[PPT] - Pedro G. Ferreira Oxford Oslo, 2015 Thursday, 15 January 15 PowerPoint Presentation

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Gravity and

Pedro G. Ferreira Oxford

Λ

Oslo, 2015

Thursday, 15 January 15

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Outline

Can gravity solve the

problem in cosmology?

Can we use cosmology to

constrain gravity?

Λ

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Modifying Gravity

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Einstein Gravity!

Metric of space time! Curvature!

1 16πG Z d4x√−gR(g) + Z d4x√−gL(g, matter)

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Lovelock’s theorem (1971) :“The only second-order, local gravitational field equations derivable from an action containing solely the 4D metric tensor (plus related tensors) are the Einstein field equations with a cosmological constant.”

See also Hojman, Kuchar & Teitelboim (1976)

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Lovelock’s theorem (1971) :“The only second-order, local gravitational field equations derivable from an action containing solely the 4D metric tensor (plus related tensors) are the Einstein field equations with a cosmological constant.”

See also Hojman, Kuchar & Teitelboim (1976)

Einstein Gravity

Curvature Metric of space-time

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The Feynman/Weinberg “Theorem”

Spin-2 field Couple to matter: Unique non-linear completion is GR... Self energy of the graviton:

Feynman (1963) Weinberg (1965) Deser (1970)

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The Problem

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Massive gravity
The naturalness problem
The hierarchy problem
The why now problem

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Effective Field Theory

but “Cutoff”:

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Modified Gravity

New degrees of freedom Higher dimensions Higher-order Non-local

Scalar Vector Tensor

f ✓R ⇤ ◆

Some degravitation scenarios Scalar-tensor & Brans-Dicke Galileons Ghost condensates the Fab Four Coupled Quintessence f(T) Einstein-Cartan-Sciama-Kibble Chern-Simons Cuscuton Chaplygin gases Einstein-Aether Massive gravity Bigravity EBI Bimetric MOND Horndeski theories Torsion theories KGB TeVeS General RμνRμν, ☐R,etc.

f (R)

Hořava-Lifschitz

f (G)

Conformal gravity

Strings & Branes Generalisations

f SEH

Cascading gravity Lovelock gravity Einstein-Dilaton- Gauss-Bonnet Gauss-Bonnet Randall-Sundrum Ⅰ & Ⅱ DGP 2T gravity Kaluza-Klein arXiv: 1310.1086 1209.2117 1107.0491 1110.3830

Lorentz violation Lorentz violation

Tessa Baker 2013

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Three (failed) attempts

Massive gravity
Unimodular gravity
Non-local gravity

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Massive gravity

Why bother?

Technically natural (a la t’Hooft)- a small

parameter such that the restores a symmetry (GC invariance in this case) remains small.

Massive gravity may be used to degravitate

(i.e. supress effect of long wavelength sources).

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Massive gravity

Massive gravity: weak field Static, spherically symmetric solution: Modified gravitation

Fierz-Pauli Action

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Massive Gravity: non-linear theory

Hassan-Rosen

where we define with eigenvalues and

DeRahm-Gabadadze-Tolley

Massive gravity

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Massive gravity

Only an effective theory valid up to:
Not clear if bigravity is well-posed

(hyperbolicity).

Simplest DRGT does not give flat FRW

universe.

Bigravity is cosmological unstable

Burrage, Kaloper, Padilla 2013 Noller, Scargill, Ferreira 2014 D’Amico et al, 2011 Comelli et al 2013 Koennig et al 2014 Lagos & Ferreira 2014 Cusin et al 2014

L. Lehners (private comm.)

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Unimodular gravity

Why bother?

Less degrees of freedom than GR
Completely insensitive to vacuum

fluctuations (i.e. no term)

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Unimodular gravity

Replace diff invariance by transverse diff and Weyl New theory: gauge fix:

Alvarez et al, 2006 Ellis et al 2010

Trace free field eqn:

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Unimodular gravity

does not source gravity.
Einstein equations are recovered with as

an integration constant.

Can be made massive with a technically

natural mass, just like GR.

Λ

Bonifacio, Ferreira & Hinterbichler 2014 Ellis et al 2010

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Unimodular gravity

Is protected from radiative corrections?
Massive unimodular has same problems as
rdinary massive gravity.
Unimodular is essentially equivalent to GR.

Λ

Smolin 2010 Padilla and Saltas, 2014 Bonifacio, Ferreira & Hinterbichler 2014 Einstein 1918

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Non-local Gravity

Generic in effective action of gravity with

massless (gauge) fields

No naturalness problem
No “why now?” problem

Why bother?

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Non-local gravity is general! Integrating out ultra-light (or massless) d.o.f. e.g.- one loop effective action for gravity

Barvinsky & Vilkovisky 1995 Barvinksy & Mukhanov 2002

Non-local Gravity

No extra degrees of freedom

Deser & Woodard 2010

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Non-local screening of

Non-local Gravity

Late time/large scale effect with and

Deser & Woodard 2007

Generalize to corrections.

Maggiore et al 2012 Arkani-Hamed et al 2002

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No systematic way of constructing model a

la EFT.

Action is not enough- causality!
Generic theory will have instabilities.

Maggiore et al 2012 Ferreira & Maroto 2012

Non-local Gravity

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Λ

Can gravity solve the problem in cosmology? Not yet...

