Anisotropic signatures in cosmic structures from primordial tensor perturbations

Size: px

Start display at page:

Download "Anisotropic signatures in cosmic structures from primordial tensor perturbations"

Matthew Ferguson
5 years ago
Views:

1 Anisotropic signatures in cosmic structures from primordial tensor perturbations Emanuela Dimastrogiovanni FTPI, Univ. of Minnesota Cosmo 2014, Chicago

2 based on:!! ED, M. Fasiello, D. Jeong, M. Kamionkowski! arxive: !!!

3 Outline Inflation and all that Gravitational fossils in CMB and LSS TSS predictions from some inflationary models Conclusions

4 Inflation Era of accelerated expansion in the primordial Universe Mechanism for the generation of cosmological fluctuations Simplest realization: single-scalar field in slow-roll (SFRS): (~x, t )='(t)+ (~x, t ) Inflaton quantum fluctuations Ḣ H 2 2 MP V ' 1 V CMB and LSS perturbations

5 SFSR Inflation Scalar sector: = Ḣ ' Power spectrum: h ~k1 ~k2 i =(2 ) 3 (3) ( ~ k 1 + ~ k 2 ) 2 2 k 3 1 P (k 1 ) H 2 k n s 1, n s =1 4 2 P (k) 1 M P nearly scale-invariant

6 Tensor sector: ds 2 = a 2 ( ) d 2 +( ij + ij (,~x)) dx i dx j Power spectrum: transverse, traceless P H M P 2 k n T, n T Energy-scale of inflation!

7 Several directions to search for imprints of primordial GW, e.g. : CMB polarization (B-modes) Lensing effects from GW on galaxy distribution [Dodelson-Rozo Stebbins 2003, Schmidt-Jeong 2012, Dai-Kamionkowski-Jeong 2012,...], CMB [Cooray-Kamionkowski-Caldwell 2005, Dodelson 2010,...] and 21-cm fluctuations [Pen-Masui 2010, Book-Kamionkowski-Schmidt 2012]; Anisotropic effects introduced in the scalar power spectrum for CMB and LSS [Dai-Jeong-Kamionkowski ] primordial GW as tensor fossils

8 Fossils from the inflationary era primordial (scalar, vector or tensor) fields interacting with Inflaton the 3-p.f. of a long-wavelength fossil field with 2 short-wavelength scalar modes can be observable in the CMB or LSS as an anisotropic contribution to the scalar power spectrum Primordial tensor modes from the metric inevitably couple with the Inflaton: in some cases one may expect an anisotropic imprint from primordial GW in the scalar power spectrum QUADRUPOLAR asymmetry long-wavelength tensor mode [Dai-Jeong-Kamionkowski ] short-wavelength scalar modes observable patch

9 Squeezed limit for TSS correlators e.g. : L SFSR a 2 ij@ j h p ~ k1 ~k2 ~k3 i (3) ( ~ k 1 + ~ k 2 + ~ k 3 )B p (k 1,k 2,k 3 ) T S k 1 k 3 S k L k 1 k 2 ' k 3 k S k 2 Bp obs (k L,k S,k S )=B p (k L,k S,k S )+ 1 2 P (k L)P (k S ) p ijˆk Sˆk i j ln P (k s ln k s observed Bispectrum primordial Bispectrum [Pajer-Schmidt-Zaldarriaga, Dai-Jeong-Kamionkowski 2013] = B SFSR (k L,k S,k S ) (up to O 2 kl k S corrections)

10 Bp obs (k L,k S,k S )=B p (k L,k S,k S )+ 1 2 P (k L)P (k S ) p ijˆk Sˆk i j ln P (k s ln k s observed Bispectrum primordial Bispectrum = B SFSR (k L,k S,k S ) (up to O 2 kl k S corrections) single-clock models predict a very small (unobservable) tensor-scalar-scalar correlation [Pajer-Schmidt-Zaldarriaga 2013, Dai-Jeong-Kamionkowski 2013] models violating consistency conditions for single-clock inflation can predict observably large signals! [Inflation with non-bunch Davies initial states: Brahma-Nelson-Shandera 2013]

11 Consistency conditions in inflation h ~q ~p ~q P (q) ~p i 3+p i P (p)+... i h ij ~q ~p ~q ~p i P (q) = 1 2 ˆP ijkl l P (p)+... single-clock models of inflation, with perturbations that become constant at late times : long wl mode (q) only produces rescaling of background for the short wl can be derived from symmetries of the action (invariance under space diffs) (Justin Khoury s talk for inflation workshop, see also Lasha Berezhiani s talk) [Maldacena 2003, Creminelli-Zaldarriaga 2004, Goldberger-Hui-Nicoli 2013, Hinterbichler-Hui-Khoury 2014, Berezhiani and J. Khoury 2014, etc.... ] )

12 Consistency conditions in inflation h ~k1 ~k2 ~k3 i (1 n s )P (k L )P (k S ), k 1 = k L, k 2 ' k 3 = k S observation of a scalar-scalar-scalar correlation in the squeezed limit would rule out a very large class of inflationary models! h p ~ k1 ~k2 ~k3 i 1 2 P (k L)P (k S ) p ijˆk i Sˆk j ln P (k S ln k S, k 1 = k L, k 2 ' k 3 = k S Remember, for tensor-scalar-scalar: Bp obs (k L,k S,k S )=B p (k L,k S,k S )+ 1 2 P (k L)P (k S ) p ijˆk Sˆk i j S so just like for the scalar bispectrum, also tensor-scalar-scalar correlators are a powerful probe for ln P (k s ln k s

