Santiago Casas
Cosmologist, Physicist, Data Scientist.
Next-generation forecasts for screened and unscreened models of modified gravity
Santiago Casas, TTK, RWTH Aachen University
With collaboration from Euclid TWG WPs 1-6-7 and more...
Cosmic Microwave Background
Planck 2018 CMB Temperature map (Commander) . wiki.cosmos.esa.int/planck-legacy-archive/index.php/CMB_maps
Large Scale Structure
Illustris Simulation: www.nature.com/articles/nature13316
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- LCDM is still best fit to observations.
- Concordance Cosmology:
- Combination of different observables.
- Lensing
- CMB
- Clustering
- Supernovae
- Clusters
Gμν+Λgμν=8πGTμν
G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi G T_{\mu \nu}
The Standard ΛCDM model
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- LCDM is still best fit to observations.
- Some questions remain:
- Λ and CDM.
- Cosmological Constant Problem:
O(100) orders of magnitude wrong
(Zeldovich 1967, Weinberg 1989, Martin 2012).
Composed of naturalness and coincidence
sub-problems, among others.
Quantum Gravity?
Gμν+Λgμν=8πGTμν
G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi G T_{\mu \nu}
The Standard ΛCDM model
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The Standard ΛCDM model
- ΛCDM is still best fit to observations.
- Some questions remain:
- H0 tension, now ~5σ
- σ8 - Ωm discrepancy at ~2σ
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Alternatives to ΛCDM
Ezquiaga, Zumalacárregui, Front. Astron. Space Sci., 2018
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Constraints on Theories
- Background is well constrained to be around w=−1
- Gravitational Wave speed = c
- Galaxy morphology and solar system
- Black holes
- Coupling to baryons
- Non-linear regime still pretty much unconstrained
- Fifth forces
- Neutrinos?
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Scalar field models
At lowest order in the perturbation of the scalar field φ≡ϕ−ϕ0
- Matter is coupled to the perturbed Jordan metric
- In the case of a cosmological-stress energy tensor and a non-negligible scalar field mass :
L2=2Z(ϕ0)(∂μφ)2+2mϕ2(ϕ0)φ2−δgμνδTμν
\mathcal{L}_2=\frac{ Z(\phi_0)}{2} (\partial_\mu\varphi)^2 +\frac{ m^2_\phi(\phi_0)}{2} \varphi^2 - \delta g_{\mu\nu} \delta T^{\mu\nu}
Review: Brax, Casas, Desmond, Elder, arXiv:2201.10817
Geff=(1+Z(ϕ0)2β2(ϕ0)e−m(ϕ0)r)GN
G_{\rm eff}=\left(1+ \frac{2\beta^2(\phi_0)}{Z(\phi_0)}e^{-m(\phi_0)r}\right) G_N
Yukawa term: Short range forces
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Screened Scalar fields
Different types of screening:
- Chameleon: The mass m(ϕ0) increases sharply inside matter
- Damour-Polyakov: The coupling β(ϕ0) vanishes inside matter
- K-mouflage and Vainshtein: Z(ϕ0)≫1
Geff=(1+Z(ϕ0)2β2(ϕ0)e−m(ϕ0)r)GN
G_{\rm eff}=\left(1+ \frac{2\beta^2(\phi_0)}{Z(\phi_0)}e^{-m(\phi_0)r}\right) G_N
Review: Brax, Casas, Desmond, Elder, arXiv:2201.10817
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Screened models
Z(ϕ0)=1+a(ϕ0)rc2mPl□φ+b(ϕ0)Λ4(∂φ)2+c(ϕ)Λ5□2φ+…
Z(\phi_0)= 1 + a(\phi_0) r_c^2 \frac{\Box\varphi}{m_{\rm Pl}} + b(\phi_0) \frac{(\partial \varphi)^2}{\Lambda^4}+ c(\phi)\frac{\Box^2 \varphi}{\Lambda^5}+\dots
As an effective field theory, the normalization factor can be expanded in a power series:
K-mouflage: first derivative term ∂φ/Λ2 dominates, which implies:
∣∇ΦN∣≥2β(ϕ0)mPlΛ2
\vert \vec \nabla \Phi_N \vert \ge \frac{\Lambda^2}{2\beta(\phi_0) m_{\rm Pl}}
Screening where Newtonian acceleration a=−∇ΦN large enough
Vainshtein: second derivative term □φ dominates, which implies:
∇2ΦN≥2β(ϕ0)rc21
\nabla^2 \Phi_N \ge \frac{1}{2\beta(\phi_0) r_c^2}
Screening where spatial curvature is large
When the □2φ dominates → massive gravity
Review: Brax, Casas, Desmond, Elder, arXiv:2201.10817
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Screened models
∇kΦN≳C
\nabla^k \Phi_N \gtrsim C
- Chameleon: k=0 (surface N. potential is large)
- K-mouflage: k=1 (N. acceleration is large)
- Vainshtein: k=2 (curvature is large)
To summarize, screening mechanisms can be characterized by the inequality:
For DE applications and under some assumptions:
- Chameleon screens everything above a certain potential threshold
- K-mouflage does not screen galaxy clusters
