Modify Gravity and Dark Energy Rubn Arjona IFT-UAM/CSIC 13 16 May - - PowerPoint PPT Presentation

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Modify Gravity and Dark Energy Rubn Arjona IFT-UAM/CSIC 13 16 May - - PowerPoint PPT Presentation

Aug 12, 2023 243 likes •794 views

The effective fluid approach for Modify Gravity and Dark Energy Rubn Arjona IFT-UAM/CSIC 13 16 May 2019 Second Minkowski Meeting on the Foundation of Spacetime Physics arXiv:1811.02469 R.Arjona, W.Cardona, S.Nesseris arXiv:1904.06294

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Rubén Arjona IFT-UAM/CSIC

The effective fluid approach for Modify Gravity and Dark Energy

arXiv:1811.02469 R.Arjona, W.Cardona, S.Nesseris arXiv:1904.06294 R.Arjona, W.Cardona, S.Nesseris

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13 – 16 May 2019 Second Minkowski Meeting on the Foundation of Spacetime Physics

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Summary

Modify gravity and Dark energy models are alternative scenarios for explaining the late-time acceleration of the Universe. Provide simple analytical formulae for the equivalent dark energy effective fluid pressure, density and velocity for modify gravity and dark energy models. Implement the dark energy effective fluid formulae in the Boltzmann solver code called CLASS. Derive constraints from the latest cosmological data.

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Main contents

  • The Standard Cosmological Model
  • The Effective Fluid Approach
  • f(R) theories
  • Horndeski theories
  • Boltzmann solver codes: CLASS, hi_CLASS, EFCLASS
  • Cosmological Constraints (MCMC)

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Einstein equations

Friedman - Lemaitre - Robertson - Walker (FLRW) metric

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Cosmological Constant

  • General Relativity
  • The Cosmological Principle
  • The Hubble law
  • The Cosmic Microwave Background
  • The Big Bang Nucleosynthesis

Five pillars

The Standard Cosmological model (ΛCDM)

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The Standard Cosmological Model (ΛCDM)

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The Universe is expanding…. but also accelerating! ΛCDM simplest candidate

Fits most data sets. Good phenomenological model

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Small scales (UV) Large scales (Infrared) Dark energy

Modified gravity theories can be String/quantum gravity inspired due to corrections expected in higher energies

Why we need to go beyond GR ? Not renormalizable

(only at first loop)

Add extra scalar field Modified gravity Quantum fields in curved space. Birrel and Davies

Modified gravity theories

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2 leading approaches Dark energy Modified gravity

Keep GR introduce new fields and particles Covariant modifications to GR

Effective Fluid Approach

Background Linear perturbations

equation of state anisotropic stress sound speed

Explain the late-time acceleration of the Universe

The linear order perturbations could in principle be distinguishable from the standard cosmological model Departures from GR can be interpreted as an effective fluid contribution Variables describing the fluid

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Perturbed FRW metric First order of perturbations Perturbed Einstein equations Evolution equation for the perturbations arXiv:astro-ph/9506072v1 scalar μ=0 μ=i

Theoretical framework

(i,j) (0,i) (0,0)

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Evolution equation for the perturbations μ=0 μ=i

Theoretical framework

𝑊 ≡ 1 + 𝑥 𝜄 Scalar velocity perturbation Anisotropic stress parameter 𝜌 = 3 2 1 + 𝑥 𝜏

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Modified Gravity and Dark energy models

Effective fluid approach for specific models: Toy model: f(R) Horndeski theory

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The effective fluid approach

Field equations

  • Eff. Fluid approach
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The effective fluid approach

Background Eqs. Effective DE density and pressure DE equation

  • f state
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The effective fluid approach

Effective pressure, density and velocity perturbations In GR = 0!

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Sub-horizon approximation

Modes deep in the Hubble radius

Neglect time derivatives in the linearized Einstein equations

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Growth of matter perturbations

We know that there are matter perturbations…but how do they grow?

Growth of matter density perturbations

  • n sub-horizon scales

Measure how matter clusters perturbation background

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Sub-horizon approximation

Departure from GR

Anisotropic parameters

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Sub-horizon approximation

Effective pressure, density and velocity perturbations

Apply repeatedly

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Sub-horizon approximation

Effective pressure, density and velocity perturbations

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The Hu & Sawicki (HS) model

After some algebraic manipulations Small perturbation around ΛCDM arXiv:1302.6501

  • Background. Analytic approximation
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𝑊 ≡ 1 + 𝑥 𝜄 Hu & Sawicki model

DE equation of state

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Numerical solution of the evolution equations

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Numerical solution of the evolution equations

