An exploration of dark energy and beyond the standard model with analytical and numerical tools for the large scale structures of the universe

Santiago Casas

Postdoctoral Researcher

TTK, RWTH Aachen University

     @santiagocasas                                                                                        @sant87casas

santiagocasas.github.io

Dark Energy & Modified Gravity

The Horndeski Lagrangian

PhD thesis: Non-linear structure formation in models of Dark Energy and Modified Gravity, http://archiv.ub.uni-heidelberg.de/volltextserver/23120/

Beyond Einstein's GR

Scalar-Tensor theories

Effect on LSS

N-Body simulations

CONCEPT: Python and Neutrinos

GADGET2/CoDECS

Credit: Yun Ling, My bachelor student,

Jeppe Dakin (U. Zurich)

Credit: Dr. Marco Baldi, Master thesis co-supervisor

Approximate methods: COLA

ABACUS: Fits for GCspectro with 1loopEFT

Other codes tested:

gevolution

flowpm

GNQ: Growing Neutrino Quintessence (developed in Heidelberg)

Credit: Winther, Casas, Koyama, Li,...

Credit: Casas, Führer, Ayaita, Weber, Wetterich

Credit: Rademacher, Moradinezhad, Lesgourges, Casas

My Journey with Euclid

Credits: www.esa.int/Science_Exploration/Space_Science/Euclid, www.euclid-ec.org, ESA/NASA/SpaceX, Euclid Consortium

Euclid consortium scientist visits Cannes. Credits: ThalesAlenia Space

Euclid preparation: VII. Forecast validation for Euclid cosmological probes,,Blanchard et al. arXiv:1910.09273

★ Awardees of the Euclid STAR Prize Team 2019

EC Builder Status achieved 2023

Early Release Observations. ECICOM, ECEPO: Social media manager of instagram: @euclidconsortium

Euclid Launch: 1st July 2023

Large forecasting projects

The Fingertip Galaxy

WEAK Lensing and Galaxy Clusteering

SC, Lesgourgues, Schöneberg, et al., Euclid: Validation of the MontePython forecasting tools, 2303.09451 

SC, Kunz, Martinelli, Pettorino, Phys.Dark Univ. 18 1703.01271

3x2pt Photometric Cosmic Shear + Clustering

Spectroscopic Galaxy Clustering: BAO+RSD+DM+LSS+Galaxy bias

Excellent complimentarity

https://www.esa.int/Science_Exploration/Space_Science/Euclid/Euclid_test_images_tease_of_riches_to_come

FISHER Matrix FORECASTS

Code: CosmicFish

S.Casas, M.Martinelli and M.Raveri

Soon to be released: Full pythonic version

https://github.com/santiagocasas/cosmicfishpie

Cosmomathica/Fishermathica

Python, Numpy-intensive

Couples to CAMB, CLASS, HiCLASS, MGCAMB, input4cast files

GC, WL, 21cm-IM, 3x2pt, CMB

Euclid, DESI, Rubin LSST, SKAO

Wolfram Language,

Cosmomathica-FORTRAN link for CAMB

GC, WL

Euclid, SKA1

Used to produce and validate IST:F forecasts 2015-2019

Hessian of a Gaussian Likelihood. Used to approximate posterior distributions at the maximum (fiducial value)

First code to be validated against MontePython MCMC forecasts

SC, Lesgourgues, Schöneberg, et al., Euclid: Validation of the MontePython forecasting tools, 2303.09451 

Euclid preparation: VII. Forecast validation for Euclid cosmological probes,,Blanchard et al. arXiv:1910.09273

SC, Kunz, Martinelli, Pettorino, Phys.Dark Univ. 18 1703.01271

https://github.com/santiagocasas/cosmomathica

Euclid theory working group

SC, I. Tutusaus : Work Package lead of WP6, Forecasting and statistics

SC: Member of WP1,2,3,4,6,7,11 : From theory and non-linearities to likelihood

SC: Co-coordinator of the KeyPaper-Theory-1 project

SC, Cardone, Sapone, et al, Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes, 2306.11053 

Frusciante, Pace, Cardone, SC et al, Euclid: Constraining linearly scale-independent modifications of gravity with the spectroscopic and photometric primary probes, 2306.12368

Main tasks:

Constrain gravitational potentials

Test for screening mechanisms

Check theories of modified gravity

Requires expertise with modified Einstein-Boltzmann solvers,

Emulators, Halo-model,

Fisher and likelihoods

Euclid: Likelihood and Nonlinear TASKFORCES

• GCspectro: EFT 1-loop RSD in multipoles
• 3x2pt photo:
  • Covariance, nonlinear Super-Sample
  • Galaxy Bias expansion
  • Emulators for nonlinear, HMCode, Halofit, Bacco, EuclidEmu
  • Baryonic Feedback: different parameters

• Different emulators with systematic offsets
• Euclid error bars can distinguish among them

Credit: P. Carrilho for IST:NL

Credit: SC, for IST:NL

Cosmological Likelihood for Observables in Euclid

Credit: SC, for IST:L

Credit: SC, for IST:NL

SC: Main developer and core member of CLOE. KeyPaper co-lead of 3x2pt in IST:NL

Preparation of DR1 analysis

• Biasing when failing to analyse data with correct model of baryonic feedback

Other Surveys and CROss-correlations

Vera Rubin Observatory, LSST Project Office - http://www.lsst.org/gallery/telescope-rendering-2013

DESI telescope in Tucson, Arizona, in the Schuk Toak District on the Tohono O’odham Nation

Square Kilometer Array Observatory https://www.skao.int/

SC, Carucci, Pettorino et al (2022), Constraining gravity with synergies between radio and optical cosmological surveys, 2210.05705 

CMB Stage-IV experiments:  https://kipac.stanford.edu/research/projects/cmb-stage-4

Invited talk at the Manchester Optical x Radio Synergy meeting

Neutrinos and LSS with Euclid & more

Euclid Preparation: Sensitivity to Neutrino parameters. (Under internal review). Archidiacono, Lesgourgues, SC, Pamuk, et al.

• \(M_{\nu}\) and \(N_{\rm eff}\)
• Combination of different probes breaks degeneracies

• For our given \(\ell_{\rm max}\) the effect of baryonic feedback is small <10%
• Euclid (all) 1\(\sigma\) error: 30-60 meV

Text

future avenues of work

Merci!!

In collaboration with Johanna Schaffmeister and Sven Günther, students at RWTH

• More work on uncertainty-aware emulators. https://github.com/santiagocasas/looti
• Both for non-linear power spectra, as well as for baryonic feedback, MG-effects and neutrinos.
• Work on 1loop-EFT for LSS in the case of GC-spectro (currently in prep. with Linde, Lesgourgues and Moradinezhad. Inclusion of consistent treatment for Neutrinos and Modified Gravity. (in collab with Linde, Pietroni, Fidler).
• JAX-COSMO: Campagne, Lanusse, Zuntz, SC, et al, 2302.05163.
• Implement auto-differentiability into commonly used codes in the field: CLASS, CAMB, HMCode, Looti, and Euclid codes: CLOE.
• Use auto-diff emulators: CosmoPower (Spurio-Mancini, et al)
• SC: Invited participant at 3-month MIAPP Differentiable physics workshop
• This allows for fast, efficient variational parameter estimation, orders of magnitude faster than conventional tools. Data compression, automatic Fishers, optimization, etc....
• Careful study of the effect of emulators and baryonic feedback on the Euclid 3x2pt observables. Parameter estimation biases, efficient sampling, sensible priors....
• Preparation of consistent (and alternative) pipelines for Euclid data release analysis, including cross-correlations with Clusters, Voids or other non-Gaussian observables and correlations with other surveys such as CMB, radio 21cm IM, SNIa and gravitational wave sirens.

BACKUP

https://www.esa.int/Science_Exploration/Space_Science/Euclid/Euclid_test_images_tease_of_riches_to_come

Do galaxies just randomly spread out across the sky?

https://www.esa.int/Science_Exploration/Space_Science/Euclid/Euclid_test_images_tease_of_riches_to_come

No they do not, there is actually a 2-point correlation (and higher orders) among them

Expresses the excess probabilty of finding another galaxy as a function of scale

Strong hint that some physical mechanism is at play

https://www.esa.int/Science_Exploration/Space_Science/Euclid/Euclid_test_images_tease_of_riches_to_come

Shape and orientation of galaxies is also correlated -- due to Weak Gravitational Lensing -- and this tells us about (dark) structures in the Universe

Dynamical Dark Energy + Neutrinos

Euclid Preparation: Sensitivity to Neutrino parameters. (Under internal review). Archidiacono, Lesgourgues, SC, Pamuk, et al.

machine Learning and variational methods

• In era of Big Data (billions of raw data points) and hundreds of possible models and simulations:
  • Important to be as computationally efficient as possible
     
• Likelihood codes for Euclid 2-3s per evaluation, Einstein-Boltzmann codes 1-100 seconds (depending on model -> too slow!!
  
