Pursuing Signatures of the Cosmological Light Cone Effect or something else Yasushi Suto Department of Physics The University of Toyo
SDSS sample of galaxies
Non-trivial success of observational cosmology Tegmar et al. (004 3
So what s next? Precision cosmology, not yet? We have to move on; determine all the cosmological parameters within 0.% accuracy, for instance. For what? Really interesting? Can convince taxpayers? Beyond precision cosmology? Stop playing with the values of parameters,, but try to understand their meaning,, i.e., matter context in the universe Nature of dar matter and dar energy First objects in the universe initial conditions (physical model of inflation Revisit the cosmological observations in a more general framewor Equation of state of the universe Validity of the cosmological principle Validity of the general relativity on cosmological scales Or simply beyond cosmology itself! Anthropic principle, Extrasolar planet, something else 4
Precise age and mass of a person Sometimes it is essential to now the critical values Alcohol, driver s s license, Olympic sports, some attraction in the Disney land Otherwise it is unliely that we now our own weight within % precision, simply useless at all To be precise is not always appreciated, or even may be hated. Beyond some certain accuracy/precision, we need to convince ourselves why we need more? Especially if it costs a lot. 5
Cosmological light-cone effect A conventional view (e.g., Matsubara & (e.g., Matsubara & Suto 996; Yamamoto & Suto 998 Clustering of cosmological objects is sensitive to yet unspecified many factors Cosmological parameters Evolution of objects and bias In turn, a detailed comparison between predictions and observations constrains the values of such parameters (e.g., the next tal by Yahata An alternative view To chec if quasars are really at cosmological distance To chec if general relativity applies at high redshifts 6
Physical law vs. matter content in the universe 96 general relativity 97 cosmological term R Λ = 8 µν Rgµν gµν π GTµν 980 s vacuum energy R µν Λ Rgµν = 8π G Tµν gµν 8π G 990 s: decaying cosmological constant Λ=Λ(t 000 s : : dar energy p=wρ or even p=w(t w(tρ 000 s : : modification of gravity (physical law instead of assuming dar energy (matter content: modify the left- hand-side again! ~ Gµν = 8π GT µν 7
An example of attempts to loo at the old observations in a new framewor Constraining deviations from the Newtonian gravity on cosmological scales using SDSS galaxy power spectrum Shirata, Shiromizu, Yoshida & Suto to be submitted to Phys.Rev.D 8
Different attitudes in general relativistic cosmology standard precision cosmology framewor: general relativistic universe model cosmological observations parameter estimation: Ω b Ω Λ m h amazingly successful, but too conventional! It is time to as something beyond that. inversely, let us assume that we now the correct set of cosmological parameters, and then as how accurate is the Newtonian gravity? or more generally, attempt the accurate test of general relativistic predictions on cosmological scales. 9
Current constraints on deviations from Newton s law Consider the Yuawa-type deviation: m = m r V ( r G α exp r λ excluded (still allowed wea, if any, constraints on cosmological scales AU E.G. Adelberger et al. Ann.Rev.Nucl.Part.Sci. 53 (003 77 0
recent inspirations from brane world scenario cosmic acceleration induced by dar energy or by extra-dimension? material content in the universe vs. law of physics? an example: the DGP model; gravity leaing to extra dimensions modified Friedmann equation = H Ω z { } 3 Ω ( z Ω Ω Ω rc H 0 ( M rc rc 4r c H 0 modified Newton Potential V ( r G = γ r ( 4 r r ln O( r : r << rc ~ r c r π c H 0 Dvali, Gabadadze & Porrati, PLB 485 (000 08 Deffayet, Dvali & Gabadadze, PRD 65 (00 04403 in reality, barely indistiguishable from dar energy model
