Santiago Casas
Cosmologist, Physicist, Data Scientist.
En búsqueda de la Energía Oscura con Euclid y experimentos cosmológicos de cuarta generación
Santiago Casas
Postdoctoral Researcher
TTK, RWTH Aachen University
La Vía Láctea
http://www.esa.int/Science_Exploration/Space_Science
El Universo Local
Laniakea: https://projets.ip2i.in2p3.fr//cosmicflows/
La red cósmica
Millenium Simulation: https://wwwmpa.mpa-garching.mpg.de/
Grandes estructuras del Universo
Illustris Simulation: www.nature.com/articles/nature13316
Radiación Cósmica de Fondo de Microondas (CMB)
Planck 2018 CMB Temperature map (Commander) . wiki.cosmos.esa.int/planck-legacy-archive/index.php/CMB_maps
Radiación Cósmica de Fondo de Microondas (CMB)
Planck 2018 CMB Dust polarization map . wiki.cosmos.esa.int/planck-legacy-archive/index.php/CMB_maps
La Historia de Expansión del Universo
- Inflation
- Baryo/Leptogenesis
- Recombination
- Neutral Hydrogen
- Dark Matter structures
- Galaxies
- Accelerated expansion
La Historia de Expansión del Universo
La composición del Universo
El Modelo Estándar: ΛCDM
Gμν+Λgμν=8πGTμν
G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi G T_{\mu \nu}
Ecuación de campo de Einstein
Supernovas 1998, Premio Nobel 2011
Relatividad General y
condiciones iniciales cuánticas
Concordancia de observaciones, CMB (Premio Nobel 2006, COBE)
The Standard ΛCDM model
- ΛCDM is still best fit to observations.
- Predictive model with few free parameters.
Gμν+Λgμν=8πGTμν
G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi G T_{\mu \nu}
Concordance Cosmology:
- Lensing
- CMB
- Clustering
- Supernovae
- Clusters
The Standard ΛCDM model
Gμν+Λgμν=8πGTμν
G_{\mu \nu} + \Lambda g_{\mu \nu} = 8\pi G T_{\mu \nu}
- ΛCDM is still best fit to observations.
- Some questions remain:
- Λ and CDM.
- Cosmological Constant Problem:
Quantum Gravity?
O(100) orders of magnitude wrong
(Zeldovich 1967, Weinberg 1989, Martin 2012).
Composed of naturalness and coincidence
sub-problems, among others.
String Theory Landscape?
Cómo Sabemos Todo Esto?
1. Lentes Gravitacionales
Cómo Sabemos Todo Esto?
2. Radiación Cósmica de Fondo
Satélite Planck de la ESA
Datos y teoría calzan
Cómo Sabemos Todo Esto?
3. Galaxy Clustering
Efectos de la gravedad sobre el espacio tiempo
Funciones de correlación
Tensiones en ΛCDM
H0 tension at 5σ
Clustering amplitude σ8
- σ8 - Ωm discrepancy at ~2σ
- Tension between late and early-time Universe
- Tension in clustering amplitude and matter content
Neutrinos Masivos en Cosmologia
Neutrinos Masivos en Cosmologia
- Neutrinos and Photons initially at thermal equilibrium
- Neutrinos decouple at ≈ 1MeV
- Energy injection into photons from e+e− annihilation
Neutrinos Masivos en Cosmologia
Neff=3.0440
N_{\rm eff} = 3.0440
Froustey et al, arXiv:2008.01074, arXiv: 2110.11296
- If neutrinos are massless: relativistic, dilute as a−4
- If massive: non-relativistic, one has to follow the Friedmann function evolution
Perturbaciones Lineales
The power spectrum is calculated from the linear density perturbations solving the Vlasov-Poisson system
Perturbaciones Lineales
Vlasov-Poisson system is a set of diff.eqn. in which all matter-radiation species are coupled
Slides by: Dennis Linde
Neutrinos masivos: Free streaming
- Neutrinos free stream below a scale of k_FS.
- They do not cluster below that scale.
- Suppression of the power spectrum.
- The non-relativistic transition imposes a minimum in k_FS
- Cosmology-dependent
Neutrinos masivos: Free streaming
Pfν(k)=(1−fν)2P(k)
P^{f_\nu}(k) = (1-f_\nu)^2 P(k)
Suppression of the power spectrum, at first order depends on energy density ratios
Neutrinos masivos: Free streaming
CMB angular spectrum and matter power spectrum are both dependent on neutrino mass, N_eff and ordering
Euclid Space Satellite
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!
Credits: Rodlophe Cledassou, CNES
Euclid Space Satellite
Localizado en el punto de Lagrange L2
Credits: Rodlophe Cledassou, CNES
VIS
Instrumento VIS:
- Medirá 1000 millones de galaxias en el espectro visible e infrarrojo.
- Con esto podemos medir los débiles lentes gravitacionales.