   
•  Automatic-Differentiable (AD) codes: Leverage variational methods, such as Hamilton MC, AD-Variational Inference, Exact Fisher and beyond

In collaboration with Johanna Schaffmeister and Sven Günther

jaxcosmo library https://github.com/DifferentiableUniverseInitiative

Campagne, Lanusse, Zuntz, SC, et al, 2302.05163

Parametrized modified gravity

Beyond \(\Lambda\)CDM the two linear gravitational potentials \(\Psi\) and \(\Phi\) are not equal to each other

We can describe general modifications of gravity (of the metric) at the linear perturbation level with 2 functions of scale (\(k\)) and time (\(a\))

Only two independent functions!

Parametrized approach for perturbations:

Parametrized modified gravity

• Using Planck satellite data in 2015 and 2018, constraints were obtained on these two functions \(\mu\) and \(\eta\).
• Late-time parametrization: dependent on Dark Energy fraction

Parametrized modified gravity

Forecasts for Stage-IV : Euclid, DESI, SKA1, SKA2, only GC and WL

SC, Kunz, Martinelli, Pettorino, Phys.Dark Univ. 18 1703.01271

• Study more general case of free \(\mu\), \(\eta\) functions at each bin
• Non-linearities crucial for constraints
• Z-PCA decorrelation
• Constraints on \(\mu\), \(\eta\) of O(10%)

• For late-time and early-time scenario:
  Constraints on \(\mu\), \(\eta\) of O(3%)
• When combining GC+WL+Planck priors

Vera Rubin LSST

Square kilometer array (SKAO)

• Modelling is very analogous to GCsp, with brightness temperature on top and different biases
• GCsp-IM Cross-correlation in overlapping bins
• DESI : Two galaxy samples
• SKAO: HI Galaxies and 21cm-IM

\(P^{\rm IM}(z,k) = \bar{T}_{IM}(z)^2 \rm{AP}(z) K_{\rm rsd}^2(z, \mu; b_{\rm HI}) \)
\(FoG(z,k,\mu_\theta) \\ \times P_{\delta\delta,dw}(z,k)  \)

\( K_{\rm rsd}(z, \mu; b_{\rm HI}) = [b_{\rm HI}(z)^2+f(z)\mu^2] \)

\( b_{\rm HI}(z) = 0.3(1+z) + 0.6 \)

\( \bar{T}_{\mathrm{IM}}(z)= 189h \frac{(1+z)^2 H_0}{H(z)}\Omega_{HI}(z) \,\,{\rm mK} \)

\(\Omega_{HI}  = 4(1+z)^{0.6} \times 10^{-4} \)

Carucci et al (2020) 2006.05996

Jolicoeur et al (2020) 2009.06197

\(P^{{\rm IM} \times \rm{g}}(z,k) = \bar{T}_{\rm IM}(z) {\rm AP} (z) r_{\rm IM,opt}  K_{\rm rsd}(z, \mu; b_{\rm HI}) \)
\( \times K_{\rm rsd}(z, \mu; b_{\rm g}) FoG(z,k,\mu_\theta) P_{\delta\delta,dw}(z,k) \)

\( \times \exp[-\frac{1}{2} k^2 \mu^2 (\sigma_{\rm IM}(z)^2+\sigma_{\rm sp}(z)^2)]  \)

SC, Carucci, Pettorino et al (2022) 2210.05705

Brightness temperature of 21cm emission line

Fraction of neutral hydrogen in the Universe

Vera Rubin LSST

Radio x Optical Cosmology

SC, Carucci, Pettorino et al (2022) 2210.05705

• WL is better at measuring \(\Sigma\) (40% relative error)
• GC is better at measuring \(\mu\) (20% relative error)
• SKAO-all-probes constrains at 3-5% relative error
• At Planck best fits

• DESI(GCsp)xSKAO(IM) helps in \(h, \sigma_8\) but not in MG parameters
• Combination of SKAO + one Stage-IV probe is as good as two Stage-IV
• Different noise and systematics -> break degeneracies

other models (To Be tested) with STAGE-IV

SC, Rubio, Pauly et al (2017) 1712.04956

Higgs-Dilaton inflation: early-late Universe connection

Model-independent anisotropic-stress \(\eta\)

