In collboration with: Rachel Bean, Alejandro Aviles
G.Valogiannis & R. Bean, Phys. Rev. D 99, 063526 (2019), arXiv: 1901.03763
G.Valogiannis, R. Bean & A. Aviles, submitted to JCAP (2019), arXiv: 1909.05261

Georgios Valogiannis
Cornell University

V. Springel et al. (2006)

Cosmic Controversies
ChicagoOctober 8th, 2019

Peacock et al. 2001

Cosmological tests of modified gravity theories• Modified gravity (MG) could be responsible for cosmic acceleration
ModifiedDar

Dark energy?

Gravity?
Λ?

• MG-ΛCDM degeneracy broken in large scales• Modeling structure formation in MG necessary• Full MG N-body sims are computationally expensive, due to non-linear screening• Motivates analytical predictions for statistics of:• Biased tracers of underlying dark matter density field (N. Kaiser, 1984)• Redshift Space Distortions (RSD) in galaxy clustering (N. Kaiser, 1987, G. Efstathiou et al., 1988)

Halo formation in chameleon MG• Density spherical collapse threshold now depends
on mass & environment 𝛿"# = 𝛿"# (M, 𝛿$%& , 𝑧 )• B. Li & G. Efstathiou (2012), L. Lombriser et al. (2013)• Birkhoff’s theorem violated in MG

F4F5f(R) Hu-Sawicki,
2007
F6

Valogiannis & Bean (2019), arXiv: 1901.03763

Halo formation in chameleon MG• Density spherical collapse threshold now depends
on mass & environment 𝛿"# = 𝛿"# (M, 𝛿$%& , 𝑧 )• B. Li & G. Efstathiou (2012), L. Lombriser et al. (2013)• Birkhoff’s theorem violated in MG

F4• Halo mass function not universal for all MG models
F5f(R) Hu-Sawicki,
2007
F6

Valogiannis & Bean (2019), arXiv: 1901.03763

Peak-Background Split Lagrangian biases in MG• Peak-Background Split (PBS) formalism for bias
• N. Kaiser (1984), J. Bardeen et al. (1986), H. J. Moet al. (1997), F. Schmidt et al. (2013)• Needs to be adapted in MG• PBS Lagrangian biases in MG• 𝑏*+,< 𝑏*,- , in agreement with simulations by C. Arnoldet al., (2018)
f(R) Hu-Sawicki,(2007)

Valogiannis & Bean (2019), arXiv: 1901.03763

2-point correlation function for halos in MG
Theory:• f(R) (chameleon)
Hu-Sawicki, 2007

z=1GR

• nDGP (Vainshtein)G. Dvali et al. 2000
N-body simulations:• f(R) Lightcone project:• z=1, L=1536 Mpc/h• 3 mass bins
• C. Arnold et al. (2018)• f(R) & nDGP ELEPHANT sims:• z=0.5, L=1024 Mpc/h• 1 mass bin• M. Cautun et al. (2017)

Theory matches Nbody data
across mass bins

Valogiannis & Bean (2019), arXiv: 1901.03763

MG

Necessary ingredients to model RSD in MG• Real-to-redshift space mapping• Scale-dependent Gaussian Streaming model (GSM) ✓(B. Reid & M. White, 2011, L. Wang et al. 2013)

RedshiftspaceRealspace

GSM ingredients in MG• Real-to-redshift space mapping• Scale-dependent Gaussian Streaming model (GSM) ✓(B. Reid & M. White, 2011, L. Wang et al. 2013)• GSM ingredients• Real-space ξ(r) for biased tracers in MG ✓• Pairwise velocity 𝒗𝟏𝟐 (𝒓) for biased tracers in MG• Dispersion 𝝈𝟐𝟏𝟐 (𝒓) for biased tracers in MG7• Model 𝑣*7 (𝑟) & 𝜎*7(𝑟) using LPT• Ψ̇ ≠ 𝑓 𝐻 Ψ in MG – scale-dependence!!

Pairwise velocity (v) model matches sims well
Theory:• f(R) (chameleon)
Hu-Sawicki, 2007
• nDGP (Vainshtein)
G. Dvali et al. 2000
N-body simulations:• f(R) Lightcone project:• z=1, L=1536 Mpc/h• 3 mass bins
• C. Arnold et al. (2018)• f(R) & nDGP ELEPHANT sims:• z=0.5, L=1024 Mpc/h• 1 mass bin• M. Cautun et al. (2017)

Valogiannis, Bean, Aviles (2019)arXiv:1909.05261

Accurate monopole predictions across MG
modelsz=0.5

Valogiannis, Bean, Aviles (2019)arXiv:1909.05261

Accurate quadrupole predictions across MG
modelsz=0.5

Valogiannis, Bean, Aviles (2019)arXiv:1909.05261

Summary• Accurate modeling of 2-point statistics for biased tracers in MG• Valogiannis & Bean, 2019 , arXiv:1901.03763, Phys. Rev. D 99, 063526• In redshift space: Gaussian Streaming Model in MG• Valogiannis, Bean & Aviles (2019), arXiv:1909.05261, submitted to JCAP
• Bias & RSD simultaneously modeled in MG for the first time!

• Great agreement (monopole & quadrupole) for variety of MG models withdifferent amounts of screening, screening mechanisms, and mass ranges.
• Flexible analytical model• Can be applied to any scalar-tensor theory

In collboration with: Rachel Bean, Alejandro Aviles
G.Valogiannis & R. Bean, Phys. Rev. D 99, 063526 (2019), arXiv: 1901.03763
G.Valogiannis, R. Bean & A. Aviles, submitted to JCAP (2019), arXiv: 1909.05261

Thank you!

Accurate predictions across different mass bins
z=1

z=1

Accurate
bias
predictions!

3 halo-massbins

Valogiannis. Bean, Aviles(in prep.)Modeling velocity dispersion (s2)+ shift
z=1

z=0.5

• Non-linear contributions to s2 not fully
captured by LPT.
• Usually well-modeled by a constantoffset for all r(B. Reid & M. White, 2011, L. Wang et al.
2013)• Alternative uses EFT term based termin x(Z. Vlah et al. 2016)

Constant shift
added to matchlarge-scales• Constant calibrated off a single large
scale measurement then models
smaller scale effects.

Valogiannis. Bean, Aviles(in prep.)Necessary ingredients to model RSD in MG• Real-to-redshift space mapping ?

• “Direct” Lagrangian mapping to redshift space ✘• Plane-parallel approximation

𝑙=0

𝑙=2

redshift

realmapping|𝑓-D| = 10FG (F6) Hu-Sawicki model

Valogiannis et al. (in prep.)2-point correlation function results• Consistency for varying degrees of f(R) screening z=0.5 !

Valogiannis & Bean (2019)2-point correlation function results• Consistency for varying degrees of Vainshtein screening at z=0.5 !

Valogiannis & Bean (2019)

Power spectrum results

Valogiannis & Bean (2019)