- Vainshtein screens all structures that turn non-linear
Review: Brax, Casas, Desmond, Elder, arXiv:2201.10817
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Examples of screened models
- Chameleon: f(R) Hu-Sawicki
- K-mouflage: k-essence + universal coupling
- Vainshtein: nDGP (3+1)d brane embedded in 5d
- Solar system and other local constraints and instabilities forbid self-acceleration in these models
- ΛCDM-like background
- Just one free parameter each
- Universal couplings
Review: Brax, Casas, Desmond, Elder, arXiv:2201.10817
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f(R) Hu-Sawicki model
Modification of the Einstein-Hilbert action
S=16πGc4∫d4x−g[R+f(R)]
\newcommand{\sg}{\ensuremath{\sigma_{8}}}
\newcommand{\de}{\mathrm{d}}
S = \frac{c^4}{16\pi G} \int{\de^4 x \sqrt{-g} \left[R+f(R)\right]}
Induces changes in the gravitational potentials *
*for negligible matter anisotropic stress
−k2Ψ=c44πGa2μρˉΔ
-k^2\Psi =\frac{4\pi\,G}{c^4} \,a^2\mu\bar\rho\Delta\,
−k2(Φ+Ψ)=c48πGa2ΣρˉΔ
-k^2\left(\Phi+\Psi\right) = \frac{8\pi\,G}{c^4}\,a^2 \Sigma \bar\rho\Delta
Scale-dependent growth of matter perturbations
Small changes in lensing potential
μ(a,k)=1+fR(a)11+3k2a−2mfR−2(a)1+4k2a−2mfR−2(a)
\mu(a,k) = \frac{1}{1+f_R(a)}\frac {1+4k^2a^{-2}m_{f_R}^{-2}(a) }{1+3k^2a^{-2}m_{f_R}^{-2}(a)}
Σ(a)=1+fR(a)1
\Sigma(a)=\frac{1}{1+f_{R}(a)}\,
Free parameter: fR0
f(R)=−6ΩDEH02+∣fR0∣RRˉ02
f(R) = - 6 \Omega_{\rm DE} H_0^2 + |f_{R0}| \frac{\bar R_0^2}{R}\,
Hu, Sawicki (2007)
"Fifth-force" scale for cosmological densities
λC=32Mpc∣fR0∣/10−4
Euclid: Casas et al (2022) in preparation
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f(R) as a scalar field theory
Veff(ϕ)=V(ϕ)+(A(ϕ)−1)ρ
V_{\rm eff}(\phi)= V(\phi) +(A(\phi)-1) \rho
g~μν=A2(ϕ,X)gμν+B2(ϕ,X)∂μϕ∂μϕ
\tilde{g}_{\mu \nu} = A^2(\phi,X) g_{\mu \nu} + B^2(\phi,X) \partial_\mu \phi \partial_\mu \phi
A(ϕ)=eβϕ/mPl
A(\phi)= e^{\beta \phi/m_{\rm Pl}}
dRdf=e−2βϕ/mPl
\frac{df}{dR}= e^{-2\beta \phi/_{\rm m_{Pl}}}
V(ϕ)=2mPl2(dRdf)2RdRdf−R
V(\phi)= \frac{m^2_{\rm Pl}}{2} \frac{ R \frac{df}{dR}-R}{(\frac{df}{dR})^2}
Universal coupling through a conformal transformation between Einstein and Jordan metrics
General Chameleon scalar models are given by specifying V and A
- With a coupling function:
- Map to a scalar field by:
- Carefully chosen potential can realize chameleon mechanism:
- Objects screened when:
ΦN≳23∣fR0∣
\textcolor{green}{\Phi_N\gtrsim \frac{3}{2}\vert f_{R_0} \vert}
Review: Brax, Casas, Desmond, Elder, arXiv:2201.10817
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f(R) Hu-Sawicki predicitons
Codes used: for linear perturbations: MGCAMB and EFTCAMB
Scale-dependent growth
Fitting formula for non-linear power spectrum:
Winther, Casas, Baldi, Koyama, Li (2019)
*Forge Emulator not available at time of first review
Euclid: Casas et al (2022) in preparation
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Scale-independent models
Euclid: WP1-WP6 et al (2022) in preparation
nDGP, K-mouflage and Jordan-Brans-Dicke have scale-independent growth
"Extreme cases" far away from LCDM and close to current upper bounds
Preliminary
Preliminary
nDGP: free parameter Ωrc (related to the transition scale)
KM: free parameter ϵ2 (related to the conformal coupling amplitude)
JBD: free parameter ωBD (related to the scalar coupling)
ReACT
HMCode
Halo+PT
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Scale-independent models
- K-Mouflage presents a large enhancement of the lensing potential
- Definitely detectable with next-generation WL observations
Preliminary
Euclid: WP1-WP6 et al (2022) in preparation
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Next-generation Galaxy Surveys
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DESI telescope
- 14 000 square degrees in the sky
- 30 million accurate galaxy spectra
- Redshifts: 0 < z < 2
- Quasars up to z~3.5
- 5 years of observation
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Vera Rubin Observatory
- Located in Chile, 8.4m telescope
- 20 billion galaxies
- Redshifts: 0 < z ~< 3
- 18,000 square degrees
- 11 years of observation
Santiago Casas, Oslo, 23.10.2020
Euclid Space Satellite
- Two instruments:
- VIS (visible photometer): shape and orientation of 1.5 billion galaxies!