13 ccs can be easily violated, e.g., in multi-field models... Non-attractor single-field inflation: example of single-field model which violates ccs for scalar correlators non-attractor phase at the initial stage of inflation (t<t*) during the non-attractor phase curvature fluctuation is not conserved [Namjoo-Firouzjahi-Sasaki 2012, Chen-Firouzjahi-Komatsu-Namjoo-Sasaki 2013]

14 Non-attractor single-field inflation: t<t*: the field climbs up the potential until it stops a 6! [k ah] a 3 t>t*: field rolls back down constant, conserved super-horizon [Chen-Firouzjahi-Komatsu-Namjoo-Sasaki 2013]

15 TSS from Inflation with a non-attractor phase curvature fluctuation not conserved during non-attractor phase h i violates ccs (order k 0 L ) [Namjoo-Firouzjahi-Sasaki 2012, Chen-Firouzjahi-Komatsu-Namjoo-Sasaki 2013] tensor modes are conserved outside the horizon h i obeys ccs (order k 0 L ) interesting dependence from the transition time (t*) at order [ED, M. Fasiello, D. Jeong, M. Kamionkowski 2014] k 2 L

16 Solid Inflation S.Endlich, A.Nicolis, J. Wang 2013 Very different symmetry-breaking pattern than standard inflationary models e.g. EFTI of C. Cheung et al, 2008 = (t) time translation are broken, Goldstone mode π adiabatic perturbations Now Background quantities are space-dependent key fact h I i = xi Nevertheless, can recover homogeneity and isotropy by employing internal symmetries of the fields

17 Internal Symmetries { I I! I + ai! OJI hence the Solid nomenclature J Most general low-energy theory for three scalar fields obeying Poincare + the internal symmetries Building blocks B IJ I µ [B] [B 2 ] [B 3 ] L = F(,, ) [B] [B] Excitation about the background [..] = Trace curvature fluctuations, observables

Checks Inflating background X (sub)luminal propagation of fluctuations X Strong coupling scale above H X Observables Larger non-gaussianity and specific, very distinct shape-function S.Endlich, A.

18 Checks Inflating background X (sub)luminal propagation of fluctuations X Strong coupling scale above H X Observables Larger non-gaussianity and specific, very distinct shape-function S.Endlich, A.Nicolis, J. Wang 2013 Most relevant in our context Figure 1: The shape of non-gaussianities for our model, according to the standard conventions and definitions of ref. [4]. The non-standard nature of these model manifests itself also in the form of non-conserved both ζ, As for apparent contradiction number 2: In our model the role of the physical clock will be played by the metric. More precisely, it will be played by (gauge invariant) observables, made up of our scalars and of the metric, like for instance the energy density or the pressure. These can depend on time even for purely space-dependent scalar backgrounds, because in the presence of a non-trivial stress-energy tensor, the metric will depend on time, in a standard FRW fashion. Doesn t this correspond to a spontaneous breakdown of time translations too? At some level it is a matter of definition, but we will argue in sect. 4 that the operationally useful answer is no, in the sense that there is no associated Goldstone boson, and that one cannot apply to our case the standard construction of the e ective field theory of inflation as given in [2]. Formal considerations aside, our peculiar symmetry-breaking pattern has concrete physical implications, with striking observational consequences. For instance, it predicts a threepoint function for adiabatic perturbations with a shape that is not encountered in any other model we are aware of. Without going into details here, we display it in fig. 1 for the γ outside the horizon, i.e. violation of consistency conditions

19 Quadrupolar anisotropy P ( ~ k S ) p ( ~ k L ) = P (k S ) h i 1+Q p ij (~ k L )ˆk Sˆk i j S Q p ij (~ k L )= B cc(k L,k S,k S ) P (k L )P (k S ) p ij (~ k L ) smallest wavenumber probed by observ. Q hq ijq ij i = 4 15 Z k min S k min L k 2 L dk L apple Bcc (k L,k S,k S ) P (k L )P (k S ) 2 P (k L ) longest wavelength GW modes produced during inflation [Dai-Jeong-Kamionkowski 2013]

20 some implications of current bounds on quadrupole for n.a. and s.i. : non-attractor Inflation: the non-attractor phase must have ended no later than the time our current Universe exited horizon during inflation solid inflation: the quadrupole constraints reads Q 2 si = apple 5 18 FY Fc 2 L H MP 2 ln k min L H 1 0 apple 1 parameter space of solid inflation allows for values respecting quadrupole bounds and predicting (on smaller scales) an off-diagonal correlation [Jeong-Kamionkowski 2012] in the scalar power spectrum which can be at reach for LSS surveys! [ED, M. Fasiello, D. Jeong, M. Kamionkowski 2014] clustering-fossil signature

21 Conclusions correlations of a long-wavelength primordial tensor modes with 2 short-wl scalar fluctuations can generate anisotropic contributions to the scalar power spectrum for CMB/LSS an anisotropic signal can be the result of primordial GW in inflationary models evading consistency conditions: test for single-clock models 2 models that predict a violation of ccs in the tensor sector and/or in the scalar sector (solid inflation and inflation with a non-attractor phase) yet another indication that testing statistical isotropy for the scalar power spectrum can be very helpful for constraining inflationary models

Inflation Daniel Baumann

Inflation Daniel Baumann University of Amsterdam Florence, Sept 2017 Cosmological structures formed by the gravitational collapse of primordial density perturbations. gravity 380,000 yrs 13.8 billion yrs