Amendola, Pinho, SC 1805.00027

SC, Amendola, Baldi, Pettorino et al 1508.07208

Coupled Quintessence: DM-DE

Surviving Horndeski EFT

Frusciante, Peirone, SC, Lima, 1810.10521, Phys.Rev.D 99

Text

Growing Neutrino Quintessence

SC, Pettorino, Wetterich 1608.02358

CosmicFish Code

Code: CosmicFish

S.Casas, M.Martinelli and M.Raveri

Soon to be released: New full pythonic version

https://github.com/santiagocasas/cosmicfishpie

Fisher Information Matrix:

Curvature (Hessian) of the Likelihood

Example: Fisher Matrix for a Gaussian likelihood of angular power spectra:

Classifying by screening

• Modified Gravity theories should recover GR at small scales, especially in dense regions, screening needed!

Brax, SC, Desmond, Elder 2201.10817,  Universe 8 (2021), Review: Testing Screened Modified Gravity

• Perturbations of \(\phi\) and matter coupled in Jordan frame -> Yukawa-like fifth forces:

Different types of screening:

• Chameleon: The mass \(m(\phi_0)\) increases sharply inside matter
• Damour-Polyakov: The coupling \(\beta(\phi_0)\) vanishes inside matter
• K-mouflage and Vainshtein: \(Z(\phi_0) \gg 1\)

Classifying by screening

Screening mechanisms can be characterized by the inequality:

• Chameleon: \(k=0\) (surface N. potential is large)
• K-mouflage: \(k=1\) (N. acceleration is large)
• Vainshtein: \(k=2\) (curvature is large)

• \( f(R) \) Hu-Sawicki  (see later)
• \(k\)-essence + univ. coupling
• nDGP (3+1)d brane embedded in 5d

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

Brax, SC, Desmond, Elder 2201.10817,  Universe 8 (2021), Review: Testing Screened Modified Gravity

Text

SC et al, Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes, 2306.11053

f(R) Hu-Sawicki model

Modification of the Einstein-Hilbert action

Induces changes in the gravitational potentials *

Scale-dependent growth of matter perturbations

Small changes in lensing potential

Free parameter: \(f_{R0}\)

\(\lambda_C =32 \rm{Mpc}\sqrt{|f_{R0}|/10^{-4}}\)

"Fifth-force" scale for cosmological densities

Hu, Sawicki (2007)

Text

f(R) Hu-Sawicki model

Codes used: for background and scale-dependent linear perturbations: MGCAMB and EFTCAMB

Non-linear matter power spectrum:

Winther et al (2019) fitting formula

Scale-dependent growth, change in forecasting pipeline

Current Euclid KP-JC6-SP paper in preparation (ledy by Kazuya), investigating biasing by Emulators/ReACT compared to simulations

SC et al, Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes, 2306.11053

Text

f(R) Hu-Sawicki model

 \(\sigma_{\log f_{R0}}=0.05\) (1%)

Current cosmological limits ~approx:

\( |f_{R0}|<10^{-6}\)

Full probe combination, optimistic Euclid constraints:

\(f_{R0}=(5.0^{+ 0.58}_{-0.52} \times 10^{-6})\)

Paper also contains impact of:

• Non-linear scales
• Cross-correlations
• Pessimistic settings
• LCDM-limit (numerical)

SC et al, Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes, 2306.11053

Text

Scale-independent Modifications of GR

Forecasts for:

• Jordan-Brans-Dicke  (no-screening)
• nDGP (5D brane model)
• k-Mouflage
• We work mostly in QSA MGCAMB or hiclass and non-linear modelling: Halo model or fits to simulations

Fruciante, Pace, Cardone, SC et al, Euclid: Constraining linearly scale-independent modifications of
gravity with the spectroscopic and photometric primary probes, 2306.12368

Current cosmo bounds \(\omega_{BD} \gtrapprox 1000 \), GR: \(\omega_{BD} \rightarrow \infty \)

\(r_c = G_5 / 2G_N \, , \Omega_{rc} \equiv c^2 / (4 r_c^2 H_0^2 ) \)

Current cosmo bounds \(\Omega_{rc} \lessapprox 0.27 \), GR: \(r_{c} \rightarrow \infty \)

Vary just \(\epsilon_{2,0}\) which in the limit \(\epsilon_{2,0} \rightarrow 0 \) turns the Kinetic term into a cosmological constant

Current cosmo bounds \( −0.04 \lessapprox \epsilon_{2,0} \lessapprox 0\)

Perform forecasts for limits close-to and far-from LCDM

Planck 2018 CMB Temperature map (Commander) .  wiki.cosmos.esa.int/planck-legacy-archive/index.php/CMB_maps