Credits: Rodlophe Cledassou, CNES
NISP: Near-Infrarred Spectrograph
Instrumento NISP:
- Medirá 100 millones de espectros de galaxias en el espectro infrarrojo.
- Con esto podemos medir las distancias y velocidades de las galaxias.
- Crear mapa 3D del Universo.
Credits: Rodolphe Cledassou, CNES
Euclid Mask
15,000 square degrees
Credits: Tobias Liaudat, CosmoStat
Euclid Shape Pipeline
Credits: Rodlophe Cledassou, CNES
Euclid
https://www.esa.int/ESA/Our_Missions
Otros satélites de la ESA
Lentes Gravitacionales
Galaxy Clustering
BAO
Clustering
RSD
Spec-z
Euclid Collaboration, IST:Forecasts, arXiv: 1910.09273
Galaxy Clustering
Slides by: Dennis Linde
Galaxy Clustering
Angulo et al, 1406.4143
The Matter Power Spectrum
Current data:
Image: https://www.cosmos.esa.int/web/planck/picture-gallery
The Matter Power Spectrum
Euclid:
Scales from: ~ 10−3 to 10 hMpc−1
Euclid: IST:Forecasts
Awardees of the Euclid STAR Prize Team 2019
Euclid preparation: VII. Forecast validation for Euclid cosmological probes. arXiv:1910.09273
Euclid: IST:Forecasts
Euclid preparation: VII. Forecast validation for Euclid cosmological probes. arXiv:1910.09273
Fisher Matrix Forecasts
Euclid preparation: VII. Forecast validation for Euclid cosmological probes. arXiv:1910.09273
Bayes Theorem:
Probability of the model parameters given the data
Fisher Information Matrix:
Curvature (Hessian) of the Likelihood
Gaussian Likelihood in data space:
−2lnL(x∣θ)=(x−μ(θ))tC−1(x−μ(θ))
-2\ln {L}({\bm x}|{\bm\theta})=\left({\bm x}-{\bm \mu}({\bm\theta})\right)^t{ C}^{-1}\left({\bm x}-{\bm \mu}({\bm\theta})\right)
Fisher Matrix Forecasts
Euclid preparation: VII. Forecast validation for Euclid cosmological probes. arXiv:1910.09273
Fisher Matrix for a Gaussian likelihood:
Parameter covariance:
Defines an ellipse:
MCMC Forecasts
Euclid IST:L and IST:NL in preparation
- Define Likelihood pipeline in real and redshift space
- Run Markov-Chain-Monte-Carlo sampling parameter space and probability
- Plot probability density contours
- Deviations from Gaussian due to non-linear dependencies in the posterior
Neutrino constraints from Planck
Neutrino forecasts for Euclid
Plots by: Sabarish Sabarish Venkataramani
Ωm=0.314±0.00086Ωb=0.049±0.0013h=0.67±0.00108ns=0.966±0.00179σ8=0.81±0.00172Mν=0.06eV±0.0320Neff=3.044±0.151
\Omega_m = 0.314 \pm 0.00086\\
\Omega_b = 0.049 \pm 0.0013 \\
h = 0.67 \pm 0.00108 \\
n_s = 0.966 \pm 0.00179\\
\sigma_8 = 0.81 \pm 0.00172\\
M_\nu = 0.06 \, \mathrm{eV} \pm 0.0320\\
N_{\rm eff} = 3.044 \pm 0.151\\
Euclid Full:
GC spectro + 3x2pt photo
Code: CosmicFish
S.Casas and M.Martinelli
CosmicFish Code
Code: CosmicFish
S.Casas, M.Martinelli and M.Raveri
Soon to be released: New full pythonic version
Gravedad Modificada y Energia Oscura
Ezquiaga, Zumalacárregui, Front. Astron. Space Sci., 2018
Gravedad Modificada y Energia Oscura
Parametrized modified gravity
ds2=−(1+2Ψ)dt2+a2(1−2Φ)dx2
\rm{d}s^2 = -(1+2\Psi) \rm{d}t^2 + a^2(1-2\Phi) \rm{d}x^2
In ΛCDM the two linear gravitational potentials Ψ and Φ are equal to each other
We can describe general modifications of gravity (of the metric) at the linear level with 2 functions of scale (k) and time (a)
Σ(a,k)=21μ(a,k)(1+η(a,k))
\Sigma(a,k) = \frac{1}{2}\mu(a,k)(1+\eta(a,k))
Only two independent functions!
Vera Rubin LSST
- Located in Chile, 8.4m telescope
- 20 billion galaxies
- Redshifts: 0 < z ~< 3
- 18,000 square degrees
- 11 years of observation
Vera Rubin LSST
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
- Starting 2021
Vera Rubin LSST
Euclid vs. DESI+Rubin
- Forecasts for Modfied Gravity parametrizations
- Euclid using spectroscopic and photometric probes, is roughly as powerful as Rubin+DESI
Vera Rubin LSST
Text
The Square Kilometer Array Obs. (SKAO)
- Next-generation Radioastronomy observatory
- Largest radiotelescope in the world: eventually 1km^2 area.
