Similarity of DMDE and TeVeS HongSheng Zhao SUPA

ΛCDM WDM Tuned DM-DE(~ Tuned TeVeS μ )

I Much ado about mu

microin disk galaxies with

Famaey (Brussels) Angus (SUPA) Gentile (NMSU)

Nipoti Londrillo Ciotti (Bologna)

amp high-z elliptical lensing galaxies with

Bacon Taylor Horne (SUPA) Shan (Beijing)

in cosmology with

Skordis (Perimeter) Mota (Oslo)

III TeVeS (Bekenstein 2004)

bull Einstein-like equations for g U scalar by varying the action wrt each of these fields

bull In a quasi-static system with a weak gravitational field N+

dτ2 = (1-2) dt2 -(1+2) ( dx2 + dy2 + dz2 )

where obeys a B-M equation and plays the role of the dark matter potential (dynamics and lensing are governed by the same physical metric g)

bull Define y = (3krsquo2a02) Y Y=(g-UU)

where krsquo k 4 is a parameter of the theory

y ()2 gt0 in quasi-static situation

y -(t)2 lt0 in cosmology

bull Equation for the scalar field in a quasi-static system

[s(y)] = 4G (similar to B-M)

bull In spherical symmetry gravity

s = (1- )

Analogy as dielectric and as inertia

bull Conservative Field g or E = -Φ = d2xdt2

bull Poisson equation ρ = D or gN

ndash Electric displacement D = μ E = E + PolarisationField

ndash TeVeS-like theory gN = μ g = g - ScalarField

bull

bull Newtonian F = minertia g minertia= m

Scalar field in TeVeS resembles DM

bull Scalar field (Polarisation Halo of luminous baryon 1-to-1 gravity)

bull ~ tuned Dark Halo surrounding baryons

bull NFW profile micro

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

ΛCDM WDM Tuned DM-DE(~ Tuned TeVeS μ )

I Much ado about mu

microin disk galaxies with

Famaey (Brussels) Angus (SUPA) Gentile (NMSU)

Nipoti Londrillo Ciotti (Bologna)

amp high-z elliptical lensing galaxies with

Bacon Taylor Horne (SUPA) Shan (Beijing)

in cosmology with

Skordis (Perimeter) Mota (Oslo)

III TeVeS (Bekenstein 2004)

bull Einstein-like equations for g U scalar by varying the action wrt each of these fields

bull In a quasi-static system with a weak gravitational field N+

dτ2 = (1-2) dt2 -(1+2) ( dx2 + dy2 + dz2 )

where obeys a B-M equation and plays the role of the dark matter potential (dynamics and lensing are governed by the same physical metric g)

bull Define y = (3krsquo2a02) Y Y=(g-UU)

where krsquo k 4 is a parameter of the theory

y ()2 gt0 in quasi-static situation

y -(t)2 lt0 in cosmology

bull Equation for the scalar field in a quasi-static system

[s(y)] = 4G (similar to B-M)

bull In spherical symmetry gravity

s = (1- )

Analogy as dielectric and as inertia

bull Conservative Field g or E = -Φ = d2xdt2

bull Poisson equation ρ = D or gN

ndash Electric displacement D = μ E = E + PolarisationField

ndash TeVeS-like theory gN = μ g = g - ScalarField

bull

bull Newtonian F = minertia g minertia= m

Scalar field in TeVeS resembles DM

bull Scalar field (Polarisation Halo of luminous baryon 1-to-1 gravity)

bull ~ tuned Dark Halo surrounding baryons

bull NFW profile micro

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

I Much ado about mu

microin disk galaxies with

Famaey (Brussels) Angus (SUPA) Gentile (NMSU)

Nipoti Londrillo Ciotti (Bologna)

amp high-z elliptical lensing galaxies with

Bacon Taylor Horne (SUPA) Shan (Beijing)

in cosmology with

Skordis (Perimeter) Mota (Oslo)

III TeVeS (Bekenstein 2004)

bull Einstein-like equations for g U scalar by varying the action wrt each of these fields

bull In a quasi-static system with a weak gravitational field N+

dτ2 = (1-2) dt2 -(1+2) ( dx2 + dy2 + dz2 )

where obeys a B-M equation and plays the role of the dark matter potential (dynamics and lensing are governed by the same physical metric g)

bull Define y = (3krsquo2a02) Y Y=(g-UU)

where krsquo k 4 is a parameter of the theory

y ()2 gt0 in quasi-static situation

y -(t)2 lt0 in cosmology

bull Equation for the scalar field in a quasi-static system

[s(y)] = 4G (similar to B-M)

bull In spherical symmetry gravity

s = (1- )