- NISP (near infrared spectrograph): 30 million galaxy spectra!
- 15 000 square degrees in the sky
- 16 countries, ~1500 members
- ~170 Petabyte of data!
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Photometric cross-correlations
Euclid preparation: VII. Forecast validation for Euclid cosmological probes. arXiv:1910.09273
Also known as 3x2pt analysys
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Weak Lensing
Cijγγ(ℓ)=H0c∫E(z)r2(z)W^iγ(z)W^jγ(z)PΦ+Ψ(kℓ,z)dz
C_{ij}^{\gamma\gamma}(\ell) = \frac{c}{H_0}
\int{\frac{{\hat{W}}_i^\gamma(z) {\hat{W}}_{j}^\gamma(z)}{E(z) r^2(z)}
P_{\Phi+\Psi}\left ( k_{\ell}, z \right ) dz}
PΦ+Ψ=[3(cH0)2ΩM0(1+z)Σ(k,z)]2Pδδ
P_{\Phi+\Psi} = \left[3\left(\frac{H_0}{c}\right)^2\Omega_\mathrm{M}^{0} (1 + z) \Sigma(k,z) \right ]^2 P_\mathrm{\delta \delta}
The cosmic shear angular power spectrum depends on the Weyl spectrum (of gravitational potentials Φ+Ψ)
Which is related to the matter power spectrum (of density contrast δ) through
Information about background geometry, matter content and clustering
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Spectroscopic Galaxy Clustering
BAO
Clustering
RSD
Spec-z
Euclid preparation: VII. Forecast validation for Euclid cosmological probes. arXiv:1910.09273
Slides by Dennis Linde, RWTH
Spectroscopic Galaxy Clustering
For mildly non-linear scales we need to use perturbation theory
- SPT is not enough
- EFT smoothing over terms -> UV counterterms
(see previous talk by Filippo) - Already being implemented into MCMC and Fisher pipelines like CosmicFish and CLOE
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The Matter Power Spectrum
Current data:
Image: https://www.cosmos.esa.int/web/planck/picture-gallery
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The Matter Power Spectrum
Euclid:
Scales from: ~ 10−3 to 10 hMpc−1
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Euclid: IST:Forecasts
- Here: Flat w0waCDM
- GCsp+WL+GCph+XC
- Figure of Merit:
1257 - Non-flat FoM:
500
- Optimistic:
σw0=0.025
σwa=0.092
Euclid preparation: VII. Forecast validation for Euclid cosmological probes. arXiv:1910.09273
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Forecasts for f(R) from Euclid probes
Euclid: Casas et al (2022) in review
- Combined constraints from GCsp and Photo probes
Preliminary
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Forecasts for f(R) from Euclid probes
Euclid: Casas et al (2022) in review
- Combined constraints from GCsp and Photo probes
Preliminary
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Forecasts for f(R) from Euclid probes
Euclid: Casas et al (2022) in review
- Transform into original space
- Current LSS data: "just" upper bounds of the order of <10−4
Preliminary
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Forecasts for nDGP
Preliminary
- GCsp does not constrain the free parameter very well
- Most gain is at NL-scales for Photo probes
Euclid: WP1-WP6 et al (2022) in preparation
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Forecasts for K-Mouflage
Preliminary
- For KM1:
GCsp can constrain the free parameter at ~10% - Photo at ~1% (remember ΣWL )
- KM2 is basically ΛCDM, non detectable
Euclid: WP1-WP6 et al (2022) in preparation
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Bonus: Forecasts on parameterized MG
Casas, Pettorino, Camera, Martinelli, Carucci (in preparation)
Preliminary
- DESI+Rubin have similar power than Euclid alone (under many assumptions)
- Optical + Radio is also competitive and can remove systematics / degeneracies
- Constraints on μ,Σ of the order of ~5-10% under optimistic assumptions
- PPN-approach screening assumed
Santiago Casas, ADE Marseille, May 2022
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Conclusions
- Screening mechanisms can save scalar field models
- Current constraints don't allow for self-acceleration
- Screening mechanisms can be classified by the derivative order
- Euclid and next-generation surveys will be powerful probes for Cosmology.
- Primary LSS probes: Galaxy Clustering and Weak Lensing
- Many challenges ahead in non-linear modelling
- Next-generation surveys can constrain free parameters with percent precision accuracy
Thanks!
Merci!
Next-generation forecasts for screened and unscreened models of modified gravity Santiago Casas, TTK, RWTH Aachen University With collaboration from Euclid TWG WPs 1-6-7 and more...
Marseille-Seminar
By Santiago Casas
Marseille-Seminar
On the quest for Dark Energy with nonlinear observables in the era of Euclid
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