What happened in between, if in its infancy it was a fairly Gaussian, linearly perturbed, homogenous and isotropic Universe?

the road ahead of horndeski

The "surviving Horndeski" Lagrangian:

In the EFT formalism, FLRW, linear and
(unitary gauge time \(\rightarrow \phi\) ) :

Parametrize free functions and check for stability in solutions

We have shown that certain classes of models will not be distinguishable from LCDM, even with future surveys,  at 1\(\sigma\), while others will be measured with 10%-60% precision in their parameters

Frusciante, Peirone, SC, Lima, 1810.10521, Phys.Rev.D 99

CODES

Code: CosmicFish

S.Casas, M.Martinelli and M.Raveri

Soon to be released: New full pythonic version

https://github.com/santiagocasas/cosmicfishpie

Looti

jaxcosmo library https://github.com/DifferentiableUniverseInitiative

Campagne, Lanusse, Zuntz, SC, et al, 2302.05163

Cosmomathica/Fishermathica

Euclid Space Satellite

• Two instruments:
•  VIS (visible photometer): shape and orientation of  ~1 billion galaxies!
•  NISP (near infrared spectrograph): ~20 million galaxy spectra !
• 6 years nominal mission

• 15 000 square degrees in the sky
•  16 countries, ~1500 members
•  ~170 Petabyte of data!

VIS cosmic shear map

https://www.euclid-ec.org/blog/

Euclid preparation: I. The Euclid Wide Survey of ESA, R. Scaramella et al.

VIS cosmic shear map

photometric primary probe

Directly constrains MG function \(\Sigma\) through Weyl potential

https://www.esa.int/Science_Exploration/Space_Science/Euclid/Euclid_test_images_tease_of_riches_to_come

With Stage-IV surveys we will have \(\approx 10^9\) galaxy shapes with photometric (approximate) and \(\approx 10^6\) (precise) redshifts and positions

Only 1/64th of the complete Euclid field of view is represented here, which in turn is equivalent to a mere quarter of the apparent size of the Moon. Consider the vast expanse of 15,000 square degrees, encompassing one-third of the entire sky!

• CMB LEnSING and ITS Cross-Correlation with LSS

• Cosmic VOIDS

• NON-Gaussian and HIGHER ORDER STatistics

• CLUSTERS of GALAXIES

• ....

• \(\Lambda\)CDM is still best fit to observations.
• Some questions remain:
• \(\Lambda\) and CDM.
• CDM hasn't been found directly
• Cosmological Constant Problem:

photometric primary probe

• Photometric galaxy density distribution.
• Bins convolved with photometric redshift PDF
• 10-15 bins in future Stage-IV surveys

• Window functions (Kernels projecting correlations into angular space) -> Limber
•  Cosmic Shear Kernels are "delocalized" in z -> k
• Localization techniques such as BNT to allow for clear cuts

Euclid: Forecasts for $k$-cut $3\times 2$ Point Statistics, P. Taylor, V. Cardone, ..., SC, et al.  2012.04672

spectroscopic probe

BAO / AP-effect

Clustering

RSD

Euclid will also measure the 2pt corr-func of spectroscopic galaxies in redshift space

Euclid preparation: VII. Forecast validation for Euclid cosmological probes, Blanchard et al. arXiv:1910.09273

FoG

BAO-damping / IR-resummation

Fisher Matrix Forecasts

Bayes Theorem:

Probability of the model parameters given the data

Fisher Information Matrix:

Curvature (Hessian) of the Likelihood

Gaussian Likelihood in data space:

How do we actually perform those forecasts?

J. Schaffmeister

Euclid preparation: VII. Forecast validation for Euclid cosmological probes, Blanchard et al. arXiv:1910.09273

Fisher Matrix Forecasts

Fisher Matrix for a Gaussian likelihood of angular power spectra:

Parameter covariance:

Defines an ellipse:

Euclid preparation: VII. Forecast validation for Euclid cosmological probes, Blanchard et al. arXiv:1910.09273

http://caastro.org/research-highlights/science-animations/

In this 2-point correlation function we can see geometric features that are directly related to the expansion history of the Universe

spectroscopic probe

Rademacher, Linde, Lesgourgues, Moradinezhad, SC in prep.

