded: modified vacuum Equilateral: derivative interactions Squeezed: local interactions

16 Constraining DBI Inflation Non-Gaussianity in the Dirac-Born-Infeld (DBI) model is parametrically larger than the slow-roll case due to the nonstandard kinetic term: (Alishahiha, Silverstein, Tong ʻ03, ʻ04; Chen ʻ04, ʻ05) This has an infinite set of corrections: This produces a lower bound on the equilateral ng: making the model experimentally falsifiable:

17 Running ng in DBI Inflation In DBI models c s may change over evolution, varying ng at different times and thus scales, We must also allow for dependence upon the overall scale of the triangle, analogous to the power spectrum running:, If the running is extreme, a constant ng-template could evade detection by CMB.

18 Bounds on ng Scale-dependence n NG =0.6 n NG =0.2 Previous bounds on ngrunning were from galaxy cluster number counts (LoVerde, Miller, Shandera, Verde ʻ07). n NG =0 Future CMB experiments This can be greatly strengthened by combining LSS data with future CMB data, probing vastly different scales k p = 0.04 Mpc -1

19 Bounds on ng Scale-dependence Complete analysis of the WMAP, Planck, and CMBPol experiments, for both local and equilateral templates, at several fiducial values of f NL, n NG 1σ constraints on f NL equil (Sefusatti, Liguori, Yadav, MGJ, Pajer ʻ09)

20 Constraining Inflation Models from the Running of ng For the UV DBI models, The non-gaussianity is We can now constrain certain models: (Sefusatti, Liguori, Yadav, MGJ, Pajer ʻ09)

21 Extreme non-gaussianity: DBI Models with Modified Vacua Both modified vacua and DBI models have been presented, each producing large ng Now letʼs combine them: there are two reasons for considering such a combination: 1. Effective Hubble Horizon is H/c s, making the Transplanckian magnitude H/Mc s. 2. DBI models are effective low-energy theories, which should generically yield modified initial states. Meerburg, v.d. Schaar, MGJ ʻ09

22 General Small-c s Models Letʼs consider a more general class of small-c s models, DBI is just a special case, Meerburg, v.d. Schaar, MGJ ʻ09

23 Extreme non-gaussianity: Small c s with Modified Vacua The ng will be multiplied, since this is equivalent to particles interacting strongly since early times: Modified initial state Cutoff time Huge enhancement, p ~ (10 3 ) 3 Mixing of positive and negative frequency modes, ~ k 3 =k 1 +k 2 -k 3, etc Meerburg, v.d. Schaar, MGJ ʻ09 Oscillating function ~ which peaks near k j =0

24 Constraining Small-c s Models We must project our signal onto the ʻequilateralʼ, ʻorthogonalʼ, and ʻlocal templates (Babich, Creminelli, Zaldarriaga ʻ04; Furgesson and Shellard ʻ08; Senatore ʻ10) This lets us use the existing bounds on f NL local, f NL equi, f NL ortho to constrain this type of ng: Opposite of intuition Meerburg, v.d. Schaar, MGJ ʻ09

25 Constraining Vacuum Modification Bounds from Power Spectrum (Flauger et al ʻ09) Local template projection: Orthogonal template projection: Meerburg, v.d. Schaar, MGJ ʻ09

26 Third Observable: CMB Polarization Sourced by scalar and tensor perturbations Sourced by vector and tensor perturbations Motivates the need for a polarization-dedicated experiment: CMBPol Utility studied in NASA/Fermilab White Paper (Baumann, MGJ, 57 others ʻ08) Conclusion: Polarization can differentiate between competing inflation models based on two criteria: 1. Scale of inflation, 2. Distance the inflaton traversed.