Analogy as dielectric and as inertia

bull Conservative Field g or E = -Φ = d2xdt2

bull Poisson equation ρ = D or gN

ndash Electric displacement D = μ E = E + PolarisationField

ndash TeVeS-like theory gN = μ g = g - ScalarField

bull

bull Newtonian F = minertia g minertia= m

Scalar field in TeVeS resembles DM

bull Scalar field (Polarisation Halo of luminous baryon 1-to-1 gravity)

bull ~ tuned Dark Halo surrounding baryons

bull NFW profile micro

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

III TeVeS (Bekenstein 2004)

bull Einstein-like equations for g U scalar by varying the action wrt each of these fields

bull In a quasi-static system with a weak gravitational field N+

dτ2 = (1-2) dt2 -(1+2) ( dx2 + dy2 + dz2 )

where obeys a B-M equation and plays the role of the dark matter potential (dynamics and lensing are governed by the same physical metric g)

bull Define y = (3krsquo2a02) Y Y=(g-UU)

where krsquo k 4 is a parameter of the theory

y ()2 gt0 in quasi-static situation

y -(t)2 lt0 in cosmology

bull Equation for the scalar field in a quasi-static system

[s(y)] = 4G (similar to B-M)

bull In spherical symmetry gravity

s = (1- )

Analogy as dielectric and as inertia

bull Conservative Field g or E = -Φ = d2xdt2

bull Poisson equation ρ = D or gN

ndash Electric displacement D = μ E = E + PolarisationField

ndash TeVeS-like theory gN = μ g = g - ScalarField

bull

bull Newtonian F = minertia g minertia= m

Scalar field in TeVeS resembles DM

bull Scalar field (Polarisation Halo of luminous baryon 1-to-1 gravity)

bull ~ tuned Dark Halo surrounding baryons

bull NFW profile micro

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

bull Define y = (3krsquo2a02) Y Y=(g-UU)

where krsquo k 4 is a parameter of the theory

y ()2 gt0 in quasi-static situation

y -(t)2 lt0 in cosmology

bull Equation for the scalar field in a quasi-static system

[s(y)] = 4G (similar to B-M)

bull In spherical symmetry gravity

s = (1- )

Analogy as dielectric and as inertia

bull Conservative Field g or E = -Φ = d2xdt2

bull Poisson equation ρ = D or gN

ndash Electric displacement D = μ E = E + PolarisationField

ndash TeVeS-like theory gN = μ g = g - ScalarField

bull

bull Newtonian F = minertia g minertia= m

Scalar field in TeVeS resembles DM

bull Scalar field (Polarisation Halo of luminous baryon 1-to-1 gravity)

bull ~ tuned Dark Halo surrounding baryons

bull NFW profile micro

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Analogy as dielectric and as inertia

bull Conservative Field g or E = -Φ = d2xdt2

bull Poisson equation ρ = D or gN

ndash Electric displacement D = μ E = E + PolarisationField

ndash TeVeS-like theory gN = μ g = g - ScalarField

bull

bull Newtonian F = minertia g minertia= m

Scalar field in TeVeS resembles DM

bull Scalar field (Polarisation Halo of luminous baryon 1-to-1 gravity)

bull ~ tuned Dark Halo surrounding baryons

bull NFW profile micro

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Scalar field in TeVeS resembles DM

bull Scalar field (Polarisation Halo of luminous baryon 1-to-1 gravity)

bull ~ tuned Dark Halo surrounding baryons

bull NFW profile micro

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)

bull Standard (I)

(x) = x (1+x2)12

bull Exponential

(x) = 1 - e-x

bull Bekenstein toy model

(x) = [(1+4x)12 -1] [(1+4x)12 + 1]

bull Simple (III)

(x) = x (1+x)

s (gs) = (1- )gs = g - g

(g)

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

External Field Effect

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Milgromrsquos standard micro = x(1+x2)12

bull Excellent description of datandash Deviation capped ~ a0 ndash Fast transition of law

from Newtonian solar system into non-Newtonian outer galaxy

bull But hellip incompatible with TeVeS

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Fast transitions (implied by data amp mu-standard) challenging for TeVeS

bull Less freedom in mu than in 1-field MOND ndash Bekenstein mu excluded by RC data

bull Scalar field must increase from galaxies (a0) to solar systemndash untailored mu will overrun Pioneer limit

(lt10a0)

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Problems with earlier laws of bull Milgromrsquos standard -law too sharp

ndash leads to multi-valued TeVeS L and problems with external field

bull Bekensteinrsquos too gradual ndash unlike in real galaxy RC

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

bull The standard and exponential functions are excluded (multi-valued) but good to fit RCrsquos

bull Bekensteinrsquos toy is ok in TeVeS but poor fit to the TVC of the Milky Way (Famaey amp Binney 2005) same conclusion in spiral galaxy NGC 3198

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

A narrow range of mu is allowed

bull alpha-model in Angus Famaey Zhao [Poster] amp Gentile Famaey Zhao [Poster]

bull Curl-field correction [Nipotirsquos talk]

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

bull The Simple Function

= x (1+x) = (a0 + )gives a good fit to RCrsquos and

corresponds to a plausible TeVeS s(y)

bull Simple rsquos corresponding scalar field function is

s = (a0 - α ) α=1 (Zhao-Famaey)

= s (1+ s ) = a0

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Deeper Physics Beyond Simplicity