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Horndeski theories

Most general scalar-tensor theory whose equations of motion contain derivatives up to second order

Scalar field Kinetic term arXiv: 1807.09241 23

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Horndeski theories

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Horndeski after GW170817

GRB170817A+GW170817

arXiv: 1710.05901 25 sound speed tensor perturb. tensor speed excess

propagation eq. of GW scalar-tensor gravity

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More on Horndeski theory

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  • A. Background

First order Linear Perturbations Gravitational Field Equation Scalar Field Equation First order Linear Perturbations

  • B. Perturbations
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Subhorizon and quasi-static approximation

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The Effective Fluid Approach

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By adding and substracting the Einstein tensor on the LHS of

  • Eq. (1) and moving everything to the RHS we can rewrite the

EOM as the usual Einstein equations plus an effective DE fluid along with the usual matter fields.

Gravitational Field Equation Eq.(1)

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The Effective Fluid Approach

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f(R)

Quintessence, K-essence Kinetic Gravity Braiding Designer Model (HDES)

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Designer model (HDES)

30 Modified Friedmann Equation Scalar Field Conservation Equation H=H(X) and solve the system Family of Designer Models Background exactly equal to that of ΛCDM model but perturbations given by the Horndeski theory

HDES

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Numerical solution

A) Full-DES. Numerical solution of the full system of equations. B) Eff. Fluid. Numerical solution of the effective fluid approach. C) ODE_Geff. Numerical solution of the growth factor equation. D) The ΛCDM model.

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A) B) C) D)

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Growth of matter perturbations

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Define growth rate f(a): However, the measurable quantity is fσ8=f(a)* σ 8(a) where

Redshift dependent rms fluctuation of the linear density field with spheres of radius R.

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Growth of matter perturbations

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Numerical solution of the evolution equations

Future surveys: Euclid and LSST Constrain with higher accuracy

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HDES: Modifications to CLASS

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hi_class implements Horndeski’s theory in the modern Cosmic Linear Anisotropy Solving

  • System. It can be used to compute any linear observable in seconds, including cosmological

distances, CMB, matter power and number counts spectra.

EFCLASS

Using

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low-l multipoles TT CMB spectrum

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Data for the MCMC

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1048 data points from Pantheon, 3 from the CMB shift parameters, 10 from the BAO measurements, 22 from the growth and 36 H(z) points Total: N=1118.

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HDES MCMC

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MCMC codes

alleviates tension

Akaike Information Criterion (AIC) statistically equivalent

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Conclusions

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  • Theoretical expressions for the effective dark energy pressure,

velocity and sound speed (Effective Fluid Approach).

  • Presented Designer Horndeski models (HDES).
  • Numerical solutions for HDES in Good agreement with fσ8 data.
  • Our EFCLASS modification is accurate to the level of ~0.1%.
  • MCMC on our HDES model. Both models are statistically

consistent.

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Thank you for your attention!

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arXiv:1811.02469 R.Arjona, W.Cardona, S.Nesseris arXiv:1904.06294 R.Arjona, W.Cardona, S.Nesseris

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Back-up slides

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Numerical solution of the evolution equations

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Why GR is not renomalizable (only at first loop)

GR

Fermi Th.

Super-renormalizable Renormalizable Non-renormalizable Primitive degree

  • f divergence

Coupling dimension

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Quantum fields in curved space. Birrel and Davies.

Renormalizing GR to first loop order for Ricci scalar

Conformal coupling and Gauss Bonnet term Higher order corrections to GR

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RMS

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The purpose of CLASS is to simulate the evolution of linear perturbations in the universe and to compute CMB and large scale structure observables.

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C L A S S th the e Cosmic smic Linear near An Anisotro sotropy py So Solving ving Sy Syste tem

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Akaike Information Criterion (AIC)

number of free parameters To compare different models Positive evidence against the model with higher value Strong evidence Consistency of the two models

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Ezquiaga et al. 1710.05901

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Growth rate data

Surveys can provide measurements of the perturbations in terms of the galaxy density δg:

bias parameter matter perturbations Early measurements: Unreliable datasets of β(z) Independent of the bias Nesseris et al. 1703.10538

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Euclid Consortium A space mission to map the Dark Universe

Future surveys

Launch is planned for 2021 Science operations starts in 2023

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Redshift space distortions

Redshift-space distortions are an effect in observational cosmology where the spatial distribution of galaxies appears squashed and distorted when their positions are plotted in redshift-space (i.e. as a function of their redshift) rather than in real-space (as a function of their actual distance). The effect is due to the peculiar velocities of the galaxies causing a Doppler shift in addition to the redshift caused by the cosmological expansion.