- 15 countries + partners
- Australia + South Africa installations
- ~2 billion Euros up to 2030.
- 5Tbps data rate and 250 Pflops needed for computation
Vera Rubin LSST
Text
The Square Kilometer Array (SKA)
- SKA Phase 1: SKA1-Low and SKA1-Mid
- SKA1-Low: 130,000 dipole antennas, 65km max. baseline
- SKA1-Mid: ~200 dishes of ~15m diameter, max. baseline 150km
- Precursors: ASKAP, MEERKAT, HERA...
Vera Rubin LSST
Text
The Square Kilometer Array (SKA)
- 15,000-20,000 square degrees in the sky
- Precursors: 10^7, SKA-phase1: 10^8, SKA-phase2: 10^9 galaxies
- SKA1-MID: 0 < z < 3
- SKA1-Low: 3 < z < ~ 20
- Cosmology is just one small area, Exoplanets, Craddle of Life, Reionization, Cosmic Magnetism....
Vera Rubin LSST
Text
The Square Kilometer Array (SKA)
SKA Probes
Image credit: Isabella Carucci
-
Continuum emission: Allows detection of position and shapes of galaxies.
-
Line emission of neutral Hydrogen (HI, 21cm):
-
Using redshifted HI line -> spectroscopic galaxy survey
2. Intensity Mapping: Large scale correlations in HI brightness temperature -> very good redshift resolution,
good probe of structres
Vera Rubin LSST
Text
The Square Kilometer Array (SKA)
SKA Probes
SKA Surveys
- IM: Intensity mapping survey
0.4<z<2.5 - Very good redshift resolution: Δz≈O(10−3)
- We use: 11 redshift bins
-
Single dish mode:
Nd=197
tobs=10000hr
We limit to the scales
0.001<k<0.25[h/Mpc]
SKA1 Medium Deep Band 1: 20000deg2
Vera Rubin LSST
Text
The Square Kilometer Array (SKA)
SKA Probes
SKA Surveys
Galaxy Clustering - IM Synergies
- SKA1 and Euclid probe complementary redshifts in spectroscopic GC.
- IM and GC cross-correlation offers gain in information and reduction of systematics
- 4 overlapping z-bins
Vera Rubin LSST
Text
The Square Kilometer Array (SKA)
SKA Probes
SKA Surveys
Galaxy Clustering - IM Synergies
Casas, Martinelli, Pettorino, Carucci, Camera (in preparation)
f(R) Hu-Sawicki model
Text
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
f(R) Hu-Sawicki model
Text
Euclid: Casas et al (2022) in preparation
Codes used: for background and scale-dependent linear perturbations: MGCAMB and EFTCAMB
For non-linear power spectrum:
Winther et al (2019) fitting formula
f(R) Hu-Sawicki model
Text
Euclid: Casas et al (2022) in preparation
σlogfR0=0.05 (0.9%)
Full probe combination, optimistic Euclid constraints:
fR0=(5.0−0.52+0.58×10−6)
Paper also contains impact of:
- Non-linear scales
- Cross-correlations
- Pessimistic settings
- LCDM-limit
f(R) Hu-Sawicki model
Text
Euclid: Casas et al (2022) in preparation
N-body simulations for Dark Energy
f(R) Hu-Sawicki model and degeneracies
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]}
- Degeneracy:
- Suppression from neutrinos
- Enhancement from fifth-force (modified G)
- Degeneracies can be broke by looking at non-gaussian terms beyond the Pk
More exotic models
More exotic models
The problem of non-linearities
- Euclid Likelihood Code: CLOE
- Baryonic physics
- N-body simulations
- Non-linear power spectrum
- Strong parameter biases
The problem of non-linearities
- Euclid Likelihood Code: CLOE
- Baryonic physics
- N-body simulations
- Non-linear power spectrum
- Strong parameter biases
Text
Text
Conclusiones
- Euclid va a proveer una cantidad de datos sin precedentes en la cosmología.
- Gracias a sus imágenes detalladas y la determinación de distancias y posiciones, podemos hacer un mapa 4D del Universo (espacio y tiempo).
- Los neutrinos tienen importantes efectos en los observables cosmológicos
- Aún muchas teorías de gravedad modificada son compatibles con los datos
- Muchos challenges en el modelaje no-linear
Muchas Gracias!!
En búsqueda de la Energía Oscura con Euclid y experimentos cosmológicos de cuarta generación Santiago Casas Postdoctoral Researcher TTK, RWTH Aachen University
Cosmologia con Futuros Surveys
By Santiago Casas
Cosmologia con Futuros Surveys
La misión espacial Euclid: En búsqueda de la energía oscura.
- 119