empirical constraints on deviations from Newton s law of gravitation using power spectrum of SDSS galaxies there is no established relativistic theory to predict the non-newtonian gravity an empirical modeling (Sealfon et al. astroph/0404 adopt the standard Friedmann model with dar matter and cosmological constant adopt the standard interpretation of CMB anisotropy as the initial condition for the primordial fluctuations assume scale-independent bias of SDSS galaxies different from Dvali et al. s model. fairly empirical rather specific. we are currently repeating the analysis on the basis of Dvali et al. s model
Yuawa-type additional gravitational potential = 3 ρ(r V ( r G d r α e r r rr λ Note that this is a bit different parameterization Gravitational force F(r G/r current model r/λ G(α/r small-scale: Newtonian gravity r << λ : V ( r G d 3 ρ(r r r r large-scale: G G(α r >> λ : V ( r G( α stronger (weaer gravity on large scales if α>0 (α<0 d 3 ρ(r r r r 3
Conclusion by Sealfon et al. astro-ph/0404 = 3 ρ(r V ( r G d r α e r r rr λ for the range of 5 h - Mpc <λ<50 h - Mpc dfgrs: SDSS: α = 0.0 α = 0.8.3.3.4.8 4
5 5 linear perturbation analysis Sealfon, Verde & Jimenez, astro-ph/0404 attempted exactly what we had planned to do, but unfortunately their analysis is not satisfactory in the following two respects they consider only the st-order term in α, although their final constraints extend even beyond α >! they incorrectly assumed that the perturbation solution is a function of the scaling variable s=a(t/λ, but this is not the case 0 ˆ / ( / ( 4 ˆ ˆ = Λ Λ d a a G d H d CDM CDM λ λ α ρ π & & && [ ] = = Λ λ α t a s s d t t CDM ( ˆ( ( (
our method (Shirata et al. 004 directly solve the linear perturbation equation under the modified Newtonian potential: && ( a / λ H & 4πGρ α ( / a λ = assuming the initial conditions of d ( aini =, CDM ( aini, da Λ = a= a d, ΛCDM da a= ini a ini 0 apply the nonlinear correction using the Peacoc-Dodd formula Still preliminary results! 6
7 7 exact solution in the Einsteinde Sitter model 0 / ( / ( 4 = λ λ α ρ π a a G H & && 4 4( 4 0 α λ ± = a 0 λ = 3 /, 4 9, 4 5 8 8 5, 4 5 8 8 5, 4, 4 5 8 8 5, 4 5 8 8 5 a F a C a F a C α α α α
Linear theory prediction: comparison with Sealfon et al. (004 Yuawa Λ CDM Shirata et al. (004 =30h - Mpc =0h - Mpc =5h - Mpc linear perturbation theory ΛCDM model, α= Before applying nonlinear correction Sealfon et al. (004 [h Mpc - ] 8
Nonlinear correction using the Peacoc-Dodds fit Yuawa Λ CDM Shirata et al. (004 with nonlinear correction =30h - Mpc =0h - Mpc Effect of nonlinear correction ΛCDM model α= =5h - Mpc [h Mpc - ] 9
Power spectrum: λ dependence (α= (=4π 3 P( α= =5h - Mpc =0h - Mpc =30h - Mpc α=0 Thic: Shirata et al. (004 Thin: Sealfon et al. (004 SDSS galaxies (Tegmar et al. 004 3 ρ(r V ( r = G d r α e r r rr λ Yuawa Λ CDM [h Mpc - ] 0
Power spectrum: α dependence (λ=0h - Mpc (=4π 3 P( =0h - Mpc α= α= α=- α=0 SDSS galaxies (Tegmar et al. 004 α=- = 3 ρ(r V ( r G d r α e r r [h Mpc - Thic: Shirata et al. (004 Thin: Sealfon et al. (004 ] rr λ
(Preliminary constraints on α and λ from SDSS galaxy P( = 3 ρ(r V ( r G d r α e r r rr λ excluded Allowed region from SDSS P( (<0.6hMpc - excluded α h 0.8 < Mpc b <. < λ < 30h Mpc Marginalized over λ and bias SDSS P( (<0.6hMpc - λ (h - Mpc Still preliminary! α α = 0. 0.9 0.8 Shirata, Shiromizu, Yoshida and Suto (004, in preparation
Summary and outloo The SDSS galaxy clustering can be used to constrain the possible deviations from the Newtonian gravity The current constraint may not yet be too restrictive to rule out a class of interesting possibilities Include fully nonlinear effect using N-body simulation to tighten the constraints Validity of hierarchical clustering ansatz in higher-order statistics We plan to repeat the analysis using a self-consistent (? model of cosmic expansion and local gravity law (e.g., Dvali et al. 000 as a specific example 3