The more-realistic GCspectro model, based on Senatore, Ivanov, Simonovic, Vlah, et al

CLASS 1-loop Code in development

1-loop PT of density and velocity in redshift space

4 counterterms, 4 shot-noise, 4 higher-order biases

Trade-off: larger error bars, more accuracy, less biasing

• In MG -> much more complicated (Kernels, Einstein-de-Sitter approx., screening, RSD)
• PyBird, PBJ, Fast-PT
• In Euclid:Bose et al (in prep.) we show that for conservative Euclid error bars, approximations are fine in terms of \(\chi^2\), for f(R), DGP, ...

Modified Gravity and Dark Energy

• Add a scalar degree of freedom to the Einstein-Hilbert action
• (Non-)Minimal coupling, Kinetic terms

Vera Rubin LSST

DESI telescope

• 14 000 square degrees in the sky
• 20-40 million accurate spectra
• Redshifts: 0 < z < 2 (spectroscopic)
• Quasars up to z~3.5
• 5 years of observation
• Starting 2021
• Power spectra, Bispectra, Corr. Func.

Just 7 months of DESI data

5000 robotically controlled optical fibers

Tucson, Arizona, in the Schuk Toak District on the Tohono O’odham Nation

Credits: https://www.desi.lbl.gov

Just 7 months of DESI data

Vera Rubin LSST

Square kilometer array (SKAO)

• SKA Phase 1: SKA1-Low and SKA1-Mid
• SKA1-Low: 130,000 dipole antennas, 65km max. baseline (Australia)
• SKA1-Mid: ~200 dishes of ~15m diameter, max. baseline 150km (South Africa)
• Precursors: ASKAP, MEERKAT, HERA...
   
• €1.3 Billion, 16 countries, 710 Petabytes, 8 years construction

https://www.skao.int/

a SCALAR-tensor theory

Gregory Horndeski
https://www.horndeskicontemporary.com/works

Costa Rica - Arenal Volcano

• Horndeski theory: most general theory for an extra scalar degree of freedom, with second order equations of motion in 4D and no ghosts
• 5 Lagrangian terms, which have been largely ruled out by:
  • Late-ISW
  • GW170817
  • No self-acceleration -> uninteresting?

Gregory Horndeski
https://www.horndeskicontemporary.com/works

Credits: Tobias Liaudat, CosmoStat

Euclid Shape Pipeline

Credits: Rodlophe Cledassou, CNES

Euclid

doi: 10.1146/annurev.nucl.012809.104521

Age of the Universe

Temperature of the Universe

• Planck measurements, essentially cosmic-variance limited in TT
• Percent precision in cosmological parameters
• Degeneracies in \(\Omega_k\), \(\Omega_m\) and \(H_0\) broken with BAO and lensing
• \(H_0 = 67.37 \pm 0.54 \, \textrm{km/s/Mpc}\)

Planck 2018 results. VI. Cosmological parameters https://arxiv.org/abs/1807.06209

https://www.cosmos.esa.int/web/planck

Possible solutions and new directions

• \(\Lambda\) ?
• Inflation ?
   
• \(m_{\nu}\) ?
   
• LSS  ?
  
   
• Big data?

Outline of working fields

• Coupled Quintessence
• Higgs-Dilaton
• Modified Gravity
• Horndeski/EFToDE
   
• EFToLSS
• Emulators
   
• Machine Learning
• Variational inference
• Stage-IV surveys
  Radio and Optical

• In general: confidence on the distance ladder
• Concerns on calibration, anchors dust or
  metallicity, have basically
  faded out
• Riess et al 2022*:
  \(H_0 = 73.30 \pm 1.04 \, \textrm{km/s/Mpc}\)
  
  using Cepheids and
  high-z SNIa

* The Astrophysical Journal Letters, 934:L7 (52pp), 2022 July 20

Neutrinos Masivos en Cosmologia

Neutrinos masivos: Free streaming

CMB angular spectrum and matter power spectrum are both dependent on neutrino mass, N_eff and ordering

Linear Perturbations

Vlasov-Poisson system is a set of diff.eqn. in which all matter-radiation species are coupled

Slides by: Dennis Linde

https://www.pablocarlosbudassi.com/2021/02/the-infographic-and-artistic-work-named.html

f(R) Hu-Sawicki model

Text

Modification of the Einstein-Hilbert action

Induces changes in the gravitational potentials *

Scale-dependent growth of matter perturbations

Small changes in lensing potential

Free parameter: \(f_{R0}\)

Hu, Sawicki (2007)

"Fifth-force" scale for cosmological densities

\(\lambda_C =32 \rm{Mpc}\sqrt{|f_{R0}|/10^{-4}}\)

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