27 1. Scale of Inflation The scale of inflation is directly proportional to r,, Sensitivity to r ~ 0.01 is the goal of CMBPol A detectably large tensor amplitude would demonstrate that inflation occurred at a very high energy scale, comparable to GUTs, implying we should see Transplanckian effects in the power spectrum

28 2. Traversal of the Inflaton The tensor-to-scalar ratio is also related to the evolution of the inflaton field (Lyth ʻ96; Baumann and McAllister ʻ06), The total field excursion is then This is important because effective actions take the form And so we would not trust anything more than Δφ ~ Λ/γ. In particular, string-based models where Δφ is the brane translation in the compact dimensions cannot produce Δφ > M pl or so. A detection of large r excludes most stringy models! Is there a fundamental reason for this? Work in progress.

29 Categorizing Single-Field Slow-Roll Inflation Models Consider a simple model, Define so that Thus there is a direct relationship between these two parameters and the first three derivatives of the potential (recall that r also gives V): We can use this to categorize models on 3 criteria:

30 Limiting Model Parameter Space Using CMBPol 1. Models predict either red (n s < 1) or blue (n s > 1) spectra, 2. Models have positive (η > 0) or negative (η < 0) curvature at the time when CMB scales exit the horizon, 3. Models are of the large-field (Δφ > M pl ) or small-field (Δφ < M pl ) type according to the total field excursion during the inflationary phase WMAP 5-year data Baumann, MGJ, 57 others ʻ08 Baumann, MGJ, et al. ʻ08 CMBPol Low-Cost proposal with pessimistic foreground subtraction

31 Fourth Observable: Cosmic (Super)strings Cosmic strings form when a U(1) symmetry is broken during reheating and are common in stringy and nonstringy models of inflation. Most important quantity is Gµ, G ~ M pl -2, µ ~ scale of symmetry breaking. The CMB power spectrum has ruled out cosmic strings as the major source of structure formation, but Bevis, Hindmarsh, Kunz, Urrestilla ʻ07 find a 10% contribution from strings with Gµ ~ 4-6 x 10-7 yields a better fit at l < 1000 with WMAP3 data.

32 Cosmic Strings as a source of B-mode Polarization Cosmic strings source vector modes very efficiently (Seljak, Pen, Turok ʻ97; Battye ʻ98) and could be a major source, if not the major source, of B-mode polarization Will be measured soon by QUaD, BICEP, EBEX, QUIET, PolarBearR, etc. CMBPol could be sensitive to much lower Gµ ~10-9 (Seljak and Slosar ʻ06). Low-l signal has Gµ ~ 1.6 x 10-7 r High-l signal has similar amount of <BB> even if <TT> cs /<TT> inf ~ 0.03 Pogosian, Wyman ʻ07

33 Distinguishing Types: Cosmic String Collisions When strings collide, two things can happen: reconnection: probability P nothing: probability 1-P Gauge theory strings always reconnect for v < v c ~ c (Shellard ʻ87; Matzner ʻ89; Achúcarro and de Putter ʻ06). String theory reconnection is probabilistic (Polchinski ʻ88; MGJ, Jones, & Polchinski ʻ04; MGJ ʻ07)

34 Calculating P for Cosmic superstrings These are calculated from first principles in string theory, representing the straight incoming strings as winding modes on a large torus of some relative angle θ: (MGJ, Jones, Polchinski ʻ04; MGJ ʻ07): Calculations done in type 0 string theory so that we can use wound tachyon modes to represent straight incoming cosmic strings:

35 Calculating P for Cosmic superstrings It does not matter which particular final kinked configuration these straight wound strings scatter into, so we sum over all of them: P = (kinematic factors) x The probability of reconnection is: So we expect P ~ Less reconnection means more string, and more gravity waves produced for detection by <BB> or gravitational wave detectors.

36 Measuring P(θ,v) As the kinks accumulate, there is a recorded history of all interactions the strings has undergone By measuring the distribution of kink angles, we can determine P(θ,v) θ 1 θ 3 θ 5 θ2 θ 4

37 Conclusion The next few years will yield spectacular amounts of precision cosmological data. There are several key observables encoded in the CMB, each of which probes high-energy physics. Now is the ideal time to develop our understanding of how this new physics is encoded.