In spherical symmetry

Newtonian FN = minertia g minertia= m

ExtraForce |Fs|= minertiaa0

with a0 ~c

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Test mu where it is not made for Elliptical Lenses SNe Cosmology

Metric of Homogeneous Universe

Hubble expansion in TeVeS

Scalar field density tracks matter density

As good as ΛCDM but no Λ

Updating Scores LCDM TeVeS

bull Solar System

bull Tides on Globulars amp dSph

bull Rot curves HSBLSB

bull

bull Lensing by EllipticalsClusters

bull

bull SNIaCMB

bull

• Similarity of DMDE and TeVeS HongSheng Zhao SUPA
• ΛCDM WDM Tuned DM-DE (~ Tuned TeVeS μ )
• Slide 3
• Slide 4
• Slide 5
• Analogy as dielectric and as inertia
• Scalar field in TeVeS resembles DM
• I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)
• External Field Effect
• Milgromrsquos standard micro = x(1+x2)12
• Slide 11
• Fast transitions (implied by data amp mu-standard) challenging for TeVeS
• Problems with earlier laws of
• Slide 14
• A narrow range of mu is allowed
• Slide 16
• Deeper Physics Beyond Simplicity
• Test mu where it is not made for Elliptical Lenses SNe Cosmology
• Metric of Homogeneous Universe
• Slide 20
• Scalar field density tracks matter density
• As good as ΛCDM but no Λ
• Slide 23
• Updating Scores LCDM TeVeS

Scalar field density tracks matter density

As good as ΛCDM but no Λ

Updating Scores LCDM TeVeS

bull Solar System

bull Tides on Globulars amp dSph

bull Rot curves HSBLSB

bull

bull Lensing by EllipticalsClusters

bull

bull SNIaCMB

bull

• Similarity of DMDE and TeVeS HongSheng Zhao SUPA
• ΛCDM WDM Tuned DM-DE (~ Tuned TeVeS μ )
• Slide 3
• Slide 4
• Slide 5
• Analogy as dielectric and as inertia
• Scalar field in TeVeS resembles DM
• I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)
• External Field Effect
• Milgromrsquos standard micro = x(1+x2)12
• Slide 11
• Fast transitions (implied by data amp mu-standard) challenging for TeVeS
• Problems with earlier laws of
• Slide 14
• A narrow range of mu is allowed
• Slide 16
• Deeper Physics Beyond Simplicity
• Test mu where it is not made for Elliptical Lenses SNe Cosmology
• Metric of Homogeneous Universe
• Slide 20
• Scalar field density tracks matter density
• As good as ΛCDM but no Λ
• Slide 23
• Updating Scores LCDM TeVeS

As good as ΛCDM but no Λ

Updating Scores LCDM TeVeS

bull Solar System

bull Tides on Globulars amp dSph

bull Rot curves HSBLSB

bull

bull Lensing by EllipticalsClusters

bull

bull SNIaCMB

bull

• Similarity of DMDE and TeVeS HongSheng Zhao SUPA
• ΛCDM WDM Tuned DM-DE (~ Tuned TeVeS μ )
• Slide 3
• Slide 4
• Slide 5
• Analogy as dielectric and as inertia
• Scalar field in TeVeS resembles DM
• I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)
• External Field Effect
• Milgromrsquos standard micro = x(1+x2)12
• Slide 11
• Fast transitions (implied by data amp mu-standard) challenging for TeVeS
• Problems with earlier laws of
• Slide 14
• A narrow range of mu is allowed
• Slide 16
• Deeper Physics Beyond Simplicity
• Test mu where it is not made for Elliptical Lenses SNe Cosmology
• Metric of Homogeneous Universe
• Slide 20
• Scalar field density tracks matter density
• As good as ΛCDM but no Λ
• Slide 23
• Updating Scores LCDM TeVeS

Updating Scores LCDM TeVeS

bull Solar System

bull Tides on Globulars amp dSph

bull Rot curves HSBLSB

bull

bull Lensing by EllipticalsClusters

bull

bull SNIaCMB

bull

• Similarity of DMDE and TeVeS HongSheng Zhao SUPA
• ΛCDM WDM Tuned DM-DE (~ Tuned TeVeS μ )
• Slide 3
• Slide 4
• Slide 5
• Analogy as dielectric and as inertia
• Scalar field in TeVeS resembles DM
• I Constraining the law of (Zhao amp Famaey 2006 ApJ letters)
• External Field Effect
• Milgromrsquos standard micro = x(1+x2)12
• Slide 11
• Fast transitions (implied by data amp mu-standard) challenging for TeVeS
• Problems with earlier laws of
• Slide 14
• A narrow range of mu is allowed
• Slide 16
• Deeper Physics Beyond Simplicity
• Test mu where it is not made for Elliptical Lenses SNe Cosmology
• Metric of Homogeneous Universe
• Slide 20
• Scalar field density tracks matter density
• As good as ΛCDM but no Λ
• Slide 23
• Updating Scores LCDM TeVeS