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Testing Gravity

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Modified Gravity

New degrees of freedom Higher dimensions Higher-order Non-local

Scalar Vector Tensor

f ✓R ⇤ ◆

Some degravitation scenarios Scalar-tensor & Brans-Dicke Galileons Ghost condensates the Fab Four Coupled Quintessence f(T) Einstein-Cartan-Sciama-Kibble Chern-Simons Cuscuton Chaplygin gases Einstein-Aether Massive gravity Bigravity EBI Bimetric MOND Horndeski theories Torsion theories KGB TeVeS General RμνRμν, ☐R,etc.

f (R)

Hořava-Lifschitz

f (G)

Conformal gravity

Strings & Branes Generalisations

f SEH

Cascading gravity Lovelock gravity Einstein-Dilaton- Gauss-Bonnet Gauss-Bonnet Randall-Sundrum Ⅰ & Ⅱ DGP 2T gravity Kaluza-Klein arXiv: 1310.1086 1209.2117 1107.0491 1110.3830

Lorentz violation Lorentz violation

Tessa Baker 2013

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Hulse-Taylor Pulsar

Testing gravity

Parameter Bound Effects Experiment γ − 1 2.3 x 10 − 5

Time delay, light deflection Cassini tracking

β − 1 2.3 x 10 − 4

Nordtvedt effect, Perihelion shift Nordtvedt effect

ξ 0.001

Earth tides Gravimeter data

α1 10 − 4

Orbit polarization Lunar laser ranging

α2 4 x 10 − 7

Spin precession Solar alignment with ecliptic

α3 4 x 10 − 20

Self-acceleration Pulsar spin- down statistics

ζ1 0.02

Combined PPN

bounds

ζ2 4 x 10 − 5

Binary pulsar acceleration PSR 1913+16

ζ3 10 − 8

Newton's 3rd law Lunar acceleration

ζ4 0.006

Usually not

independent

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Curvature, ξ (cm

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10 Potential, ε DETF4 Facility BAO ELT S stars LOFT + Athena PPN constraints Tidal streams

(GAIA)

AdLIGO eLISA A P

Atom Triple

Inv. Sq.

EHT

Sgr A* M87

Planck PTA

Baker, Psaltis & Skordis, 2014.

Baker et al 2014 ArXiv:1412:3455

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The Universe: large scale structure

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linear quasilinear nonlinear X-large scales

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Extending Einstein’s equations

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Skordis 2010 Baker, Ferreira, Skordis 2012

Linear Regime Linear in ˆ

Φ, ˆ Γ, ˆ χ, ˙ ˆ χ

ˆ Γ = 1 k ⇣ ˙ ˆ Φ + Hˆ Ψ ⌘

(ˆ Φ, ˆ Ψ)

Bardeen potentials: Example: Completely general but 15 free functions...

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Use general principles to restrict Example- assume locality, scalar field, etc leads to only 7 free functions of time.

Pearson, Battye 2011 Bloomfield et al 2012 Gleyzes et al 2013 Langlois et al 2013

“Integrability condition” can help

Most general action with 1 d.o.f. (use unitary gauge)

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De Felice et al 2011 Baker et al 2012 Silvestri et al 2013 Baker et al 2014

Quasi-static then only two functions ...

kτ 1

−k2Φ = 4πGµa2ρ∆ γΨ = Φ

Caldwell et al 2007 Amendola et al 2007 Bertschinger, et al 2006 Amin et al 2007 Pogosian et al 2009 Bean & Tangmatitham 2010 Baker et al 2013

... actually 5 functions of time

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Leonard et al 2015

DETF-IV (scale indep.) constraints

Growth (e.g. RSDs) Lensing

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Leonard et al 2015

DETF-IV constraints

Crucial to constrain Percent level constraints for scale indep. part ... ... order of magnitude greater for scale dependence part.

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Example: Jordan-Brans-Dicke Theory

Cosmology Now: Euclid: Solar System Now:

What does this actually mean?

Avillez & Skordis 2013 (RSDs only ) Baker, Ferreira & Skordis, 2013 Cassini

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The Universe: large scale structure

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linear quasilinear nonlinear X-large scales

More statistical power ...

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The non-linear regime

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Courtesy of Hans Winther

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The non-linear regime

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Tessore et al 2015

ΛCDM F5 F6 DGP, r = 1.2 DGP, r = 5.6 zS = 1.4 zS = 1.0 zS = 0.5 zS = 0.2

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The non-linear regime

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Courtesy of Hans Winther

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Baryon, feedback and bias

Semboloni et al 2012

The non-linear regime

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X-large scales

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linear quasilinear nonlinear X-large scales

Beyond quasistatic

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X-large scales

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Access to more and different information

Bonvin & Durrer 2011 Challinor & Lewis 2011

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X-large scales

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Corrections beyond quasi-static

Alonso et al 2015

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X-large scales

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Red: Blue: Solid: Dashed: narrow bin wide bin SKA cosmology working group

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X-large scales

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Bull 2014

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No gravitational solution to the

problem.

Fundamental assumptions are being

explored.

Cosmological tests of gravity completely

understood in the quasi-static regime.

Non-linear regime interesting but difficult.
X-large scales yet to be done.

Conclusions

Λ

Thursday, 15 January 15